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Random and deterministic (nonrandom) aspects of athletic behavior with special reference to National.. MacDonald, Neil William 1990

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Random of  and  Deterministic  (Nonrandom)  Athletic  Behavior  with  Special  to  National  League  Aspects Reference  Hockey  by Neil B.A.,  William  M . A . The U n i v e r s i t y M.S. Ph.D.  A Thesis  the  British  The U n i v e r s i t y The U n i v e r s i t y  Submitted  for  of  Macdonald  in  Degree  Partial of  of of  C o l u m b i a 1958,  Oregon  Master  of  1967  Minnesota  Fulfillment  1960  of  Physical  1966  the  Requirement  Education  in The  Faculty  School  We a c c e p t  this  thesis  The  of  as  of  Graduate  Physical  conforming  University  of  December  Studies  Education  to  British  1990  the  required  Columbia  standard  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Department The University of British Columbia Vancouver, Canada  DE-6 (2/88)  ABSTRACT Various  parts  of  the  question  deterministic  attributes  contests  been  to  have  extend  the  postulates  data  the  researchers.  base  and  random and course  This  formulate  the  interaction.  The 1988-89  National  Hockey League  primary  of  1937-38  Basketball  and  First  earlier  studies  against  is or  quite  goals,  are  shots)  are  measurement:  random p a t t e r n s  three  games  period  probability win  was  no  The  pattern  examined. distributed  tests  or  showed  likely  of  outcomes all  21  major  be  u n i f o r m l y minute  was  Football  outcomes  the  made  of  National  Association  overwhelmingly  supported  (wins/losses,  argued  that  the  shots  random p a t t e r n and g o a l s  randomly whether of  outcomes  independent  of  the  held  whether  sets  were  followed is  goals by  was  1988-89  The p a t t e r n  (goals)  team's  season  sequence.  game-to-game  to  the  1987-88  (wins/losses,  four-game  more  If  that  distributed  relatively  50% o f  the  attempted  initial  examination  The d a t a  developed  examined).  is  and  a random  pervasive  combined  games  argued  model  last  seasons.  followed  axiomatic  outcomes  total  which  NHL, the  athletic  random/deterministic  Supplemental  season  Division  shots)  The  1946-47  Association  English  goals,  attention.  of  study  the  describe  focus  a model  by  during  how  to  the  for  intertwine  explored  research  concerning  one  minute  for,  home,  away  of  the two  unit  Conditional  were  independent  by  than  by  on  plotted (except  how  the  time-wise, for  of  period,  outcomes a win  or  (win/losses,  period,  examined.  dependent are  size  of  the  a  (a  loss). data  is  goals last  are  minute  of  play).  home, will the  away  If  goals  or  both  approximate time-spaces  distribution when  period  only  season  outcomes  Finally, suggested  the  goals  emerge.  season  of  game  (or  resultant binomial are  found  on  a  points,  hockey,  basketball  may v a r y  tallied  first,  distribution However,  were  if  and  demonstrated  second  favorably  goals  f r o m one  for  geometric  effects  correlate  losses,  upset"rates  are  distribution.  tallied,  based to  period)  frequency  Deterministic  outcomes  were  (wins,  comparison  per  negative  between  seasons  that  shots  teams,  the  will  artificial  or  for,  third  with  real  goals  soccer sport  or  to  against).  outcomes another.  iv TABLE  OF CONTENTS  Abstract  1.  i i  List  of  Tables  v  List  of  Appendix Tables  vi  List  of  Figures  ix  Acknowledgments  x  Introduction  1  Purpose 2.  1  L i t e r a t u r e Review Studies  Showing  2 Randomness  U n i t of Measurement S t u d i e s Monte C a r l o S t u d i e s Chance D i s t r i b u t i o n of Scores Goodness-of-fit D i s t r i b u t i o n Studies 3.  Procedure  Postulate  11 13 13  Testing  15  Distribution Testing Runs T e s t i n g Conditional Probabilities C o r r e l a t i o n a l Data Game t o Game C o r r e l a t i o n s Raw a n d B i n a r y C o r r e l a t i o n s Stationarity Tests A r t i f i c i a l and R e a l S t a n d i n g s Upsets D e s c r i p t i v e Data 5.  Discussion Comparisons with Model B u i l d i n g F i n a l Comments  Appendix References  7 8 9 10 11  Data Sources A c c u r a c y of Measurement Basic Assumptions 4.  2  15 37 42 44 48 52 55 58 59 65 67  Other  Studies  67 70 73 77 184  V LIST  OF T A B L E S  Table  Page  1.  Means  and V a r i a n c e s  2.  C h i - s q u a r e Comparison of Streak G e o m e t r i c and N e g a t i v e B i n o m i a l Means  4.  E m p i r i c a l P r o b a b i l i t i e s of C o n d i t i o n e d on the Outcome Teams C o m b i n e d  6.  R a n g e o f Raw a n d Coefficients for  for  Shots  3.  5.  and V a r i a n c e s  for  25 Frequencies with Distributions . .  R e p e a t i n g a Win o r L o s s o f P r e v i o u s Game(s) for  44  7.  Upset  Rate  8.  Chi-square Soccer  10.  11.  National  Comparison of  Pre-Game and Basketball  all  B i n a r y I n d i v i d u a l Team C o r r e l a t i o n G o a l s and Shots ( P 1 G 1 . . P 2 G 1 . . P 3 . . G n )  Various  32 32  o f I n d i v i d u a l Team C o r r e l a t i o n C o e f f i c i e n t s and G o a l s F o r and A g a i n s t  9.  .  Streaks  Range Shots  in  .  Upset  Hockey Rates  League in  Years  Hockey  .  53  for 54 .  .  61  and 63  Season  Upset  Rates  for  Hockey,  Soccer  and 64  C h i - s q u a r e Comparison of Rates between Hockey and  Pre-Game Soccer  and  C h i - s q u a r e Comparison of R a t e s between Hockey and  Pre-Game and Basketball  Season  Upset 66  Season  Upset 66  VI LIST  OF T A B L E S  IN  APPENDIX  Table Al.  A2.  A3.  A4.  A5.  A6.  A7.  A8.  A9.  A10.  All.  Page C h i - s q u a r e A n a l y s i s of U n i f o r m , Distributions o f A l l Team G o a l s T i m e (One M i n u t e D i v i s i o n s )  P o i s s o n and Normal for Actual Playing .  C h i - s q u a r e A n a l y s i s of U n i f o r m , Distributions o f A l l Team G a o l s T i m e (Two M i n u t e D i v i s i o n s )  P o i s s o n and Normal for Actual Playing  .  78  80  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , P o i s s o n and Normal D i s t r i b u t i o n s for Actual Playing Time ( F i v e M i n u t e D i v i s i o n s : d f = 11) B o t h T e a m Goals  81  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , P o i s s o n and Normal D i s t r i b u t i o n s for Actual Playing Time (Five Minute D i v i s i o n s : d f = 11) G o a l s F o r . .  88  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , P o i s s o n and Normal D i s t r i b u t i o n s for Actual Playing Time (Five Minute D i v i s i o n s : d f = 11) Goals Against  95  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , P o i s s o n and Normal D i s t r i b u t i o n s for Actual Playing Time (Ten M i n u t e D i v i s i o n s : d f = 5) B o t h T e a m G o a l s  102  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , P o i s s o n and Normal D i s t r i b u t i o n s for Actual Playing Time (Ten M i n u t e D i v i s i o n s : d f = 5) G o a l s F o r . . .  109  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , P o i s s o n and Normal D i s t r i b u t i o n s for Actual Playing Time (Ten M i n u t e D i v i s i o n s : d f = 5) G o a l s A g a i n s t .  116  T o t a l Team C h i - s q u a r e C o m p a r i s o n o f S h o t Distributions with T h e o r e t i c a l Normal, Uniform, P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l Distributions  123  T o t a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l a n d S h o t Distributions with T h e o r e t i c a l Normal, Uniform, P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l Distributions  125  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f G o a l Distributions with T h e o r e t i c a l Normal, Uniform, P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l Distributions From Time of F i r s t Goal  126  VX1 Table  A12.  A13.  A14.  Page  Means Total First  a n d V a r i a n c e s f o r I n d i v i d u a l T e a m s H o m e , Away a n d Games f o r F r e q u e n c y D i s t r i b u t i o n s F r o m T i m e o f Goal  T o t a l Team C h i - s q u a r e C o m p a r i s o n o f W i n , L o s s a n d Streak Frequencies with Normal, Uniform, Poisson, G e o m e t r i c and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s  139  Total 140  C h i - s q u a r e C o m p a r i s o n of B a c k - t o - B a c k and N o n - B a c k - t o B a c k Game P o i n t R e c o r d s f o r 1 9 8 5 - 8 6 N a t i o n a l H o c k e y League Season  143  A15.  Significance  144  A16.  I n d i v i d u a l Team S i g n i f i c a n c e Levels E a c h P e r i o d T r e a t e d a s a Game  A17.  A18.  A19.  A20.  A21.  A22.  A23.  A24.  A25.  A26.  Levels  for  Runs  Tests  Significance L e v e l s f o r Runs T e s t By P e r i o d f o r I n d i v i d u a l Teams  on  Individual  for  Runs  Test  Teams With  145  On N u m b e r  of  Shots 147  I n d i v i d u a l Team Runs T e s t R e s u l t s on a n d A g a i n s t F o r H o m e , Away a n d T o t a l  Total Games  Goals  For 148  I n d i v i d u a l Team S i g n i f i c a n c e A b o v e / B e l o w Mean V a r i a t i o n s  L e v e l s f o r Runs T e s t s on (P1G1...P2G1...P3G40) . .  .  149  I n d i v i d u a l Team S i g n i f i c a n c e A b o v e / B e l o w Mean V a r i a t i o n s  L e v e l s f o r Runs T e s t s on (P1G1...P2G1...P3G80) . .  .  150  Runs T e s t L e v e l s of S i g n i f i c a n c e f o r I n d i v i d u a l teams and S e t - t o - S e t C o r r e l a t i o n s on F o u r - G a m e S e t s T r e a t e d a s Games ( T i e s = Wins)  151  E m p i r i c a l P r o b a b i l i t y of Repeating a Win, Loss C o n d i t i o n e d on t h e Outcome o f P r e v i o u s Game(s)  152  I n d i v i d u a l Team I n t e r p e r i o d Correlations  Outcome  and  Game  or .  Tie . . .  Outcome 154  P e r i o d to P e r i o d C o r r e l a t i o n s of Goals F o r , Goals Against, Shots F o r and Shots A g a i n s t F o r I n d i v i d u a l Teams  155  I n d i v i d u a l Team P e r i o d - t o - P e r i o d Correlations  157  Goal  and  Shot  I n d i v i d u a l Team C o r r e l a t i o n s o f G o a l Differences Between P e r i o d s and w i t h T o t a l G o a l D i f f e r e n c e .  .  .  .  158  viii Table A27.  A28.  A29.  A30.  A31.  A32.  A33.  A34.  A35.  A36.  Page I n d i v i d u a l Team C o r r e l a t i o n s o f S h o t Difference Between P e r i o d s and T o t a l Shot D i f f e r e n c e  159  C o r r e l a t i o n of Wins, Goals f o r A l l Teams C o m b i n e d  160  Individual Losses for  and  Shots  Between  Periods  Team L a g g e d C o r r e l a t i o n s o f W i n s , T i e s , P e r i o d s 1 , 2 a n d 3 B e t w e e n Games n a n d n + l  I n d i v i d u a l Team C o r r e l a t i o n s o f A g a i n s t and T o t a l G o a l s Between v s . Game 2 . . n  Goals For, Goals P e r i o d s f o r Game  I n d i v i d u a l Team C o r r e l a t i o n s o f A g a i n s t and T o t a l S h o t s Between v s . Game 2 . . n  Shots F o r , Shots P e r i o d s f o r Game  l . . n  Coefficients  Coefficients 164 Coefficients 166  for  Shots  and 168  I n d i v i d u a l Team T e s t s o f S t a t i o n a r i t y Chi-square A n a l y s i s o f Mean V a r i a t i o n s on F o u r - G a m e S e t s  170  I n d i v i d u a l Team N o r m a l D i s t r i b u t i o n S e t C o r r e l a t i o n s f o r f o u r game s e t s  172  and  Real  and  A38.  C o r r e l a t i o n s f o r Outcomes B a s e d on A r t i f i c i a l as Compared t o R e a l S e a s o n Outcomes Upset Comparisons: League Seasons  Season  Checks  Artificial  A40.  l . . n  163  A37.  A39.  161  162  Raw a n d B i n a r y I n d i v i d u a l T e a m C o r r e l a t i o n for Goals (P1G1..P2G1..P3Gn) o Raw a n d B i n a r y I n d i v i d u a l T e a m C o r r e l a t i o n for Shots (P1G1..P2G1..P3Gn) I n d i v i d u a l Team C o r r e l a t i o n G o a l s F o r and A g a i n s t  .  37-38,  Set-to-  Records  46-47,  88-89  174 Seasons  National  177 Hockey 178  Chi-square Comparisons S e a s o n Rank P o s i t i o n  of  A41.  Cross  Comparisons  A42.  I n d i v i d u a l Team Means a n d S t a n d a r d D e v i a t i o n s For, A g a i n s t and T o t a l G o a l s and F o r , A g a i n s t and T o t a l Shots  Sport  Chi-Square  Upsets  Based  on  Pre-Game  vs. 179 180  182  ix  LIST  OF F I G U R E S Page  Figure  Figure  Figure  1.  2.  3.  Total (Data  League Goals Scored i n Second f i t Uniform Distribution)  Period  T o t a l G o a l s D a t a f o r A l l Teams F i t t i n g N e g a t i v e B i n o m i a l and Normal D i s t r i b u t i o n  Goals Scored Data Negative Binomial  19  .  For Boston Bruins F i t t i n g and G e o m e t r i c D i s t r i b u t i o n  .  .  .  .  26  .  29  X  ACKNOWLEDGEMENTS I  would  like  completing  this  generous  to  thesis:  enough  traditional  thank  to  type  thesis  my c o m m i t t e e  Delampady  for  Besler  generous  and  input,  programme family Thanks.  Langara  of  Dr.  helpful  doing  particularly writing. who  Keith  Finally pitched  an  me  who  Dr.  I  wish  to  thank  in  with  an  idea  non-  Committee  Besler's  who  being  job  critics;  d i d much o f  Bailey,  for  as  an  and D r . M.  and a p p r e c i a t e d Fund  a  in  excellent  I . M . Franks  Research  students  helped  supervising  and p a r t i c u l a r l y f o r study  have  D r . R.W. Schutz,  (and  members,  and  the  who  task  project  as  work  members  the  serving  support  programming;  those  my a d v i s o r ,  accept  advisor);  Murray  all  taught  for  aid  the me  all  the  here,  a  Dr. their  in  computer  data the  coding art  friends comment  of and  there.  INTRODUCTION Purpose Although occasional Canucks  the  athletic  only the  qualities  of  success  vast the  a n d game  scores,  distinct  possibility  The and  any  literature  accurate.  sports  is  has  published  No  general  is  a need The  of  rules, for  by  a basis  (2)  to  test  the  1988/89  goals,  in  laws  goal), to  most  the  goals. of  the  fans  appear  to  relative  skills  and  standings;  pattern  (e.g.,  Outcomes  are  defined  winning  There  outcomes  and p r o b a b i l i t y studies  a wide  - -  chance  the  is, is  and  as losing  however, far  a  more  with  prediction, nor  range  statistics, or  data  is  extensive,  analyses  on  streaks,  etc.,  coordinated  (partly  of  covering  journals  economics,  "theories"  have  detailed  been  various but  the  because  it  a  psychology,  etc.).  developed.  There  integration. of  this  using  to  season  structured  topics  purpose  framework as  neither  fluke  outcomes  probability,  material  diversity  are  to  attribute  expect.  sport  There  grudgingly  involved.  the  might  on  concerning  been  of  on  that  will  failure  that  final  shots  fan  fan  or  competitors  penalties,  than  of  majority  streaks,  random  sports  won b e c a u s e  attribute  period  average  study  the  structure  the  concepts and  "theoretical  National  is:  Hockey  (1) of  to  to  randomization  synthesize framework" League  start  the  a  and  determinism  published  literature;  with  season.  develop  a data  set  such  as  2 LITERATURE The  pertinent  areas: Monte  studies Carlo  literature showing  studies,  goodness-of-fit I.  Studies The  prevalence  significance is  a  study  by  basketball analysis of  Larkey,  Larkey  data  game al.  on  perceptions  73  and  219.  game  argued  focussed  74  outcomes,  investigation.  studies,  studies  to  be  random.  with  and  are  the  of  particular  The p r e m i e r  and T v e r s k y  efforts  developing of  streak  field  who  (1985,  Their test,  in  Larkey  the et  game al.  fans, in  a  activity  are  to  a  a  example  1989)  system  of  found  of  chi-square four  players complex that  A scores that  the  in  and a  Gilovich  a very  test serial  than  different  see  context. a  They  bystander's  actual  streak  goals  in  V scores  shots  70,  1,  data  individual  field  shots  al.  sequences.  and coaches game  et  The G i l o v i c h  player  describes  rather  attempted.  with  fan.  individual  5 consecutive  while  argued  data  available  a model  are  disagreed  shooting  score  goals  (1989)  isolated  that  A and V each  220  scores  nonoverlapping sets  usually  by  shooting  which  measurement  directly  Wald-Wolfowitz runs  latter's  player's  Players  athletic  streaks  the  dealing  Vallone  examining  the  the  of et  general  test.  that  consist  in  S m i t h and Kadane  than  of  five  studies.  studies,  Gilovich,  included  unit  into  d i s t r i b u t i o n of  proposed  shooting  correlation  form  of  the  stationarity  arguing  chance  randomness to  divided  Randomness  group of  be  randomness,  distribution  Showing  first  can  REVIEW  55,  p r o b a b i l i t y of  110, V s  activity. a game 71,  165  in  72,  and  hitting  3 shots  70  through  shots  1,  55,  length  can  noticed. of  shooter  would  score  for  Larkey  or  Gilovich  et  on  for  greater  al.'s  the  a  field  studies  occur  shooting  only  a  streak  without  to  on  be  and  player  A l t h o u g h on  focus  to  patterns  that  one  similar  actually  and  players  shooter.  hitting  similar  noticeable  than  appears  A  of  arguing  They found  streak  to  goal  highly  frequency  of  streaks  streakiness,  research  two  that  the  shooting. of  probability  probable  low-probability,  streak  al.,  the  much l e s s  focussed  with  et  to  They a s s e r t e d  definition  surface,  equal  reputations  baskets  their  not  etc.  study  with  reputations  is  much more  Their  memorable  fitted  110,  be  players  74  the  that  very  of different  phenomena. Admittedly, examination that  Gilovich  of  1973)  psychological Larkey  et  is  perceptions  of  Gilovich  al.  in  a  context  Gould slightly 61  to  Gould  isolated 11)  noted  home is  that  more  based  runs);  in  with  on  a  total  but  to  the  that  "ridiculously" a Nobel  the  fan  (Tversky & of  malfunctions.  game  But  person's  context.  shooting  behavior  game. most  records  runners-up  Joe  above  on  by  average  individual  that  error  a number  the  on-going out  based  W W W L L L  concerns  superior  Purcell,  than  shooting  pointed  also  appropriately,  mainly  deal  is  The o r i g i n a l  one  from the  incrementally  streak  or  primarily  60  errors.  a perceptual  a player's  p.  research  probable  research  (1989,  Ruth's  hitting  more  functions  al.'s  et  al.'s  perceptual  W L L W L W is  Kahneman,  et  (e.g.,  DiMaggio's  Keeler  laureate  in  are  only Maris'  56-game  and R o s e ' s physics,  44.  did  a  4 comprehensive nothing  ever  study  of  happened  all in  baseball  predicted  by  coin-tossing  streak  50  games  of  baseball But  Purcell  likely need  began.  with  four  would  .400  1,000  games.  average  is  .367  and o n l y  Baseball  hits  allow  a  writer streak  and a  was  officials  see  of  that  purity  DiMaggio's streak  analysis. and .792  4  c a n be If  at-bats of  it  and Wasserman  Probability  per at  least  of  analysis  restricted  their  is  .00000213  entire  p.  to  career  13)  p.  hits,  short,  since  possible  would  batters  averages 15)  over  of  argued  two  a  streak  lifetime  may  to  be  desires  means  scored  safely  streak  .350.  that  "errors"  unconscious  argued  o n how  one  changing  .325  one  hit  of  of  in  32  a n d who  batting  any in  had  had  single 56  players  the to  probability  view  asumptions  DiMaggio  hitting  the  that  wishes  the  lifetime  assumed,  of  once  probability).  v a r i e d by  game  .350  lifetime  or  hit  baseball  (Henrich bunting  (a  a  chance  highest  1989,  In  continue  frequency  that  percent,  the  that  happened.  lifetime  cheap  conscious  of  50  (Gould,  bat).  depends  probability  over  52  two  by  the  make D i M a g g i o ' s  men h a v e  by  (1989,  DiMaggio's  getting  is  by  to  has  actuality,  Holway  DiMaggio  any  or  noted  occur  than  narrow escape  prolonged  contaminating  to  to  concluded  and beyond  what  that  three  aided  artificially to  In  John  complex  0-for-3  Short  about  hitters  of  as  is  and  Purcell  expected  calculated  careers  DiMaggio's  above  a probability greater  lifetime  streaks  methods. be  And t h a t also  baseball  behind  average the game  4,000  batted  at-bats  is  the  used,  probability and  successive who  it.  the  games. .325  or  of  or  more,  If better with  5 an  average  these of  a  32  streak  of  the  at-bats  barely  current  Cook seven  championship Cook  of  571 at  least  the  of  his  in  one  games  of  any  .338.  just  probability  season  is  is  by  the  32  .0157.  .0455,  what  an e x t e n s i v e  observations  The  streak  becomes  about  season,  represented  56-game  probability  per  single  player-seasons  pioneered  closely (1964, games is  and a l s o  suggests  that  and s e r i e s  2)  There  extremely winning  of  won  pennant  the  slugging  games  p.  6)  between  found 1945 as are  (Cook,  small  of  At  which  is  happened.  mathematical study  appear r e l e v a n t  teams most 1964,  and the  quite  evenly of  1976,  to  of  the  become  to  a  to  last  extend  in  p e r f o r m a n c e on  to  the  an e x t e n s i v e  league  the  standings  Los Angeles differing  in  the  games.  outcome  is  limit.  s c o r i n g of  in  as  agreed  for  influence  1961  of  the  seven  (e.g.,  only  by  (1977)  game  between  Series  tendency  equal,  7)  over  is  Simon  been  least) truly  expected  matched teams,  p.  and f i e l d i n g p e r c e n t a g e s place).  has  play  "in a World  chance."  at  likely  Series  distribution  there  final  4 games  World  concluded that  that to  won i n  the  a matter  variations  by  games  followed  largely  (from  decimal  a n d 116  hitter  And a g a i n  1977)  Series  random  .338  the  game,  Several  a n d 1961  as  a  The d i s t r i b u t i o n  chance.  This  per  game  a combined average  for  chance  per  investigation:  1)  World  56  (1964,  baseball.  with  have  significant.  Cook  1903  at-bats  But over  players, four  3.81  players  .0000277.  few  of  runs,  Cincinnati  with the  of  batting, second  6 3)  Applying  slumps, as  Cook  (1964,  a batting  slump  participating games; p.  .400  141)  4) be  in  for  "there  batsman  Pascal's  will  45 is  within  10  estimate  games  games; just  no  the  Cook  needed points  the  .632  way  to  one  and n e a r l y  individual's  19 in  or  how  145)  determine  for  know  problem of p.  batting  "there  expected  and  produce  that  to  is  career  hit  games, which  less  noted  that  years  hits  per  true  career  (1412  performance  a  .300-  game."  was  correctly  may  play  batting  98  1964,  average  year's  games)  in  (Cook, games  two  hitter  .131  98  and thing  A .300  but  base  such  about  of  a batter's  a player's  nine  to  streaks  no  healthy... player."  may b e  (1964,  to  expansion  concluded  a normal,  inevitably  determined, was  140)  for  162  Addressing  games)  p.  binomial  (383  average needed  to  within  five  points. 5) "the  Cook  most  large  (1964,  favorable  number  winning  of  chance  with  interpreted p.  153)  alignment  of  first  equations all by  concluded of  the  i n d i v i d u a l l y small  percentage  distribution  p.  its  place  because  complex  application  that  greatest  teams  have  baseball  is  the  laws  of  results  from  p r o p o r t i o n of  variables."  interactions of  winning  F o r 60  followed  years,  the  Gaussian  inherently  being  a  a game  of  confidently  probability  (Cook,  1964,  312). Targeting  concluded,  the  "While the  may p r e c i s e l y There hold  for  crux  is  of  his  investigations.  probability  be  d e t e r m i n e d . . . no  no  reason  hockey  to  outcomes.  of one  believe  a base will  the  Cook hit  ever  same  (1977,  or know  a  p.  54)  strike-out 'when'!"  conclusions  should  not  7 Schutz  and J a n s s e n  analysis after  a  to  compare  change  performance. as  terms  coaches  (1977)  scores  of  used  box-score  football  II.  Measurement group  outcomes  of  from  outcomes  of  game  day  might  was  provided  not  form a  concerned.  studies  of  1985-86  closest  prowess. Major  of  likely a  single  as  to  managers.  between  on  the  1960  and  unpredictable that  much more  the  in data  random  suspect.  unit  to  the  League  be  true far  Fischler  back-to-back Hockey League a doubleheader  unit  Goodman  single  necessarily  National  team  misinterpreted  concluding to  on  variance  very  subject  addressed  in  pairs  more  summary o f  of  games  were  would  effect  and  Studies  Sportswriters  a  situation  observers  athletic  were  are  before  and g e n e r a l  analysis  statistics,  games  doubleheaders  Doubleheaders  the  most  determine  one  three-way  teams  had been  owners  games  than  the  hockey  League  or  to  by  regression  detectable  random outcomes  a  fluctuation  used  no  Ivy  score  A second  found  linear  hockey  football  of  of  two  League  that  Unit  of  Ivy  found  that  and  multiple  all  and  suggested  used  records  incompetence  Haberman  1966  the  Inherently  coaching  final  of  (1987)  of  (1969)  baseball  games  on  swept  than  single as  were  split,  unit.  which  hockey  to  of  game  days.  suggesting  p.  on play  from  inning  (1961) to  found  inning  the  in  distribution  National,  of  American  runs and  is  is  for  the  statistically  analyzed. Lindsey  one  11)  data  allowed be  the  different  team  (1986,  regular  season,  that  Two g a m e s  consistency  versus  found  consecutive  and F i s c h l e r  in  measurement  not  constant  International  8 League  baseball,  the  first,  third  sixth  pinpoints (an  the  inning,  results  and  mean  inning.  problem of  a game,  change  number  of  runs  Goodman's  determining  on what  a unit  and  unit  greatest  in  and L i n d s e y ' s  what  a double-header)  depending  being  the  of  research  performance  problem of  a researcher  the  is  how  selects  to  measure. Unit in  of  time,  games, The  measurement a game  game  of  losses,  should  wins,  ties  of  0  crisis  results. such  we  be  and  A third real-life  group games  established Freeze  (1977)  hypothetical exerted order  in  a  rather  a batting  that  enter  wins,  of  2  game  events  to  significantly  related  mean?  average),  .285  average)  and  X with  2  different  as  a  obscure  the  As X comes (X's  Y.  points  or  to  game  ties  may h a v e  may h i g h l i g h t  also  previous  from  of  chosen  average  lifetime  condition 10  lead  is  context  Isolated  to  average  bat, against  predictor?  Studies of  studies  have  by Monte C a r l o real-life used  batting  small  can  the  topic.  X with  teams  measurement  (X's  in  Any c h a i n  season's  .267  Monte C a r l o  from  complex  initial  game  measurement  of  (this  viewed  enter  changes  of  Unit  .320  but  losses.  What d o e s  use  that  small  left-handers), III.  12  exceedingly  a differing  different  The u n i t  changes.  an  0-0,  have  teams  where  question: do  starts  X will  progress  is  the  attempts  simulations  using  to  approximate  probabilities  games.  a Monte orders  influence.  than  involved  worst  Carlo  and  analysis  concluded  The e f f e c t resulted  in  of  of  that using  only  various batting the  three  order  best extra  batting runs  per  2  9 162-game order  season.  produced  (1977)  found  almost  no  only  that  change  baseball  teams.  All  is  a  this  source  Stein's  of  between be  more  adjustments  possible  of  by  about  predictor  than  were  that  a player's  projections true  from  IV.  Chance D i s t r i b u t i o n of  sports  group  scores  collegiate winners score losing lose found  scores  losers  and what  score)  than  matched expected  actual college  team  ability  the  Smith  led  of  players, that  appropriate  "shrinks" (Efron  future  to  such  differences  & Morris,  batting  1977)  averages  A l l this  tightly  to  League  possibility  suggests  clustered  than  any  suggest.  investigated (1970)  were  frequent  "operating  any  given  some  value  alone  and  where  teams  for  is  would  of  which  teams,  likely  suggest.  that  are  more  He  for  a  to  or  win  also  should  not  a  score,  closely  this  often  U.S.  games,  a winning  more  were  argued  nature  characteristic"  are  scores  the  examined  score  scores  team  scores  football  more  the  that  numerical  the  Mosteller  chance  found  National  shown  more  team.  of  averages.  would  have  randomly assembled  than in  the  and  their  that  studies  themselves.  (e.g.,  per  batting  Scores  football  and  was  of  are  best  opponent  may b e  of  real-life  averages  of  paradox  a group  abilities  of  and  1977)  Stein's  of  season's  fourth  in  80% a n d was  one  A  range  strength  equality  the  season  standings  & Morris,  a predictor,  a better  for  that  per  random r e s u l t s ,  (Efron  averages  found  runs  percentage  suggestive  As  (1977)  seven  in  paradox  analysis.  to  Peterson  be  equally  10 skilled. sports V.  College  in  football  fifth  sport  group  (e.g.,  attribute  Distribution  of  studies  goals,  with  Elderton  runs)  a known  (1909) in  the  distributions  of  four  1905,  1906  distribution concluded  sample  over of  of  that  Extending batsmen  and  the  cricket  work,  least  attributes  distribution  he  of  studied  term  which  batsmen's  had  the  (1945)  Wood was to  and  at  curve  (e.g.,  a  negative  that  series  series  a  exact is  in  progression: standard  could are  that  binomial  .54.  large  that  that  t h e mean i s t o t h e m e d i a n as 1 . 4 4 3 to 1 c e n t i l e s and q u a r t i l e s a r e i n unchanged r e l a t i o n t o t h e m e d i a n , no m a t t e r what t h e m e d i a n i s t h e c o m b i n a t i o n o f two g e o m e t r i c a l progressions cannot produce a t h i r d  distributions  a  concluded  a  the  four  examined  if  the  and  was  only  concerned  Wood,  for  described  preceding  looked  performances  According  1927)  frequency  2) 3)  distinctions  a  the  scores  a geometric  to  Wood  the  the  Such  of  distribution  1915,  being  period.  key  1)  4)  random of  distribution.  when  as  existed.  attained.  and  the  (1909,  each  batsmen's  not  mean  He  of  year  fits  geometrical  specific  pioneered  area  scores  ratio  three  have  1907.  distribution  strict  of  individual cricket  Elderton's a  matching  to  cricket the  analyzed  sports  geometric were  one  Studies  theoretical  seems  investigation  years  be  outcomes.  Goodness-of-fit A  should  as  be  deviation  of  use  difficult  in to  are  equal  distinguishing determine  appears  from c h i - s q u a r e  well  a geometric  as  by  between  cruder  analysis  to  distribution).  methods fit  a  Pollard (1971)  (1973,  found  1985,  that  the  hockey,  binomial  distribution.  concluded were (2)  that  studied (1)  football)  that  goals  mean g o a l s  minutes In that  for  and g o a l s  random  contrast  to  a random  event  for  consider  Mullet  scores  random-number  various  fit  and a g a i n s t  against  (at  Mullet shorter  or  and P o l l a r d  et  (e.g.,  a  home  time  and  away)  family,  and  were  space  Lapin  of  60  intervals. (1984)  a uniform is  and  a n d away)  longer  goal-scoring)  scoring  time  a l . ,  sports  negative  Poisson  home  used  the  (both  the  distribution could describe  production  and Benjamin  in  closely  a member o f  variables.  and d i d not  Pollard  N a t i o n a l Hockey League  d i s t r i b u t e d according to  independent  if  baseball,  (1977)  and Reep,  d i s t r i b u t i o n of  (soccer,  Mullet  1986)  noted  distribution  considered  akin  to  a  generator. PROCEDURE  I.  Data  Sources  Game-by-game, Hockey  L e a g u e was  Vancouver version  Sun.  the  teams  were  6-point  taking  then  for  identical  its  only  2 shots  1988-89  size  to  a  It  National  summaries  shorter  in  turned out  the  did  the  (e.g.,  X supposedly  in  the  goals  a newspaper  in  the  (e.g.,  in  home  first one  Detroit  period)  period)  city  as  that  records  team  of  Free  The  game-by-game  statistical  18  consulted  the  type  (e.g.,  i n v o l v e d was  on  NHL h e a d q u a r t e r s .  source  odd numbers  discovered,  from  When d i s c r e p a n c i e s  while  seemingly  from  same  press.  3 goals  taken  The d a t a  obtained  NHL u s e d daily  period-by-period data  scoring  or  were  either Press  of if  the Detroit,  Toronto  Globe  reading  of  the  the  second  point its  data  game  since  from  games  affiliate,  the  Association  Material  for  the  Bellingham Herald.  Data  Football Data  Community year  for  College five  College's data  years)  a  series  of  maintain  accuracy  were  being  used  the  in  author  checked study.  personal  repeated pick  resolved  and  1946-47  in  up  6-  Press  or  was  to seasons  was  computer.  from  Rothman's  publication.  study  at  Vancouver  grants grants  (three from  did  the  vast  material  was  double  recording.  his  chief  the  The b a s i c  A l l  computer  known d a t a  25% o f  of  Association's  taken  research  of  or  Basketball  summary s e c t i o n  computer  students  against About  were  work  the  National  Football  special  to  Bailey,  were  6-point  frame  input,  the  careful  T h e H o c k e y News  FA's o f f i c i a l  computer  by  was  The A s s o c i a t e d  1988-89  1988)  main  two  the  the  and  Keith  Minitab.  for  Since  written  author's  of  from the  the  the  and  involved  newspapers  Press.  1937-38  fund.  input  programs  in  under  research  coding  double  entered  error  source:  errors  (Rollin,  Yearbook 1988-89, were  league  same  half  taken  division  the  this  Sun.  second  season  first  all  the  was  English  often  A l l discovered  for  Usually  The Canadian  from The Vancouver  Material  the  story  on  satisfaction.  the  Toronto).  Evidently  consulted.  taken  if  source.  Canadian  also  and M a i l  base  material  per  the  majority coded  of and  computer assistant,  results was  program used  before  handled was  by  13 II.  Accuracy The  of  Measurement  assumption  absolute various  preciseness  not  but  away  from  the  been  scored,  recording Eskenazi  not  (red he  is  (1969,  vary  are  counted: light)  p.  shots  and  size  a p u c k make  would III.  have Basic  Unless base the  been  used  or  occasionally  8)  and s h o t s the  not  at  use  a highly  hands  a goal  has  Accuracy  of  a on n e t  a  (which  lack  net.  distinction  his  The p r o b l e m  from  the  keeps  are  accurate.  shots  may s t e m  goals  occur.  shots)."  the  of  The h i g h  of  whether  subjective  speed  a  shot  judgment.  Assumptions  otherwise in  stated,  testing  following 1)  on g o a l  on  home-team  that  not  confident  errors  " A l l clubs  official p.  is  split-response  of  between of  or  judge  Once he  track  agreement  was  that  is  test  (goal)  keeps  1986,  to  scoring  noted  study  "...the  that  & Fischler,  needed  of  B e i n g human,  the  this  and o c c a s i o n a l l y  switch.  (Fischler  small  not  in  counted  notes  with  is  189-190)  191)  widely  data  second  pp.  split-second  statistician...He usually  but  signals."  not  the  measurement  (1969,  scored  are  of  The p r e c i s e  Eskenazi  are  scored  of  hypotheses.  available. goals  u n d e r l y i n g use  affect  outcomes  are  periods,  games  measurement).  series  1988-89 of  NHL s e a s o n  postulates  was  the  w h i c h were  data  based  on  assumptions:  Variations in  appreciably  a  the  the any  random, or  length of  they  sets  of  the  of. the  unit  postulates  will games  be  of  measurement  proposed  random whether  are  used  as  the  (e.g., periods,  unit  of  will  not  if parts  of  14 2) are  Although hockey not  sports. runs  real be  balanced  Abelson scored  time.  used 3)  the  sport-specific.  reasonably  of  is  to  league  suggests  baseball  compare  A reasonably  balanced  to  that  characterize  For  seems  example:  Cincinnati won  60  130.  1974-75 lowest winless  in  way  occur  winning streak  Hockey is  not  with  outcomes  (37  of  a baseball timed,  is  first  the  9)  It  in  totally  dominated. or  number  elapsed  analysis  had  would  that  (1987)  could  be  1987), the  stage  early  years.  the  baseball  team,  suggests  Streaks  extremely  & Reif,  (.131),  from  their  professional  good  the  development  note  research  ever  game  assumed.  p.  any  sports.  sports  (1989,  to  time-bound  Abelson's  timed  elite  (Klein  to  postulates  estimating  most  extremely  percentage  extend  to  1  team  would  Nemec s  Capitals  ever  to  the  limited  a means of  studied,  postulates  the  1869.  be  league  and Palmer  the  Washington  occurence  the  Red S t o c k i n g s ,  Either to  apply  Thorn  straight  likely  4)  to  is  'non-timed'  inappropriate  they  and not  a half-inning  Since  sport  Hopefully,  (1989)  in  main  poor who  are  it most  teams. had  longest  was  The  the  road  games).  are  random a c r o s s  determined time.  by  definite  causes,  but  their  POSTULATE A  large  rationale  number o f behind  postulates  their  TESTING  are  proposed  development,  in  this  refinement  study.  and use  The  was  as  follows: (1)  expectations  postulate  had o f t e n  established (e.g.,  the  since  basketball  based  investigation  (2) this  the led  (e.g.,  al.  importance  the  literature  of  of  of  researchers  found  d i d not  of  other  who  had  chance  et  this  al.'s  research  by  etc.). unit  many p o s t u l a t e s  covering  similar  individual  percentage,  goals,  a  context  exceed  Gilovich  concept  —  a particular  shooting  shots,  the  in  1989>  streaks  scope  on  an e x t e n s i o n to  <1985,  a player's  streaks  a period)  validity  shooting on  scientific  a d v a n c e d by o t h e r  et  expanded  team  to  the  postulate's  player's  at  been  Gilovich  expectancies  looking  from  units  of  measurement  from  (e.g.,  covering two  —  one  periods,  unit a  Oo  game,  four (3)  games).  personal  experience  —  psychology  and communications  of  postulates  several  intelligence period I.  test  (e.g.,  other  author's  background  probably predisposed a p p l y i n g the  construction  correlated with  the  to  concepts  an e x a m i n a t i o n  periods  and t o t a l  the  in development  involved  of  game  how  in  each  outcome).  Distribution Testing The  first  behavioral large (e.g.,  series  of  outcomes  number o f a goal)  postulates  (e.g.,  variables to  occur,  goals) must  it  is  examined across  come  the  time.  together  impossible  distribution  to  for  Since an  predict  an  of  extremely  intended  act  precisely  16 when was  this  examined by la.  the  specific There final  This  is  because to  testing  following  This  specific  general  hypothesis  postulates:  i s an i n c r e a s e two m i n u t e s o f  not  the  Games  considered  pulling  were  observed  of  divided  and n e g a t i v e  pattern  of  goals  1985,  a  The 1)  the  time the  same a s and an e n t i r e goals  for  and  for  a  time of  scoring during  postulates  is  for  the  lb,  enough  change  series.  Comparison  normal,  of  uniform,  made.  The  distributed  negative  & Benjamin,  and  event  segments.  randomly  1977),  la  significant  goals  c o u l d be  Pollard  testing  each  binomial  1971)  or  d i s t r i b u t i o n was  d i s t r i b u t i o n was  negative is  tested  a distribution is  an a v e r a g e  it  goal  (Pollard,  uniform  1984).  whether  because  time  of  of  d i s t r i b u t i o n s were  (Mullet,  Reep,  Poisson  at  total  and d i f f e r e n t  various  binomial  Poisson  rationale  new  frequencies  (Lapin,  tells  2)  into  across  1986;  distribution  a negation  an e n t i r e l y  Poisson  to  i n the r a t e game t i m e .  a goaltender  and e x p e c t e d  according  i s the period  and  postulate:  constitute  1973,  the  occur.  The p a t t e r n o f outcomes i n any p e r i o d the p a t t e r n o f outcomes f o r any o t h e r game. (includes: goals for, goals against, a g a i n s t f o r e a c h team)  lc.  as  combination w i l l  G o a l s i n NHL h o c k e y a r e s c o r e d e v e n l y a c r o s s t i m e . (includes: goals for, goals against, t o t a l goals for a g a i n s t f o r e a c h team)  lb.  and  "right"  a  randomly  follows:  fit  because  distributed  it over  rate,  binomial the  for  as  d i s t r i b u t i o n was  Compound  Poisson  (it  tested assumes  for a  a  fit  Poisson  17 distribution 3)  the  geometric  because 4)  the  it  related  was  tested  (Lapin,  it  is  the  1950,  as  sequence  idea  the in  to  must  it is  sojourn  may b e  a Markov becomes of  start  a  fit  fit  indicative  because  of  its  a random  for  a possible  distributions  appearence  the  study  that At  in  the  —  it  a wide might  was  past  that  history  of  between  arrivals  chain  the  moving  between).  the  where  the  w2  there  f r o m one  is  state  all  only to  (Feller,  the  (Cinlar,  process.  if  no  same  or  are  win  process  processes,  wl,  a Poisson  or  whole  random  times  be  the  non-negative  sojourn  process  have  stochastic  process,  distributed  if  of  of  permits  replica  and must  an  a goal  a probabilistic times  has  scoring).  (goal),  waiting  fit  range  arrival  a renewal  chain  employed  each  a renewal  in  of  sense  a Markov  a particle  times  for  goals-per-game  terminology  identically  process  a  binomial,  normal d i s t r i b u t i o n  independent  the  of  of  future.  as  be  In  the  the  the  constitutes  are  becomes and  at  The s u c c e s s i v e  distribution.  The  frequency  describe  from s c r a t c h  1966)  1975)  to  was  "parent"  (e.g.,  aftereffect  process.  may b e  normal d i s t r i b u t i o n  assumption  starts  1984)  for  and  expected  conclusions  tested  uniform d i s t r i b u t i o n  situations  no  later  negative  overwhelming  had  was  the  since  The  games),  to  process, the  individual  distribution  is  appearance  4)  for  variables. It  equal  one  another  to  state with  one (the random  18 Three  methods  employed (A)  and d a t a  real-time  scored  in  scored  each  each  between  The  2,  uniform since  series of  total  first  second play  period  a hockey  the  for  outcome all  d u r i n g each the  most  predicted  the  data  21  the  but  to  goal  scoring  Table A l second  number  teams.  minute  occur  of  for  (pages  period.  to  not as  of  at  The  the  the  1984,  time.  79).  the  first  effect  A straight,  the  A  expected  p.  real-time  on  to  have  of  the  Figure  on  time,  10).  Given  arise.  third.  rest  was  random a c r o s s  the  appear  goals  focus  playing  (Lapin,  game.  involved  distribution  should  however,  does  goals  per  scoring  a uniform d i s t r i b u t i o n  not  due  goals  how many  1  for  When t h e 19  minutes  a uniform d i s t r i b u t i o n .  (probably  goaltender)  in  fitted  of  goals  counts  likely  to  of  the  minute-by-minute  removed,  conformed  of  of  period,  was  game  probability  in  are  analysis  that  summarized  counting  a uniform d i s t r i b u t i o n  suggested  goals  goals  were  randomness.  number  (e.g.,  number  a random-number g e n e r a t o r  Chi-square  pulling  the  counts:  real-time  scored  goals  goals,  of  of  goals  time),  Counts  enough  third  real  time  the  time-spaces  R e a l - T i m e Outcome  like  of  of  of  demonstrate  counting  apart.  acting  minute  should  counting  d i s t r i b u t i o n was  and  distribution  counts:  across  etc.  goals  team  three  series  event  the  minutes  examination of  all  counts:  3,  first  number  a  minute  (C)  Results  for  of  frequency  1,  measuring  outcome  (B)  scored A.  of  The  goal the  relatively  last of  last  scoring  the minute of  same  game.  (page  the  19)  The d a t a  are  illustrates  Figure  1  20 horizontal to  line  c o u l d be drawn t h r o u g h  demonstrate the a c t u a l uniform The  the uniform  second p e r i o d , the t h i r d  third  but not the t h i r d .  fitted  It the  last  despite  A2  team d a t a  the f a c t  evidently  were  The d a t a a r e  The l a s t o n e -  uniformly  across  and p l a y e r s  A high-scoring  n o t on i c e d u r i n g  This score  line  (except f o r  uniformity  occurs  much more  or player i s  f o r home and away games was examined  (a) s t a r t i n g  counting  time  t h e same t i m e frame f r o m game t o game.  between g o a l s  and (b) s t a r t i n g  3 when  examined.  certain lines  e a c h game, t h e r e b y  two m i n u t e s  f r o m t h e a n a l y s i s , t h e 18-minute  distribution.  are scored  u n d e r two c o n d i t i o n s :  and  (page 8 0 ) .  than o t h e r s .  interval  examined.  f o r the f i r s t  B u t when t h e l a s t  one o r two m i n u t e s o f t h e game).  frequently  goal  was f o u n d  were  i n s c o r i n g d i d n o t appear i n p e r i o d  appears goals  The  of the data.  i n v o l v e p o o l i n g o f a l l teams s c o r i n g .  minute i n c r e a s e individual  a uniform  i n Table  data  distribution  p e r i o d were d r o p p e d  period  summarized The  nature  p a t t e r n p r e v a i l e d when two-minute i n t e r v a l s  A f i t with  of  the sawtooth c o n f i g u r a t i o n  measurement a t t h e s t a r t o f  the time from s t a r t  o f game t o f i r s t  measurement a t t h e t i m e o f f i r s t  Minute-by-minute goal  frequency  distributions  home and away games.  The c o r r e l a t i o n  between  goal.  were c o n s t r u c t e d f o r minute-to-minute  goal  frequency  distributions  f o r home games and m i n u t e - t o - m i n u t e  goal  frequency  distributions  f o r away games was  measurement began a t t h e s t a r t  o f e a c h game  .965 when  ( c o n d i t i o n a) and .973  when measurement began a t t h e t i m e o f t h e f i r s t  goal  (condition  21 b).  This  constant  suggests whether  Data  that  frequency  a team  is  on F i v e - M i n u t e  examined u s i n g f i v e  playing  a n d 10 m i n u t e  random sample  of  divisions  selected  binomial. the  .05 l e v e l  abandoned The that  for  data  or  of  all  and t o t a l  between  tests  expected  for  total  The  The  for  a fit  yielded the  with  Poisson,  the  negative  was  uniform A  10-minute negative  significant  divisions  results  binomial  supported the  d i s t r i b u t e d evenly  for  teams  at  was  total  goals  and a g a i n s t  team's  for,  time.  total  goals  combined showed a  frequencies  home,  across  argument  close  b a s e d on t h e  away and t o t a l  games,  between  uniform 189  observed  of and  frequencies. on o t h e r  accommodate  play,  time  and e x p e c t e d  phases  e x p e c t e d number b e c a u s e  (home,  individual  goodness-of-fit.  s h o w i n g no s i g n i f i c a n t d i f f e r e n c e  Totals  The  for  home.  ten-divisions.  regarding  every  for  divisions.  (2.9%)  and  are  goals  observed  distribution 189  kinds  tests  Data  examination of  both f i v e -  Goodness-of-fit  fit  35  on f i v e - m i n u t e  goals  against  1 of  at  relatively  team d i s t r i b u t i o n s on  and t e s t e d  less,  away o r  tested  35 i n d i v i d u a l  When o n l y  scoring is  Divisions.  and normal d i s t r i b u t i o n s were  was  of  the  of  away, total)  this  n was  expectancy  attained  total)  times  times  21  uniform for  s e c t i o n do n o t  not  always  conditions  189 i s  d i s t r i b u t i o n of  relatively  of  large  for  always enough  chi-square  b y m u l t i p l y i n g 3 game  3 goal  conditions  add t o to  analysis.  conditions  (power p l a y ,  nonpower  teams. non-power home,  play  goals  away and t o t a l  also  appears  games.  the  Total  to  be non-  22 power p l a y g o a l s distribution,  f o r , against  and combined  63 o f 63 t e s t s s h o w i n g no s i g n i f i c a n t  between o b s e r v e d and e x p e c t e d 12 c h i - s q u a r e frequencies  frequencies.  a n a l y s i s t o be made w i t h o u t  of l e s s  t h a n 5, f i t s  non-power p l a y g o a l s of  against  supported  for  f o r was o f t e n  and a g a i n s t  with  inadequate  test.  9 o f 9 combined  combined  a 2 X  having f o r and  distribution,  51  d i f f e r e n c e between o b s e r v e d and  (combining  frequencies.  f o r and  Those comparisons  away, 11 o f 11 g o a l s  and 4 o f 4 power p l a y g o a l s  the uniform  distribution.  Comparison with 311 c o m p a r i s o n s  difference  The n f o r power  f o r e a c h team t o c o n d u c t  f o r and a g a i n s t  made f o r t h e u n i f o r m  of  any c e l l s  l e d t o 21 o f 21 t e s t s s h o w i n g no s i g n i f i c a n t  Goodness-of-Fit that  difference  Where n a l l o w e d  a uniform  power p l a y g o a l s  between o b s e r v e d and e x p e c t e d goals  uniform  frequencies.  Examination of t o t a l against)  a  f o r non-power p l a y g o a l s  51 t e s t s s h o w i n g no s i g n i f i c a n t  expected  a l l fitted  a  play  proper  t h a t were p o s s i b l e  showed  home power p l a y g o a l s ,  6 of 6  against  home and away  f o r a l l games showed a f i t  In t o t a l ,  354 o f 354 f i t s  were  distribution.  the Poisson  distribution  revealed  (3.9%) showed no s i g n i f i c a n t  o b s e r v e d and e x p e c t e d  frequencies,  (81.7%) showed a c h i - s q u a r e  that only  12  d i f f e r e n c e between  whereas 254 o f 311 c o m p a r i s o n s  d i f f e r e n c e a t t h e .001 l e v e l o f  significance. The with  comparison with  the normal d i s t r i b u t i o n  172 o f 349 c o m p a r i s o n s  differences,  while  was l e s s c l e a r c u t  (49.3%) s h o w i n g no s i g n i f i c a n t  42, 29, 55 and 51 c o m p a r i s o n s were a t t h e .05,  .02,  .01 and .001 l e v e l s  are not normally examination Total  (pages  distributed  of t o t a l  across  game d a t a  data  i s s t r e n g t h e n e d by  significant  just  home o r away).  (77.9%)  showing  differences.  are comprehensively  listed  i n T a b l e s A3, A4 and A5  81-101).  paralleled  the data  significant  differences  difference  Results:  are l i s t e d Event  were a n a l y z e d  divisions  481 o f 483 (99.6%) f r e q u e n c i e s r e v e a l e d no  distribution;  differences  283 o f 483  f o r the Poisson  distribution.  i n T a b l e s A6, A7 and A8  (Goal, Shot) D i s t r i b u t i o n .  i n both  sequence t o t h e l a s t  comparison with  (pages  101-122).  The d i s t r i b u t i o n s  a c o n v e n t i o n a l and u n c o n v e n t i o n a l  c o n v e n t i o n a l manner i n v o l v e d a d d i n g  'strung out'  on 1 0 - m i n u t e  and 207 o f 483 (42.9%) l e d t o no s i g n i f i c a n c e  f o r t h e Normal  data  and e x p e c t e d  f o r the uniform  (58.6%) showed no s i g n i f i c a n t distribution;  The d a t a  on 5-minute d i v i s i o n s :  c o m p a r i s o n s between o b s e r v e d  The  time  (rather than  D a t a on T e n - m i n u t e D i v i s i o n s .  The  The c o n c l u s i o n t h a t g o a l s  game d a t a h a d 109 o f 140 c o m p a r i s o n s  statistically The  respectively.  expected  any r e m a i n i n g  manner.  numbers i n a  number and t h e n making a  n's f o r t h e v a r i o u s  distributions.  Since excessive p o o l i n g can destroy the t a i l s  of a d i s t r i b u t i o n  and  (1977) a r g u e d  it  make a l l f u n c t i o n s a p p e a r u n i f o r m . was b e s t  expectancies  to pool  just  of l e s s  The  unconventional  not  satisfy  than  Mullet  enough t o e l i m i n a t e t i m e - s p a c e s 5.  This i s the conventional  method, w h i c h l e a v e s t h e t a i l  the mathematic p u r i s t ,  that  with procedure.  numbers o u t , may  b u t i t has t h e h e u r i s t i c  value  24 of  s e e i n g what a d i s t r i b u t i o n  sufficiently violating cell. was  l a r g e t o keep t h e  chi-square's  The  i f numbers were  e x t r e m e ends o f  need e x p e c t a n c i e s  differences in results  of  were n o t  the  tail  from  5 o r more i n any great whichever  one  method  used. Zar  can  (1984, p.  be  409)  t e s t e d by  distribution expected Poisson  noted  should  be  B.  Frequency  frequency  negative  f i t with binomial  distribution  (X  2  of  for  of  the no  that with with  a  the  fairly  ideally  near  analysis.  2  focussed  t h e number o f outcomes of shots  distributions.  = 7.374),  (X  2  The  shots  and  Poisson,  data  t o t a l goals  (X  2  = 3.088) a l s o f i t t e d lowest  geometric  for  (X  2  and  a Poisson chi-square  and the  = 6.330,  = 2.807) and  (X* = 3.702) and  the  examined  revealed that  binomial  a normal d i s t r i b u t i o n  on  (e.g., g o a l s ) .  g o a l s were  = 5.087), s h o t s  the n e g a t i v e  t o t a l s h o t s , where t h e  involved  teams and  the normal, uniform,  total  5.932) a l s o f i t t e d (X  of  of t o t a l s h o t s  against  for  p r e f e r a b l y b e l o w 5,  f o r a l l 21  distributions  = 2.668) a l l f i t t e d  goals  a l s o argued  o f r e a l - t i m e outcome c o u n t s  distribution  distribution  2  Zar  the  tails  at a t a b u l a t i o n having  a sample d i s t r i b u t i o n  throughout  of t o t a l g o a l s  frequency  their  shots  1.0.  Poisson  Distribution  second s e r i e s  examination  for  than  below 10,  attempted  f r e q u e n c i e s i n the  to a r r i v e  i t i s d e s i r a b l e t o use  T h i s was  The  the  pooled  frequencies less  1.  The  t h a t the g o o d n e s s - o f - f i t f o r a  chi-square:  s m a l l mean, c e r t a i n l y  (X  m i g h t be  goals  distribution. t o t a l goals the  (X  was  The 2  =  distribution  distribution. f o r the  for  of  Except normal  25 distribution, (the  best  agreed the  a l l other  Pollard  distribution  different  levels  and  1987)  shots varies  of c o m p e t i t i o n  A l l the data  and  and  chi-squares  c o u l d be  expected  f r o m game t o game due  faced.  Figure 2  a n o r m a l and  are  This  Reep e t a l . (1971)  game i n a f r e q u e n c y  example f i t b o t h  distribution.  The  of g o a l s  t o t a l g o a l s per  in this  (pages  (1973, 1985,  o f outcome p r o b a b l y  illustrates data  lowest  f i t ) f o r the n e g a t i v e b i n o m i a l d i s t r i b u t i o n .  with  the r a t e  comparisons y i e l d e d  summarized  (page  on  since to  the  26)  distribution.  a negative  The  binomial  i n T a b l e s A9  and  A10  123-125). d a t a may  mean and  a l s o be  the v a r i a n c e s i n c e the v a r i a n c e i s expected  than  t h e mean w i t h  with  the  binomial.  c o n s i d e r e d from the p o i n t - o f - v i e w of  Poisson  the u n i f o r m  and  Means and  distribution,  g r e a t e r than  t h e mean w i t h  v a r i a n c e s are l i s t e d  Table Means and  Variances  Shots Shots  Shots on s c a l e on raw d a t a For on s c a l e on raw d a t a Against on s c a l e on raw d a t a  f o r Shots  3.54 60.95  the  i n Table  1  Mean Total  equal  Variance 0.90 89.83  4.28 30.38  2.08 52.12  4.27 7.49  2.10 8.02  t o be  the less  t o t h e mean negative 1.  26 Figure 2 T o t a l G o a l s D a t a f o r A l l Teams F i t t i n g N e g a t i v e B i n o m i a l and Normal D i s t r i b u t i o n 250  -  225  -  200  175  150  -  NUMBER 125  -  OF GAMES 100  -  75 -  50 -  25 -  0 0*2  3*4  5*6  7*8  9*10 11*12 13*14 15*16  Number o f G o a l s TIME BETWEEN GOALS IN MINUTES  27 The mean-variance d a t a s u p p o r t e d a u n i f o r m d i s t r i b u t i o n when i t was  based on the c o n v e r t e d u n i t s c a l e by which d i s t r i b u t i o n s  tested  are  (1, 2, 3, e t c . ) ; but s u p p o r t e d a n e g a t i v e b i n o m i a l  d i s t r i b u t i o n when based on the raw d a t a .  The  l a t t e r agreement i s  p r o b a b l y the more r e a l i s t i c s i n c e the raw d a t a r e f l e c t the a c t u a l mean/variance whereas the former i s a f u n c t i o n of the numbers used in  scaling.  C. Between Event Time Counts The  t h i r d s e r i e s of outcome counts examined the number of  outcomes o c c u r r i n g v a r i o u s time spaces a p a r t (e.g., 1 minute a p a r t , 2 minutes a p a r t ) . d i s t r i b u t i o n was  E i t h e r a P o i s s o n or a n e g a t i v e b i n o m i a l  expected w i t h the l a t t e r b e i n g  particularly  l i k e l y s i n c e i t had shown a c l o s e f i t u s i n g event time The g e o m e t r i c was  counts.  not e x p e c t e d t o f i t , the chance of a c c i d e n t l y  a p p r o x i m a t i n g the case where the n e g a t i v e b i n o m i a l goes over t o the g e o m e t r i c  (r = 1) not b e i n g a n t i c i p a t e d .  Team by team e x a m i n a t i o n of the d i s t r i b u t i o n of g o a l s f o r home, away and t o t a l games measured from time of f i r s t g o a l showed t h a t 60 of 63  (95.2%) comparisons  f o l l o w e d a geometric d i s t r i b u t i o n  63 of 63  (100%) f i t t e d a n e g a t i v e b i n o m i a l d i s t r i b u t i o n .  the t h r e e d i s c r e p a n t c h i - s q u a r e r e s u l t s distribution  i n v o l v e d home games.  But the s i z e of c h i - s q u a r e was  f o r the  The o t h e r was  of  geometric f o r t o t a l games.  s m a l l e r f o r the g e o m e t r i c  the n e g a t i v e b i n o m i a l i n 49 of 63  Two  and  (77.8%) c a s e s : 14 of 21  f i t than (66.7%)  f o r home games, 20 of 21  (95.2%) f o r away games and 15 of 21  (71.4%) f o r t o t a l games.  A f i t f o r the P o i s s o n d i s t r i b u t i o n  was  28 found for  i n 3 o f 63 (4.7%) c h i - s q u a r e c o m p a r i s o n s .  the normal o r u n i f o r m  variance  distributions.  i n a l l 63 c o m p a r i s o n s  individual  teams.  t h e most l i k e l y 126-139).  The d a t a  are  Boston  for total  5, 10, 15, 20 and 2 5 - p l u s  Summary; D i s t r i b u t i o n binomial d i s t r i b u t i o n goals but  distribution.  Bruin goals  and y i e l d e d  total  shots,  Data.  (as l i s t e d minutes  feasible  chi-squares  Pollard  (pages  i n Figure 3  i n T a b l e A l l , p . 117)  apart. f i t the negative both  (and b e s t  the c o n c l u s i o n that these  explanation.  The d a t a  Since the data  randomly, b u t a t a v a r y i n g r a t e from  distribution i s  the reverse J  i n the m a j o r i t y of cases  the lowest  games) f o r  i n T a b l e s A l l and A12  F i g u r e 3 ( s e e page 29) i l l u s t r a t e s of the geometric  scored  the geometric  f i t and i s summarized  found  The mean e x c e e d e d t h e  (home, away and t o t a l  suggest  configuration  No f i t was  outcomes  f o r s h o t s and fits)  on a l l  occur  game t o game seems t h e most  e t a l . (1977) p r e s e n t e d  a two  argument e x p l a n a t i o n t o e x p l a i n t h e f i t between d i s t r i b u t i o n o f goals  i n h o c k e y and t h e n e g a t i v e b i n o m i a l d i s t r i b u t i o n .  " C o n d i t i o n One", e a c h team h a s a d i f f e r e n t which v a r i e s a game." scoring on  from  game t o game, b u t w h i c h r e m a i n s c o n s t a n t  at the s t a r t  o f e a c h game, b u t t h e r a t e c h a n g e s ,  of previous goals.  " C o n d i t i o n One" i s " a p p a r e n t  play  contagion." —  scoring  rate of scoring goals within  I n " C o n d i t i o n Two", e a c h team h a s t h e same r a t e o f  the occurrence  "true  In  each g o a l  "True  According  contagion"  contagion"  depending  to F e l l e r  (1943),  and " C o n d i t i o n Two" i s  i n v o l v e s the e f f e c t  of p r i o r  i n f l u e n c e s and c h a n g e s t h e r a t e o f f u r t h e r  as a game p r o g r e s s e s .  "Apparent  contagion"  i s where t h e  TIME BETWEEN GOALS IN MINUTES  r a t e of s c o r i n g d u r i n g a game appears to change, but does n o t . Both c o n d i t i o n s w i l l r e s u l t i n a negative b i n o m i a l  distribution.  P o l l a r d e t a l . argue t h a t both c o n d i t i o n s are operant l i f e hockey s i t u a t i o n . scoring goals  i n the r e a l -  In s h o r t , each team w i l l have a r a t e of  (or t a k i n g shots) which v a r i e s from game to game and  which may vary w i t h i n each game depending on the p a t t e r n of scoring  (or shooting)  data support  t h a t develops  t h i s argument f a i r l y  E x p l a i n i n g why the geometric  d u r i n g the game.  well.  r a t h e r than the n e g a t i v e  d i s t r i b u t i o n p r o v i d e s the b e t t e r f i t i s d i f f i c u l t . the n e g a t i v e b i n o m i a l was expected but why d i d the geometric  The present  to f i t the data  also f i t ?  binomial  Theoretically, (as i t d i d ) ,  The answer may stem from the  f a c t t h a t the negative b i n o m i a l d i s t r i b u t i o n i s r e l a t e d to the geometric.  R o t h s c h i l d and L o g o t h e t i s  (1986) note t h a t i f X/, X^  . . .X_3 are independent and i d e n t i c a l l y d i s t r i b u t e d random v a r i a b l e s , each having a geometric  r  £xi  d i s t r i b u t i o n with parameter p,  w i l l have a negative b i n o m i a l d i s t r i b u t i o n with parameters p  L~l  and r .  The present a n a l y s i s may have approximated t h i s c o n d i t i o n .  What i s p r e c i s e l y being measured may a l s o h e l p e x p l a i n the data.  Measuring from g o a l to g o a l i s e x a c t l y t h a t : the procedure  measures the number of g o a l s scored i n a c e r t a i n time p e r i o d . a n a l y s i s i s based on f i v e - m i n u t e i n t e r v a l s .  Goals  The  (by e i t h e r  team) were scored on an average of .624 every 5 minutes of r e a l time.  The g o a l per game average of 7.5 goals a game t r a n s l a t e d t o  a g o a l every 8 minutes.  But t h i s p a r t i c u l a r measurement  procedure  began a t the time of the f i r s t g o a l and ended a t the time of the  31 last  goal.  about  The t i m e - s p a c e  52 m i n u t e s .  distribution  goal  (Feller,  1966)  distribution. sequence  waiting  rth  from  must In  occurs  time  the  and the  scratch  a renewal  the f i r s t  success  (r+l)st  may a l s o  streaks  3 of  the  small  losing  2,  n f o r each  streaks for  uniform,  Poisson,  and  their  and must of  into  time  that  the past  each  arrival  have  the  Feller  Bernoulli  t h e number  of  trials  between  the  the  distribution.  Distribution from  a frequency  'streaks'  of  distribution  1 win i n  9 wins  in  team,  cumulative  totals  f o r winning  streaks  and n e g a t i v e  again  manner.  that  distribution;  8 and 1 of  were  the  notes  and t h a t  has a geometric  the  same  (1950)  trials  of  arrivals  1 of  geometric  (goal)  replica  between  a  history  stochastic processes,  agreement/disagreement  distributions  unconventional  times  process.  and w i n n i n g / l o s i n g  examined  The  waiting  Boston had 5  3,  goals  assumption that  h a s t h e same g e o m e t r i c  be examined  (e.g.,  at  the  as a p r o b a b i l i s t i c  success  occurs,  success  point-of-view of  the sense future:  terminology  Streak Streaks  the  i n a sequence of  up t o  first  in  be i n d e p e n d e n t  the  7.5  the remaining  i n opposition to  The s u c c e s s i v e  constitutes  success  when  is  no c o n c l u s i o n s as t o  process.  an a v e r a g e  geometric.  explanation  process starts  whole  a  the  crams  may move  o r w i n has no a f t e r e f f e c t  permits the  The e f f e c t  toward  Pollard's  lost  analyzed  a row).  taken with  together the  binomial i n both  a  a row,  10  Due t o streaks, were  normal, distribution. conventional  32 Results. losing for  and  winning  The  total  data  favored  streaks  streaks.  and  It  is  the  the  geometric  negative  summarized  Table  in  Losing Streaks Geometric Negative Binomial Total Streaks Geometric Negative Binomial  Complete Means  results  may  and v a r i a n c e s  distribution  2.  Unconventional 2  df 6 6  ls ns ns  X 2.413 3.756  df 5 5  Is ns ns  2.643 8.211  4 4  ns ns  2.236 7.182  4 4  ns ns  7.154 7.711  6 6  ns ns  1.116 3.686  6 6  ns ns  be are  found  in  listed  Table  in  Table Means  Table  or  Streak Frequencies Binomial Distributions  Conventional 2 X 11.519 7.296  binomial  for  2  C h i - s q u a r e Comparison of w i t h G e o m e t r i c and N e g a t i v e  Winning Streaks Geometric Negative Binomial  distribution  Table  A13  (pages  140-142).  3.  3  and V a r i a n c e s Conventional  for  Streaks Unconventional  Streaks  Mean  Variance  Mean  Variance  winning losing total  2.21 1.84 2.04  2.59 1.29 2.05  2.27 1.87 2.07  3.31 1.58 2.54  33 The of  mean/variance  any  particular  Another  clue  looking  at  what  the  is  (assuming  the  Gambler's  plays the  was  .0156,  but  once  the  sixth  win  the  7th  averge,  but  design  since  about on  the  their  the  or  .500  is  chance its  change  team  .50.  of  the  prevalence  the  in  the  teams  don't  would  still  be  X.  A check  percentage  geometric  of  with not  character  of  a  row,  winning  row  play  would  did  in  by  game,  was  at  geometric  X+l  found  probability  All  game  a  is  six  next  chance  seven  won,  data  wins  the  The  of  the  team  winning  was  winning  winning  of  a  hockey).  game  distribution  as  If  probability  season w i n - l o s s - t i e  significantly  support  character  the  straight  game  the  same  clearly  Fallacy.'  of  team  straight  will  not  geometric  probability  the  did  distribution.  to  'The  data  a in  six  .0078, the  team  .500 general  theoretically  several  teams  appreciably the  be  based or  distribution  chi-square. Back-to-Back Sportswriters  convenient the  set  closest  comparison Fischler data  were  of  thing with  and  raw to  data a  Fischler  involving  (1969)  arranged for  Data  Fischler  the  (1986)  in  hockey  21  a  games.  and  This  allowed  on b a s e b a l l .  scientific  for  provided  back-to-back  findings  a d v a n c e d no  comparisons  that:  and  'doubleheader'  Goodman's  conveniently  Chi-square revealed  Fischler  Game  postulates,  some  Although their  analysis. teams  (1985-86  NHL  is  season)  a)  only  level)  1 of  points  21  (4.8%)  record  teams  had a s i g n i f i c a n t l y  f o r the f i r s t  night  different  as compared  to  the  (.05 second  night. b)  only  level) games  1 of  points point  .02  2 of  (4.8%)  record  record  back-to-back c)  21  for  (9.6%)  points  record  other  (non-back-to-back)  level) The  21  Table  when  appropriate Elderton,  — was  et  or  all  (page  of  —  three  not a part  of  added  different  other a  (.05 and  as opposed t o  did better  conditions  outcomes  were  during  their  their  different  (.05  compared.  in back-to-back  in baseball.  The d a t a  games are  are not  summarized  Testing  outcomes  binomial  Poisson  of  1915,  1977),  significant  of  were  compared  previously  1927; E l d e r t o n  (Pollard,  the normal  variety  shots)  distributions  (Mullet,  as p o s s i b l y  i n a wide  goals,  (Elderton,  negative  because  (e.g.,  theoretical  geometric  1909),  teams  had s i g n i f i c a n t l y  that  different  speculated  prevalence  their  143).  a l . , 1971);  often  a n y game  (.02  games.  A l l Distribution  several  Reep  Both  to doubleheaders  Distributions with  being  different  as o p p o s e d t o  f o r the second night  teams  suggested  A14  Summary:  night  had a s i g n i f i c a n t l y  record.  (14.3%)  points  comparable in  point  data  game  teams  games  3 of  the f i r s t  (other  other  d)  had a s i g n i f i c a n t l y  scheduling).  21  level)  teams  1973,  and  1985, 1986;  uniform  (the normal  distribution's  situations).  found  (Lapin,  1984)  distribution general  35 The  data  outcomes any  in  other  evenly  any  The  of  data  an  Postulate The  in  game lc  data  may  pooled  uniformly for  teams. does  not  increase change  in  The  occur  (Lapin, about  to in  the  equally  When e v e n t examined  the  supporting  a  and  rate  or  of  goal  was be  pattern  of  goals and  of  outcomes  were  for  scored  across  an  increase  modified  the  first  18  was  the due  the  the  considered for teams,  goals  minutes  of  entire  60  minutes  for  allow  G r o u p i n g team  two  minute.  fact  that  detection  scores  an of  la.  When  all  21  were  59  the  was  final  final  first  to  to  in  there  concerning postulate  individual the  Although  accordingly.  s c o r i n g was  for  across  lc.  scoring during  clear-cut  across  playing  time  individual  individual a  together  team  last-minute reveals  the  pattern.  evenly  X minute  are  The  pattern  second p e r i o d ,  distribution  occur  1984)  (e.g.,  enough g o a l s  scoring  predicted to  and  scoring.  uniform  game  season goal  difference  in  entire  less  together  score  the  therefore  teams  The  same  there  distributed  pooled  the  supported postulate  the  appeared  lb.  period).  time,  minute-by-minute teams  first  partially  of  was  an  third  increase  minutes  and  the  the  supported postulate  period  period  across  minutes  not  strongly  was  expected  across as  the  generated,  time X +  since goals  (a  goal  was  1 minute).  each u n i t  just  If  space w i l l  were as  enough be  likely numbers  eventually  filled. distribution negative  (e.g.,  binomial  random d i s p e r s a l  shots  or  goals  distribution of  goals  or  per  game)  prevailed,  shots  across  was  strongly games.  Examination minute  of  apart,  the  two  distribution  minutes  apart,  geometric  negative  binomial  and  affirmed  a random  distribution  suggesting within  arbitrary time  a varying  games);  the  choice  between  goals  binomial  probably  also  discrete  data.  The found the  to  fit  the  pooled  being  a  balanced  lead  to  game  1 =  chance  .50;  the  chance  between  a  streak  r  =  the  to  from  of  teams  1 + 2 + 3 = negative  situation  r  would  This  was  as  x  binomial  .50  2 = x  it  of  were  were  it  not  appears  constant.  establishing  out  to  having  top  team's  60-40  an  effect  would  chance  1 + game  if  also  was  Such  (e.g.,  counting  Again,  (the  the  the  average  40-60).  .50  perhaps  1 when  data  effect  losing  closely  of  =  streaks.  the  also  suggesting  procedure  the  binomial  (and  distributions  had  game  both  distribution.  distribution  winning  fit  game-to-game  team's  with This  game  continuous  or  one  negative  c a s e where  have  goals  of  .50  .50=  x  .50  .125).  and g e o m e t r i c  approximating  winning  the  =  .25; The  suggests situation  1.  Finally, strongly  of  the  total  winning  bottom  games  relationship  where  of  the  and  may  pool  geometric  winning  sequential  which The  and  binomial  losing  chance by  a rough  of  data  game  treating  losing  of  fits  the  distribution  and n e g a t i v e  or  yielded  events,  a geometric of  number  distribution.  from  minutes  becomes  fit.  50-50  rate  the  etc.,  of  approximated  winning  geometric  roughly  five  winning,  of  was  event  function  geometric  rate  This  a  the  geometric  of  negative  of  the  comparison of  supports  the  notion  the that  Fischler  data  back-to-back  on h o c k e y games  are  games not  37 similar  in  suggests than in  24  one  lose two  after II.  the  day  a  of  but  baseball  Goodman  to  win  baseball than  doubleheaders,  measurement  long.  tended  row  to  or  loss  two  athletic  (1969)  teams  split  in  found  both  were games  when  finding  contests  teams  games  no more  a  is  playing  rather  likely  games  that  than  to  were  win  not  more  two  games  win  one,  or  played  lose  one  day  another.  Runs The  Each  unit  hours  one; in  outcome  Testing  second s e r i e s  probed  response.  the  data  departure  from  team w i n n i n g  losses  for  a  significantly expected 2a.  2b.  by  in  in  the  following  the  streak  X % of  for of be  its  a  of  of  games  wins  its or  wins and l o s s e s "random".  (e.g.,  X of for  not  than  every each  may  pattern  will  losses  oriented.  refers  that  the  games  time  "randomness"  postulates  expectancies  team w i n n i n g  I s o l a t i n g each p e r i o d the p a t t e r n of f i r s t , f o r e a c h team w i l l be (e.g., compare p e r i o d p e r i o d 1 , game n ) .  directly  existence  won X % o f  sequences  The p a t t e r n season w i l l  not  the  that  chance  was  for  from  team  postulates  set  Randomness  chance a  of  team  to  be  the  expected  of  win-  deviate  might 100  of  be  games). for  the  as i f i t were a s e p a r a t e entity, s e c o n d and t h i r d p e r i o d outcomes "random". 1 , game 1 ; p e r i o d 1 , game 2...  2c.  If a n y two p e r i o d s a r e c o m b i n e d ( P e r i o d 1 + P e r i o d 2 , P e r i o d 1 + P e r i o d 3 , P e r i o d 2 + P e r i o d 3) a s i f they w e r e a s e p a r a t e game, t h e p a t t e r n o f o u t c o m e s w i l l be "random".  2d.  A s s i g n i n g a "win" f o r most, a " l o s s " f o r l e a s t , s h o t s on g o a l p e r game a n d p e r p e r i o d ( e . g . , p e r i o d 1 , game 1 ; p e r i o d 1 , game 2 . . . p e r i o d 1 , game n) f o r e a c h t e a m w i l l be " r a n d o m " .  38 These using two  postulates  the  undefeated  (b)  "psychological" streaks a t e a m was a t h o m e ; a t i e was o n t h e r o a d .  results  data  expected  Boston,  in  Table al.  of  and M o n t r e a l , of  101  away  data  and  were  total  games)  analyzed  these  a  from  were  (Hartford  80-game beyond The  data  not  runs  at  (only  the  .05  (1985,  1989)  argued,  Calgary  had win  win/loss  4 of  or  144).  105  streaks  are  of  wins-losses deviated  streaks four for  to  runs the  beyond  the  the  of  realm  simply  anything  tests  more  that  realm  of  chance  for  supported postulates  too  2b  The  data  13;  5.  from  many  than  of  significant  team  3 of  7  and  Yet  not  chance.  games  chance  away  (Calgary  chance.  a  runs  statistically  cases  occasional streak  and  of  Pittsburgh,  and  other  a n d home g a m e s tests  6  won  were  isolated  4 runs  the  schedule,  be  of  8;  12  pattern  example,  and  of  3 streaks  for  7  (3.8%)  level).  streaks  when team  streaks  less  9,  Finding  also  105  (page  and Los A n g e l e s )  Philadelphia). itself,  of  2a:  win  a loss when a  of  for  significant  a t i e c o u n t e d as c o u n t e d as a win  streak  overall  The  c o n s i d e r e d as  Washington,  and M o n t r e a l ,  occurences.  and wins  9;  team's  their  ties  8 and  Calgary  be  The  A15  deceptive:  streaks  -  significant  G i l o v i c h et  perceptually  a  home,  supported postulate  for  were  summarized  As  streaks  The  test  of  test.  (a)  as  one  runs  (for  viewpoints:  were  8  examined  Wald-Wolfowitz  Results.  are  were  With of  15  with and  games  and  in  105  21  teams  straight  many w i n s  2c.  The  tries  is,  playing would  or  not  losses.  pattern  39 of  randomness  of w i n s / l o s s e s  treated  as separate  periods  1 and 3;  test  results  level, 1  at  six  3 at  the  artificial  across  The The  data  game  2 at  the  1 2 3 1 1 2  t h e 21  test  results  that  might  be t r u e  deviations  significant problem seasons, the  gains  some  t h e team w i t h  significant  results  results  patterns  the  results  that  were  (5.3%)  5 were  runs  at  .02,  5 at  were  spread  the  the  A16, pages  being  chance  from  support  the best  .05  .01 and  across  the  145-146):  the best  by f u t u r e  chance. from  shown b y t h e o t h e r  The  the fact win-loss  wins-losses game  research.  (or worst)  patterns  b u t a few  latter that  one  record,  and 3 of  team, had 2 of  18  runs  tests.  Over  a number  team c o n s i s t e n t l y  teams?  prevail.  c o u l d be  occurrences,  overall  on o v e r a l l  random  significant  on the a r t i f i c i a l  may b e s o l v e d does  level:  (see Table  the hypothesis  likely  5  378  1 and 2;  teams:  as most  Calgary,  20 o f  .05  4 at  (periods  were  (16.7%) f o r 2 teams (11.1%) f o r 4 teams (5.5%) f o r 6 t e a m s  support  interpretation  the  periods  g a m e s : 6 o f 63 (9.5%) g a m e s : 1 o f 63 (1.6%) g a m e s : 4 o f 63 (6.3%) a n d 2 g a m e s : 2 o f 63 (3.2%) a n d 3 g a m e s : 2 o f 63 (3.2%) a n d 3 g a m e s : 5 o f 63 (7.9%)  considered also  Only  .03,  conditions  t h e 18 t h e 18 t h e 18  few r u n s  2 and 3 ) . at  whether  together  T h e 20 s i g n i f i c a n t  12 o f  3 of 2 of 1 of  or paired  significant  .04,  .0003.  Period Period Period Period Period Period and  periods  were the  games  prevailed  The of  deviate  from  40 The  data  dominance  also  were  significant in  Table  basis  (page  postulate  (seeing  periods  if  greater  approach 2e.  random.  4 of  2d: the patterns  84  (4.8%)  direction.  runs  of  test  The data  shot  results  are  were  summarized  147). 2d e x a m i n e d  any team than  the pattern  could  would  dominate  be e x p e c t e d This  of  shots  i n shots  on a  "gross"  for a skein  by c h a n c e ) ,  l e d to postulate  a more  of  "micro"  2e.  The p a t t e r n of g o a l s f o r and g o a l s a g a i n s t tracked f r o m p e r i o d t o p e r i o d , game t o game a s a c o n t i n u o u s s t r e a m o f 240 p e r i o d s f o r t o t a l g a m e s , 120 p e r i o d s f o r home o r a w a y g a m e s , w i l l b e " r a n d o m " ( w i l l n o t exceed e x p e c t a t i o n s based on each team's win-loss percentage). Calgary Period 1 2 3 4  The  data  supported  results  were  results  for Hartford's  significant, significant. Calgary's  a number  Team Scoring Calgary Detroit Calgary Detroit  Time 15.05 4.21 10.56 14.27  postulate  2e.  significant  in  home  but Hartford's There  modest  important.  Over  Only  seemed w a r r a n t e d .  e.g.,  be  postulate  i n the non-random  A17  Since  supported  is  of  a n d away game  a remote  preponderance  Future  research  seasons,  teams  game  4 of  of  of  teams  sequences  matching  Hartford's)  runs  test  The both  s e q u e n c e was n o t  easily  should  and t h e number  (6.3%)  s e q u e n c e s were  that  significance  should  63  direction.  possibility  sequences  (like  Only  the non-random  total  Run T e s t Number 1 0 1 0  Code GF GA GF GA  with in  may,  on runs  solve  continue home,  this  the  test  or  random  total  the s i g n i f i c a n t  data,  problem.  to reveal  away  like  game  direction  41 should for  be  this Goals  game  no more study  and  were  the  they was  did  below  be  mean,  of  an o v e r a l l  game  for  games  the  team  games  and  above  a  team  time led  would  period to  and g o a l  the  average  average  above  be  mean  game  and  the  The  mean  idea  final  40.  play  below  average  significant  If  this a  A19  (page  and  Only in  149)  were  40 so,  significant  time  period.  This  2f.  supported  significant  that  pattern  first  data  games.  is  per  shots  The  total  as  30  their  for  that  may  Outcomes ( e . g . , s h o t s , g o a l s ) f o r and a g a i n s t w i l l be d i s t r i b u t e d i n random s e q u e n c e above and b e l o w the mean.  goals  is  a game-by-game for  that  procedure  2f.  involving  A  behavior  averaging  have  above  revealed  split  above  to  This  procedure  average  their  a  below  random.  below  data  mean b a s i s .  testing  season average  for  period,  a n d means  for  average  to  used procedure).  s h o u l d be  theoretically  theoretically  postulate  this  The  148).  runs  simpler  A team  their  the  viewing  the  or  average.  below  (page  medians  underlying  could  was  and  so  chance.  period  frequently  differ  above  behind  where  by  sequence need not  lurk  80  out  by  18  from  many m e a s u r e m e n t s  the  streak  Table  above/below  more  shot  argument as  an  carried the  team  in  expected  against  on  profoundly  about  the  a hidden  also  The  number  and  examined  of  not  used.  although  for  (probably  check  the  summarized  shots  may  median  random  are  also  procedure  than  the  a random  shots, 16  for  273  and  for  test  non-random d i r e c t i o n .  The  (page  (5.9%)  against,  of  runs  and A20  of  interpretation  150).  the  patterns  home,  away  results  were  data  are  in  and  Tables  Postulate  2g  examined  four-game  sets  employed  the  were  treated  a  study  'win';  3 points  2g.  None  the  correlations suggested  21 of  The  runs  Runs test  periods,  1  tests to  increasing  of  scale.  The  stationarity  section  (4  more  games  points  or  of  equalling  'loss').  were  set  2,  from  -.357  significant.  set  relationship  2  to  between to  set  Lagged 3,  sets.  .321.  The  etc.,  also  Correlations data  are  in  Table  A21  goals  through  losses)  (based  on  a  and or  shots,  outcomes  above  of  allied  conditional  do  not  over-all games  and  This  for  against  were  followed  how  mean  across  only  the  or  time  data  length  home,  away  were of  held  for  of  games,  combinations  isolated  whether  four  chance  record).  were  and  all  exceed  periods  as  discrete  straight  or  total  analyzed  consecutive  games  (e.g., wins  length or  prevailed.  Probabilities with  runs  probabilities.  from  supported  whether  below  randomness  losses  periods,  No m a t t e r or  or  team's  game-after-game,  Closely  overwhelmingly  wins  Conditional  directly  analysis of  examined.  runs  Testing  combinations  entities  III.  a  streaks  expectations  of  set  ranged  All  postulates:  were  test  single  less,  of  151).  Summary:  for  the  as  runs  a random  sets  (page  in  effect  F o u r - g a m e s e t s t r e a t e d a s s i n g l e games w i l l show a r a n d o m p a t t e r n o f ' w i n s ' a n d 'losses'. of  between  or  the  Gilovich,  testing The  Vallone  is  latter and  the  examining  procedure  Tversky  was  (1985)  of also  who  adopted  suggested  43 that  data  wins,  on  etc.  the  probability  would  be  useful  in  a win  after  examining  3a.  The p r o b a b i l i t y of 3 w i n s w i l l be t h e percentage.  3b.  The p r o b a b i l i t y of a l o s s a f t e r o r 3 l o s s e s w i l l b e t h e same a s percentage.  3c.  The the  NHL  The  data  outcomes next.  of  The  winning tie).  21  a win,  of  of  interest  if  it  Comparing sequential  The a  than  wins  closely  Table  A22  and  sequential  This  This  (25.8%)  for  are  with  a  that  97  chance  all  of the in  ties of  one  game a  a  3c.  The  in  to  a  2 wins,  of  in tie The  around  be the a  its  (55%) games  following data  and  4.  with  840  win  Finally,  hovered  20  one  would  season percentage 11  the  was  for  latter  Table  ties  —  (there  (9.5%)  teams  1988-89  team's  seasons.  detailed  postulate  152-153).  of  the  general  following  3 wins.  percentage were  21  the  for  exceeded  a win  for  or  be  in  from  2 of  a number  showed  there  supported  (pages  were  losses  will  comparisons  season percentage  Overall,  11.9%.  wins  following  percentages  comparisons.  was  62  two  loss, 2 losses team's w i n / l o s s  independent  (15.0%)  percentage  the  compared  of  1 a  after  behavior.  randomness  sequential  a win  team's  tie  be  occurred over  sequential  split.  higher  for  of  20  a win  probabilities  of  percentages  3 of  (52.4%)  to  16  individual  11  average  on  streak  after a tie percentage.  concept  appear  percentage  following  the  probability  The  50-50  games  tie tie  on c o n d i t i o n a l  season supported  a win,  a win a f t e r 1 win, 2 wins same a s a t e a m ' s w i n / l o s s  p r o b a b i l i t y of a same a s a t e a m ' s  Results.  in  of  are  was  of (11.5%). a  tie  which  summarized  44  Table  4  E m p i r i c a l P r o b a b i l i t i e s o f R e p e a t i n g a Win o r L o s s C o n d i t i o n e d on t h e Outcome o f P r e v i o u s Game(s) F o r a l l Teams C o m b i n e d  1 win a f t e r a win 2 wins a f t e r a win 3 wins a f t e r a win Total  1 2 3  Summary: The of  loss after a losses after losses after Total  Conditional  analysis  independent  the  outcome  likely loss  to  as  a  following team's IV.  of  X +  a win  loss.  For  a win,  a  win-loss  fourth  relationship 4.  the  follow  Pet.  Losses  .452 .491 .465 .464  331 160 73 564  n 733 316 144 1193 n 733 326 157 1216  outcome  1. as  probabilities  For  loss  the  a win.  individual  of  game  teams,  following  a  X is  whole  A win  not  league,  is  as  the  loss  supported  the  associated a  likely  loss to  likelihood  is  a  concept  a  between  of  postulates  outcomes  from  probed one  the  period  of  each  correlational to  the  The c o r r e l a t i o n between outcomes i n any one p e r i o d w i l l n o t be c o r r e l a t e d w i t h o u t c o m e s i n a n y o t h e r p e r i o d o f t h e same g a m e . This includes:  as  win  Data  series  with  follow  of  function  is  percentage. •  Correlational The  conditional  game  Wins 322 147 80 549  Probabilities  games:  of  loss a loss a loss  Pet. .439 .465 .556 .460  next.  a  45 period period period and  1, 1, 2,  involves 4a. 4b. 4c. 4d. 4e. 4f. 4g. 4h. 4i.  A  final  hypothesis  was  Results. For  of  between  the  Average .084  21  each  data  4b.  the  the  basis .222 .257 .204  Average  4c.  21  to to to  for for for  The  outcomes:  outcome  and  involved game  the  outcome.  No  teams, of  in  For  teams,  period period period for  for  for for for  Table  1 vs. 1 vs. 2 vs.  these are  period period period were  period period period  three  through between  4i: periods  for  in  correlations  (pages  correlations  were  Table  between  A23  -.034, (page  periods  on  from  1 vs. 1 vs. 2 vs.  .009,  2 3 3  conditions  summarized  ranged  A24  4a  correlations  individual  goals -.172 -.343 -.226  postulates  from  data  correlations  21  1..80 1..80 1..80  the  correlations  period  ranged  summarized the  game  individual  -.232 -.111 -.149  .060.  For  game game game  concerning  supported  correlations  .  2, 3, 3,  ties/losses for against for against goals shots difference difference  teams,  to to to  154)  period period period  advanced.  The  and  vs. vs. vs.  within  wins-ties/losses .150 .393 .323  1..80 1..80 1..80  postulates  winsgoals goals shots shots total total goal shot  series  correlation  4a.  game game game  period period period  -.002  and  2 3 3 .075.  The  data  are  155-156) . between  periods  on  the  basis  of  goals .204 .239 .275  Average  4d.  teams,  the shots  21  for to to to  -.066 -.143 -.123  teams,  shots .286 .260 .246  Average  21  against to to to  -.262 -.117 -.135  For  teams,  total .268 .261 .189  Average  21  goals to to to  For  teams,  of  total  21  shots  (pages  period period period were A24  ranged for for for  .118,  (pages  and  2 3 3 .073.  The  data  are  155-156). between  periods  on  the  basis  period period period were A24  for for for  .034  and  2 3 3 .124.  The  data  are  155-156). between  1 vs. 1 vs. 2 vs.  .077,  (pages  periods  on  the  basis  period period period  .054  and  2 3 3 .106.  The  data  are  155-156). between  periods  on  the  basis  from period period period were  A25  1 vs. 1 vs. 2 vs.  .057,  (page  correlations  ranged  period period period  from  correlations  Table  .035  1 vs. 1 vs. 2 vs.  correlations  correlations in  the  for for for  ranged  summarized  .014,  period period period  from  Table  -.177 -.120 -.193  1 vs. 1 vs. 2 vs.  correlations  correlations in  of  A24  Table  summarized the  period period period  correlations  For  from  were  ranged  in  of  for for for  Table  summarized the  ranged  correlations  For  Average  4g.  -.199 -.134 -.146  in  .324 .176 .283  4f.  to to to  summarized  of  4e.  against  from  period period period  .052  and  2 3 3 .013.  The  data  are  157). between  periods  on  the  basis  .269 .278 .297 Average  4h.  -.107 -.127 .019  for for for  in  For  teams,  the goal .169 .337 .302  Average  21  -.267 -.183 -.156  teams,  21  shot .372 .167 .359  Average  The  for for for  Table  Correlational  567  teams  suggested  that  another.  The  ranged  from  (page  160).  period  .141  to  correlational  data  are  periods  on  the  basis  period period period .061  2 3 3  and  .051.  The  data  are  158). between  periods  on  the  basis  1 vs. 1 vs. 2 vs.  .101,'  period period period  .015  (page  159).  within  game  and  2 3 3 .100.  The  data  are  Data  from  .393  outcomes  to  are  -.034.  data  ranged  from  .811  The  data  comparing goal for  correlations  -.343.  This  relatively  correlations,  on w i n - t i e / l o s s e s , to  The  from  were  totals  .215  (page  A27  ranged  overall  1 vs. 1 vs. 2 vs.  period period period  period-to-period  individual  The  in  between  -.036,  ranged  correlations  summarized Summary:  -.156 -.206 -.182  .141.  157).  correlations  difference to to to  A26  and  2 3 3  from  were  Table  period period period  .087  (page  period period period  correlations  For  .098,  ranged for for for  in  of  A25  1 vs. 1 vs. 2 vs.  correlations  difference to to to  were  Table  summarized the  period period period  correlations  summarized  of  4i.  to to to  b a s e d on are  independent totals  individual  individual  strongly  summarized  difference  for  and  teams.  for in  periods shot The  of  21  one  teams,  Table  with  A28  game  difference overall  48 correlations  were  as  follows: Period  Total Total The  goal shot  difference difference  general  trend  correlated  since  period  each  was  being  and  A27  with  (pages  game  154,  The  158  and  Game Lagged outcomes period  correlational from  1,  tie/loss, (5e)  shots  one  game  game  2).  (5b)  goals  for,  (5f)  33%  of  the  are  Game  the  This  was  s h o u l d be  total  against in  expected  which  Tables  it  A23,  A26  Correlations  the  next  Seven p o s t u l a t e s , (5c)  shots  outcome  summarized  c o m p a r i s o n s were  for,  3  159).  to  to  Period .646 .616  period's  outcome.  data  2  .593 .652  each  represented  correlated.  Period  .535 .584  suggested  moderately  1  goals  against  also (e.g.,  made  period  involving against,  and  (5g)  between 1,  game  outcomes  (5d)  shots  1  (5a)  total  total  period  argued  The c o r r e l a t i o n between an outcome i n p e r i o d 1, 2 , 3 o r a n e n t i r e game w i l l n o t b e correlated w i t h i t s c o u n t e r p a r t outcome i n the following game.  similar 5a.  to  For to  .142 .185 .248 The  The the  game-to-game  within-game  the  21  teams,  game  on  the  to to to  -.331 -.248 -.293  for for for  correlations  individual  team's  of  period period period  between  "win-tie/loss" 1, 2, 3,  game  total  exceptionally  comparisons:  correlations  basis  for  c o m p a r i s o n s were  to  game game game game  games  i i i  vs. vs. vs.  periods ranged  period period period  win-tie/loss  ranged  from  .167  1, 2, 3,  from  game  from game game game  i+1 i+1 i+1  outcomes to  win-  goals,  that:  Results.  to  -.200.  for  49 The 5b.  For  .046 .326 .217  to to to  -.189 -.278 -.236  data  For  the  basis  are 21 the  .298 .115 .190  to to to  -.187 -.307 -.200  For  the  basis  are 21  in  on  the  .176 .206 .178  to to to  -.245 -.254 -.325  For  the  basis  are 21  in  on  the  .187 .198 .156  to to to  -.227 -.127 -.135  For  the  are 21  in  game  on  the  .235 .157 .154  to to to  -.153 -.177 -.155  data  are  The  basis for for for in  goals  period period period  for  1, 2, 3,  A30  game game game  (page  correlations of  goals  period period period  1, 2, 3,  A30  of  A30  game game game  period period period  for  1, 2, 3,  A31  of  period period period  Table  A31  i i i  periods  ranged vs. vs. vs.  i i i  vs. vs. vs.  ranged  1, 2, 3,  game game game  i+1 i+1 i+1  from  game  to  from  period period period  1, 2, 3,  game game game  i+1 i+1 i+1  periods  from  game  to  from period period period  1, 2, 3,  game game game  i+1 i+1 i+1  i i i  vs. vs. vs.  periods  from  game  to  from period period period  1, 2, 3,  game game game  i+1 i+1 i+1  163). between  game game game  (page  period period period  ranged  against  1, 2, 3,  vs. vs. vs.  between  (page  shots  to  162).  game game game  correlations  game  from  between  (page  shots  from  162).  game game game  correlations  periods  between  goals  1, 2, 3,  161).  162).  (page  total  period period period  i i i  against  correlations  Table  teams,  (page  ranged  basis.of for for for  A29  of  Table  teams,  game  data  for for for  Table  between  Table  teams,  game  data  for for for  in  correlations  Table  teams,  on  data  for for for in  game  The 5f.  teams,  the  The 5e.  21  summarized  on  The 5d.  the  are  game  The 5c.  data  i i i  periods  ranged vs. vs. vs.  163).  from  game  from  period period period  1, 2, 3,  game game game  i+1 i+1 i+1  to  50 5g.  For  the  game .163 .202 .180 The  21  on  teams,  the  to to to  -.186 -.235 -.176  data  are  Summary:  basis for for for in  showing  a modest  correlations the  same  period  and  an  words,  in  an  in  another  in  period  game  only  .393  to  2.  period The  -.343,  independence  between in  game game game  i+1 i+1 i+1  the  game  1  to  again  than  for  could period  outcome  it  were  in  one  game.  no more  all  The  another  same  X+l,  that  -.331,  to  an  1 seems  range  to  game  game  period  1, 2, 3,  measurements.  X,  spread  of  .326  one  period  maximum  a  from  from  outcome  in  to  from  period period period  between  outcome  game  Outcome-to-outcome  ranged  correlations  activity  of  game  relationship  activity  vs. vs. vs.  from  163).  as  X,  concept  (page  i i i  range  period  was  game game game  periods  ranged  Correlations. to  comparing  within  to  game  between  shots  1, 2, 3,  A31  Game-to-Game  only  total  Table  from  related  of  period period period  correlations  other  correlations  is  In  or  to  1029  less  activity  correlations  possibly  support  and  to  game  the  game  outcomes. Correlation: correlations game of  examined  outcome.  play  in  any  considerably 5h.  to  For game  the  Outcome the  Game O u t c o m e .  relationship  Since  a period  given  period  game  to  is  has  outcome.  the The  The 21  data,  teams,  outcome  on  in  basic  correlations  the  basis  of  of  potential  general,  Another  between  one-third  P e r i o d o u t c o m e s h o u l d be w i t h game o u t c o m e .  Results. 5h.  Period  period a game, of  supported between  of  outcome the  and  results  contributing  postulate  positively  set  was  therefore:  correlated  postulate  period  wins-ties/losses  5h.  outcome ranged  and from  51  .215 .306 .328 The  data  For  The  .624 .668 .672  are  the  game  to to to  21  teams, on  .408 .423 .496  .662 .718 .775  to to to  overall  For  The  the  game  The  data  teams,  .429 .518 .426  .723 .811 .709  to to to  overall  between  and  resembles  periods) for  Table  (Anastasi,  1954)  teams  A26  outcome  the  with  outcome ranged  .584,  from  of  the  correlations goal  a definite  suggests test.  correlation  a hockey  Items  each other  (in (a  final  score  (game o u t c o m e ) .  but  made not  of  with  game  hockey's  basic  (period  score,  and  159).  items  test  and  .642  wins-ties/losses,  with  and  outcome outcome outcome  Analysis  This  from  .593  but  "perfect"  final  period  were  revealed  and  158).  (page  selection  correlated  ranged  .535,  difference  teams  for  outcome  outcome outcome outcome  1 a n d game 2 a n d game 3 a n d game  outcome.  choice),  period  (page  shot  A27  154).  were  between  all  Table  ideal  well  with  for  (page  1 a n d game 2 a n d game 3 a n d game  differences  not  is  of  outcome outcome outcome  differences  Game O u t c o m e .  the  item  fairly  correlated  to  are  goal  all  period period period  in  a n d game  correlated  each  for for for  shot  closely  requirement  for  basis  a n d game  period  of  A23  between  correlations  are  Period  between  case,  in  the  data  Table  period period period  correlations  period  differences  for for for  are  on  Summary:  basis  correlations  21  The  in  1 a n d game 2 a n d game 3 a n d game  correlations  the  outcome  .616.  period period period  summarized  outcome  .646.  for for for  outcomes)  are This  independent each  other.  items,  VI.  Raw  and  Earlier overall  outcome  one  given  game  page  with  Z+l.  procedures  game-to-game material  in  goals  9  with  if  or the  the  comparing  for  one  is  a  Z being  data  were  based  and  another then  one-step  compared  on  total  team Y ,  simple  game  the  team  team X o u t s h o o t s  in  were  simple  shots  1 goal  '0* in  involve  11  this  the  The  results,  1).  shots  mean  two  data.  =  the  of  that  analyses The  into  Like  team X  lag  with  'outcome'  procedure  (see  whether  postulates  on raw  examined  no  the  W by  by  goal first  the  original  in  data a  code  the  be  '1'  period  W+l.  a binary  was  procedure,  a  1 or  this  The  system:  awarded;  =0,  2  compared  time-space to  involved  raw  meant  team X would  team X  in  This  opposing team.  a binary team's  period-to-period,  comparison.  converting  the  compared  expectancy  lag  used  time-space,  (e.g.,  comparison with  transforming below  awarded  first  taken  involved in  determine  time-space  shots  appeared  was  in  to  The  one-step  taken or  period a  employed  correlations. a  event  a  goals  The  test  second procedure  not,  1  if  outcome  correlation  'outcome'  Runs  b a s e d on  the  play:  The  was  37).  Two  The  of  'win.'  comparison in  between  period  a  Correlations research  difference  during is  Binary  if  more  does  not  procedure split  above  or  shots. period  is  that  or  binary  1,  game  1 with  period  period-to-period, data,  will  not  2,  game  game-to-game be  correlated.  were:  The p e r i o d - t o - p e r i o d , game-to-game correlations o f raw and b i n a r y c o n v e r t e d s c o r e s w i l l be approximately zero. T h i s w i l l h o l d f o r home, away a n d t o t a l g a m e s f o r :  53  6a. 6b. 6c. 6d. Results.  The  correlations summary  of  data  were  the  goals goals shots shots  for against for against  supported  very  range  low  of  the  and  the  four  postulates:  range  correlations  centered  os d e t a i l e d  the  around in  zero.  Table  5  (see  below). The  data  164-165) For  and  general  attributes raw  concerning goals  summarized  concerning shots information,  (e.g.,  scores.  The in  are  goals range  Table  6  Table  and  shots  individual  (page  for)  were  A32  (pages  166-167). various  calculated  team c o r r e l a t i o n s  using  is  5  Home For Raw Bin Goals Against Raw Bin Shots For Raw Bin Shots Against Raw Bin  (pages  between  R a n g e o f Raw a n d B i n a r y I n d i v i d u a l C o e f f i c i e n t s f o r G o a l s and S h o t s  High  Table  54).  Table  Low  in  A33  correlations  for of  in  summarized  Team C o r r e l a t i o n (P1G1...P2G1...P3Gn)  Low  Away High  -.122 -.092  .183 .219  Total Low High  Goals  -.198 -.137  .113 .214  -.191 -.202  .213 .199  -.196 -.160  .070 .093  -.092 -.120  .090 .151  -.065 .147  .215 .157  -.162 -.129  .197 .211  -.107 -.163  .176 .277  -.144 -.144  .180 .142  -.006 -.131  .175 .159  -.134 -.121  -.104 -.047  .142 .161  .197 .127  A  54 The  data  against  show  and  that  shots  goals  against,  for  and  were  shots  modestly  Table Range  Low .157 .112 .151 .318 .265  v SF v SA v GA v SA v SF  expected.  Goals  correlated, against the  were  fact  inferior  team.  data  are  period,  worth in  entities.  agrees  the  approximate  might  be  a real  than  the  considering  in  future  be shots  coupled  unrelated,  outshoot  (pages  to and  which  to  A34  not for  contribute  supported  results  finding  appeared  High .418 .410 .116 .124 .087  with  suggests  outscore  randomness  of  research.  a  an result. The  168-169).  Correlations  data  independent  Shots  correlated,  to  Low .247 .152 .129 .300 .129  appeared  expected.  likely  Table  and B i n a r y  game-to-game  be  against  might  correlational  with  as  goals  Total High .476 .498 .140 .064 .194  against  negatively  more  This  summarized Raw  might  be  a postulate  Summary: The  as  for/goals  t e a m may  is  correlated  as  6  Low .240 .112 .198 .362 .130  and g o a l s  modestly  superior  This  well  Away High .423 .482 .168 .072 .088  for  again  goals  as  o f I n d i v i d u a l Team C o r r e l a t i o n C o e f f i c i e n t s f o r S h o t s and G o a l s F o r and A g a i n s t Home  GF GA GF SF GA  for,  If  are  valid, that  the  uncorrelated the  concept  standings  season's final  concept  based  standings.  that  and of one  period-to-  possibly  independence period  games  can  55 The for,  general  goals  correlations  against  and s h o t s  Cross-correlations negatively for  team  X to win,  Y.  VII.  Stationarity  The two  (e.g.,  correlated.  team  seventh  were  it  as e x p e c t e d :  against  shots  After  modestly  for v s . shots  a l l ,  has to  were  goals  goals  outscore  for  and s h o t s  correlated.  against)  are a r e s u l t  (and most  were of  times  s h o t s and  outshoot)  Tests  series  of  postulates  involved  an e x a m i n a t i o n  of  concepts: (a)  the unit hold as  if  they  present  of  measurement  a unit hold  if  (b)  (Gilovich,  is  1 of If  games  to  seen 4,  expectancies, 7a. 7b. 7c.  problem Vallone another  0 of  there  4,  away,  sets  is  of will  is  -  relationships extended  shortened).  Goodman's  and L i n d s e y ' s  (1969)  (1961)  on  in  size  This data  should (just  ties  on  the  swept  differential  innings.  -  the p o s s i b i l i t y & Tversky,  in playing  as w i n n i n g  (home,  non-overlapping  with  in baseball  the streak  plateau  measurement  the u n i t  research  doubleheaders scoring  of  problem  3 of  2 of  tempo  4 of  move (a  teams from one  'winning'  streak  4 as opposed t o , s a y ,  4) .  total) four  4,  1985)  that  for  for  each  team  are grouped  comparison against  be no s i g n i f i c a n t  game o u t c o m e ( w i n s , t i e s , goals (for or against) shots (for or against)  chance  differences  losses)  for  into  Results. (1985)  as  The a  test  stationarity that  a goal  around  does  X minutes).  stage  of of  1973,  not  The  on  which  investigation model  in  weighted  this  not  (page  'artificial'  the  deviated  probability  plots  Shapiro-Wilk probability (Filliben,  from  1975)  and  argue  not  exceed  the  distribution.  that  the  limits This  sets,  & Weldon,  p.  & Wilk,  met  the  depart.  whether p.  team's  of  four  To the  goals  7)  a  this follow  assumes  mean  every  within At  requires  a  the  level  4-8)  (in  ascertain  the  of  each  or  a  using  p.  1965)  using  plot  a  specified  assumptions for  'expected' checked  to  four-game Normal  b a s e d on  for  is  of  sense,  the  Filliben's normality  exceedingly  table  is  a  team's  4-8)  test  s e a s o n was  first  expectancies.  Although n  table  were  1989,  provide  80-game  games  data  coefficient  probability their  a goal  located  mean w h i c h  each  sets  recorded.  (1989,  varying  score  constant  distribution  correlation  will  1976,  distribution  (Shapiro  were  and Weldon  n's  (Cruze  test plot  normal  implication  constant  rarely  a  games).  four-game  frequency  a  paramount  42),  20  if  is  of  averages.  created  the  only  concept  general  team  no n a t u r a l  non-overlapping  for  a  about  moving  2g  but  & Jenkins,  20  ascertain  Cruze  is  (Box  the  & Tversky  The  s c o r i n g may b e  will  into  frequencies  sets  goal  Vallone  employed.  has  average  it  having  postulate  was  time  equilibrium  exponentially  divided  it  which  model  with  the  Gilovich,  22)  d e p e n d on  nonstationary  As  p.  process of  from  remains  u s e d by  stationarity  (e.g.,  time  stationary process  of  (Nelson,  a mean  region  procedure  for  value.  for  a  small,  testing The  small  data  did  normal  determining  the  win-  57 tie-loss the  point  binomial  distribution  Wald-Wolfowitz The tests  runs  test  i n demonstrating  varied  of  t h e 21  were data  met.  linear  used to were  team's  from  interpolations  Chi-square examine  analysis  the  of  20-game  chance:  4 at  the  sets  the  and the  as  other  data.  points  .05,  from  data.  n o t as s a t i s f a c t o r y  t h e random n a t u r e  (33.3%)  significantly  by u s i n g  were  test  stationarity  Seven  the  probabilities  1 at  distribution the  .02,  2  at  .001.  Analysis  for goals  since  the middle  upper  or  None goals was  of  number  row o f  shots  agreement  The  data  by-set  team from from from  The  -.645 -.323 -.530  from  and s h o t s  the  negative  side,  not  operating.  against  and shots  were  were  a p o s s i b l e normal  be p l a c e d  team in  the  for,  significant.  correlations  goals.  This  definitely  strongly  The s e t - t o - s e t  suggesting team  plots  for set-  showed  the The s e t -  ranged:  goals goals total  Actually,  examined  distribution.  concerning goals  one s e t and t h e next  total  also  distribution  .335 as r e g a r d s .329 as r e g a r d s .256 as r e g a r d s  team  or  arbitarily  comparisons concerning goals  The normal  to to to  between  could  two c o m p a r i s o n s p e r  7b a n d 7 c .  correlations  against,  ranged:  three  concerning goals  set-to-set  correlation goals  for  with  not to deviate  required  cells.  correlations.  to-set  of  t h e 168 c h i - s q u a r e  against,  in  data  lower  and s h o t s  for against goals suggest  there  concerning goals 39 o f  63  a positive  correlations  i s no for,  (61.9%)  favored  correlation  concerning  is  shots  from from from The  data  -.241 -.630 -.339 are  to to to  .456 .554 .489  as as as  regards regards regards  summarized  in  Tables  (pages  172-173).  Future  series  analysis.  Time  procedures Vallone  u s e d by  and  postulated  (e.g.,  and  Examination  required  unit a  (pages  limited  (1985). of  for against shots 170-171}  should probably  researchers,  size  effect)  cost  A35  previous  Tversky  assumptions  analysis  shots shots total  was  the  employ  present  unit  than  one  to  Gilovich,  of  measurement  assumed i m m a t e r i a l  larger  A36  time  study  especially of  and  game  to  set  any  be  examined. VIII.  Artificial  Another  set  of  and  postulates  issues:  randomness,  concept  that  the  the  The  postulates  Standings involved  determinism,  longer  (assuming basic  Real  individual  the  unit  test,  "items"  the  a  complex  of  outcome  test  are  not  the  b u t w i l l be l e s s c l o s e l y c o r r e l a t e d b a s e d o n o u t c o m e s o f 2 - p e r i o d games p e r i o d , 1 s t and 3 r d p e r i o d , 2nd and  artificial  standings during  the  artificial outcomes,  in  single  season of the  real and .693  period  1988-89  based  data  were  wins-ties-losses  artificial  real  biased).  were:  8b.  an  the  the  Outcomes ( e . g . , f i n a l s t a n d i n g s ) b a s e d on a game o f 1 s t , 2 n d o r 3 r d p e r i o d o n l y w i l l b e correlated with real f i n a l standings;  The  and  valid  8a.  Results.  underlying  measurement  more  within  of  season with  season.  The  s e a s o n were  .569  on  second period  1-period positively  than w i l l standings o f 1 s t and 2nd 3rd p e r i o d . analyzed and  by  comparing  actual  team  correlations based  constructing  on  outcomes  first and  team  standings  between period .849  based  on  third a  period  more  first  accurate or  real  outcomes.  second p e r i o d .  considerably 3,  and  8b.  and  The  being  of  The  raw  176)  ,  177)  .  the  with  The  periods  the  to  correlation Spearman  an  real  combination 1 and  and  This  3.  s h o u l d be  more  appeared  team  to  is  be  on  win-tie-loss of  of  point  .956  than  artificial  .887  (66% best  in  a  using  1 8a  the  total  is  indicator, but  A37  in  period  (pages  Table  1. 174-  A38  four-game  Pearson  a  and  postulates  the  Table  system)  the  periods  since  of  is  were  for  expected  summarized  to  ability  periods  s e a s o n b a s e d on led  period  categories  summarized  artificial  third  supported  the  all  in  2,  "input"  correlations  correlation  the  between  periods  s e a s o n outcome  (using  rank  2  allows  over-all  of  for  a  correlations  each  that  correlations  course,  Points  for  outcome  compared  of  suggest  team d i f f e r e n c e s  The  periods  highest  data  of  .921  latter,  sampled).  yielding  (page  sets  product-moment  of  .976  system  of  and  a  ranks.  Upsets If  goals  interest. teams should is  for  data  b a s e d on  higher:  .917  combination  IX.  indicator  season standings  and  The  and In  are  in  general,  as  and a  higher  ranking.  team's  rank  position  at  are  ability,  become  defined  shots  the  more  lower  would more  position prior  of  the  across appear  random  likely  ranking  Rank  end  it the  the  position  random  to  time,  upsets  that  the  more  shots  and  goals  upsets  defined  game-time  season.  It  an  in  across  and could  (b) be  An  opponent  two a  of  homogeneous  s h o u l d become.  team d e f e a t i n g was  become  ways:  argued  upset  with (a)  team's  time  a .  a  rank  that  the  60 old  six  and  t e a m NHL games  eight-team  and  that  between  should  also  following There  the  be  an  artificial  top  more  be  six  or  elitist  postulates will  NHL w e r e  elitist  league  eight than  should  more  more  formed  teams  the  than  in  by  the  21-team  the  present  only  tallying  1988-89  league.  If  so,  upsets  in  the:  1937-38  than  the  2 1 - t e a m NHL o f  1988-89  9b.  6 - t e a m NHL o f  1947-48  than  the  2 1 - t e a m NHL o f  1988-89  9c.  8 - t e a m NHL o f 1 9 3 7 - 3 8 o f t h e 2 1 - t e a m NHL o f  t h a n games 1988-89  between  the  top  8  teams  9d.  6 - t e a m NHL o f 1 9 4 7 - 4 8 o f t h e 2 1 - t e a m NHL o f  t h a n games 1988-89  between  the  top  6  teams  basketball  exceed  and  scoring  comparison  chances  chances of  in  upsets  in  in  hockey the  the  hold:  8 - t e a m NHL o f  scoring  the  season  9a.  Since  21-  exceed  three  those  in  those  in  soccer,  sports  should  hockey a  show more  upsets  in: 9e.  English First play  Division  soccer  than  National  9f.  English First Division Association play  soccer  than  National  9g.  National play  than  League  hockey  National  League  hockey  Basketball  Basketball  Association  N o t e : The 1987-88 F o o t b a l l A s s o c i a t i o n E n g l i s h F i r s t D i v i s i o n was t h e l a t e s t d a t a r e a d i l y available at the time of the s t u d y . Due t o t i m e a n d f u n d r e s t r i c t i o n s , o n l y t h e l a s t 50% o f t h e 1 9 8 8 - 8 9 NBA s e a s o n c o u l d b e c o d e d , i n p u t a n d u s e d . Results. Upset  rates  in  The  data  did  the  NHL a r e  not  support  outlined  in  postulates Table  7.  9a  or  9b.  61  Table Upset  Rate  in  7  Various National  Hockey  League  Seasons  Rank 100%  The  old  present  88-89 46-47 37-38  six  significant, upsets. and  the  of  was  there  was,  '88-89  games.  It  appears  over  the  sorts  between  1946-47  essentially The  years.  and  played  It  the  1988-89. on  an  essential  to  could  game  'equal'  Diamond  of  decade  may  between  of  1967;  o  The  blue  o  The  center  o  The  schedule  o  P l a y e r s t a k i n g p e n a l t y s h o t s were mouth of the g o a l i f t h e y w i s h e d .  were  line was  was  widened  to  be  its  winning and  to  inches,  six-team  75%  have  and  been  changes  changes  that basis  and  the  teams  from  1946-47  introduced.  increased  from  48  to  60  allowed  games. to  go  in  of  1946-47  argued  were:  in  last  many  and  not  upset  may  that  1987) 12  were  the  of  despite  1937-38  (McFarlane,  lines  between  1937-38  also  the  difference  upsets  argued  chance  & Stubbs,  no  similarity  rate  be  than  differences  shortened  between It  changes  least,  The  the  decade  upsets  difference  s e a s o n was  from  altered  at  either.  that  fewer  chi-square  significant  leagues  constant  NHLs h a d The  the  game  era.  no  Season 37.3% 35.9% 31.1%  NHL.  when  various  to  1988-89  eight-team  relatively the  eight-team  suggesting  There  remained 50%  and  21-team  Pregame 43.3% 40.4% 35.6% •  NHL NHL NHL  to  the  era  62  The  o  The  number  o  One  referee  o  The  flooding  of  o  Goal  lights  were  essential  1967;  teams  plus  changes  Diamond  two  ice  eight  were  between  to  six.  introduced.  periods  became  obligatory.  sychronized.  between  1946-47  1987)  and  1988-89  (McFarlane,  were:  Roster  o  The  schedule  o  The  number  o  The  ice  o  T h e d r a f t was i n t r o d u c e d . L i f e - l o n g p r o t e c t i o n of junior a n d m i n o r l e a g u e p l a y e r s was d i s c o n t i n u e d . The p l a y e r p o o l was g r o s s l y e n l a r g e d a s 1 0 0 s o f i n d o o r r i n k s w e r e built, y o u t h l e a g u e s were b e t t e r o r g a n i z e d , p l a y e r s were r e c r u i t e d from Europe.  o  High  upsets  season  for  last  upset  rate  was  39%  upset  rate.  The  last in  Assembling allowed  upset  six  top  and  postulates  was  half as  and of  of  halves upset  an  8b,  games.  from  each  21.  a  introduced.  NHL  season.  showed no  comparison The  43.3%  last  full  significant  did  to  was  chi-square  to  6  white.  '88-89  '37-38  at  difference  of  the  entire  50%  pre-game  season  pre-game  the  and  '46-47  full  not  reveal  any  .01 NHL  level. seasons  significant  rate.  artificial  rates  the  was  the of  80  training  the  difference  eight 8a,  painted  compared  of  to  increased  pre-game  examination  differences  teams  examination  except  the  increased  analysis  the  versus  was  of  and  Internal  increased.  surface  tech  internal  was  from  linesmen  the  & Stubbs, size  declined  o  An in  of  to  be  teams 8c  or  in  Top  Six  and  Top  Eight  determined  for  interplay  1988-89.  The  data  8d.  The  top  eight  did  showed  '88-89  NHL  between not an  the  top  support upset  rate  63 of  45.5%  NHL)  and  (as  compared  the  top  statistical It  was  higher  rate  not  Comparison square top rank .05 in  that  '88-89  Table  The  A39  (26.7%)  and  yielding  significant  between  these  rates  upper  their  six  or  the  and  44.0%.  and  eight  '46-47  50%  chi-square for  full-team  There  the  teams Their  '88-89 was  full-team would  upset  no  rate.  have  a  rates  were  so.  significant.  and  of  homogeniety.  was  hockey  NHL y i e l d e d  This  '37-38  was  was  one  comparison  NHL u p s e t s  difference upset  a  only  on  a  of  are  the  pre-game  significant  comparisons  chi-  at  the  summarized  178). season rank  significant  differences  upset  lower  than  summarized  Table  8.  the  the  were  compared:  differences.  season upset  pre-game  Table Chi-square in  rates  chi-square  showed  significantly in  the  rate  '37-38  data  for  upset  the  The  (page  Pre-game  of  rate  an  the  NHL  comparison. level.  43.3%  significantly  with  result  eight  that  because  but  a  showed  difference  expected  higher,  six  to  upset  rate  rate.  4 of  All to  The  4  be data  8  Comparison of Upset Hockey and S o c c e r  Rates 2  100% 8 8 - 8 9 NHL 100% 3 P t 8 7 - 8 8 S o c c e r 100% 2 P t 8 7 - 8 8 S o c c e r 50% 2 P t 8 7 - 8 8 S o c c e r  Pre-game 43.3% 37.8 38.9 35.1  Season 37.3% 29.0 27.1 22.8  X 5.342 4.806 7.404 4.935  15  ls .05 .05 .01 .05  are  64 If to  differences  be  the  more  early  stable  the  and  three  points for  a win  comparably  the  in  to  comparisons  did  not  frequent  soccer  and  in  basketball.  more upset  frequent rates  in  for  than  hockey  a  the  and  in  Table  9e  than did  than  three  they  be  expected  latter  settle  or  includes  into  league  a  A40  (page  Upsets reverse  soccer.  Upsets  are  and  were  in  Pre-game 43.3 40.4 35.6 38.9 37 . 8 33.5  Season 37.3 33.1 31.1 28.1 29.0 31.3  3  point  more  equal  9g.  in  Upsets and  Table  Hockey,  Rate  a  Upsets  9  Upset  point  season  not  Pre-game  listed  3  Inter-sport  held. were  1  and  179).  postulate  basketball.  2  of  gives  win,  Both  because  system  create  pre-game  The  sports  to  The  support  used  league  A 2 point  and NBA.  9f.  was  a different  Season Upset Rates for S o c c e r and B a s k e t b a l l  8 8 - 8 9 NHL 4 6 - 4 7 NHL 3 7 - 3 8 NHL 2 pt Soccer 3 pt Soccer 50% NBA  the  English  tie.  NHL  Table Pre-Game  The  English  hockey.  data  hockey all  would  standing  uses  NBA.  for  support  The  league  comparisons.  summarized  frequent  since  before  presently  as  are  more  soccer  the  comparisons  in  standing teams  NHL o r  league  used  of  1 point  applied  scored  were  point  and  season standing  position.  Division  than  s y s t e m was  rankings  occur,  pre-game  rank  English First  points tie  than  stable  two  scoring  to  season scrambling  relatively A  were  9.  were soccer were  season  65 Chi-square 10  (see  page  None Two 89  of  of  the  were  rate  the  the  .001  the  NBA's  and  listed  in  Table  significant:  systems.  None  English first  division  soccer  of  the  '88-  the  a n d NBA  NHL a n d NBA c o m p a r i s o n s a r e  the  '46-47  the  50% NBA w e r e :  NHL's  and  Chi-square  opposed to  was  significant.  listed  66).  last  and  c o m p a r i s o n s were  the  37.3%  significant  43.3% 33.5%  pre-game was  season upset  at  the  NHL a n d  the  comparisons between  the  NBA's  '37-38  .05  last the  upset  significant  rate  as  at  opposed  to  level.  Upsets  most  upsets  likely  appear  in  Table  X.  Descriptive  the  the  31.3%  basketball  It  are  3 point  significant.  seems h o c k e y are  and  between  NHL a s  level  Summary: It  not  NHL a n d  the  page  comparions  for  rates  c o m p a r i s o n s were  significant.  (see  50% NBA w e r e '88-89  2 point  between  11  Upset  upset  chi-square  season upset  soccer  basketball Table  pre-game  six  comparisons  for  66).  the  NHL a n d  in  comparisons  A41  more  about  (pages  difference was  an  for  every  frequent equal  in  frequent than  than  soccer  upsets.  The  basketball  upsets  upsets.  Soccer  data  summarized  are  and  Data to  develop  NHL s e a s o n t o  Mean g o a l s  more  180-181) .  seemed s e n s i b l e 1988-89  are  for  per  between  average team  of  game  the 1.588  exceeded  a general  complete ranged  highest goals. 1.588.  the from  statistical 3.112  s c o r i n g and The  descriptive  to  standard  of  analysis.  4.700.  lowest  picture  The  scoring  deviation  for  teams goals  66  Table  10  C h i - s q u a r e C o m p a r i s o n of Pre-Game and Season Upset Rates f o r Hockey and S o c c e r Pre-game  Upset  Rate  Comparisons 2  Upset Rate 43.3 V 38.9 4 3 . 3 V 37 . 8  88 - 8 9  NHL v s . vs.  2 Pt 3 pt  Soccer Soccer  46 - 4 7  NHL v s . vs .  2 Pt 3 Pt  Soccer Soccer  40.4 40.4  V  NHL v s . vs.  2 Pt 3 Pt  Soccer Soccer  35.6 35.6  V  37 - 3 8  Season Upset  Rate  V  V  X 1 .232 2 .426  1 1  Is ns ns  df  38.9 37.8  0 .079 0 .273  1 1  ns ns  38.9 37.8  0 .410 0 .209  1 1  ns ns  2 X 7.328 6.112  df 1 1  Is .01 .02  Comparisons  Upset Rate 37.3 v 28.1 37.3 v 29.0  88-89  NHL v s . vs.  2 pt 3 pt  Soccer Soccer  46-47  NHL v s . vs.  2 pt 3 pt  Soccer Soccer  33.1 33.1  28.1 29.0  1.154 0.781  1 1  ns ns  Soccer Soccer  Upset Rate 31.1 v 28.1 31.1 v 29.0  2 X 0.415 0.205  df 1 1  Is ns ns  37-38  NHL v s . vs.  2 pt 3 pt  Table Chi-square Rates  v v  11  Comparison of Pre-Game and Season Between Hockey and B a s k e t b a l l  Pre-game  Upset  Rate  Comparisons Pre-game  50% NBA v s .  100%  88-89 46-47 37-38  NHL NHL NHL  50%  100%  88-89 46-47 37-38  NHL NHL NHL  NBA v s .  Rank  Upset Rate 33.5 v 43.3 33.5 v 33.5 33.5 v 35.6 S e a s o n Rank 31.3 v 37.3 31.3 v 33.1 31.3 v 32.0  2 X 1 2 . 164 2 . 438 0 . 217 5 . 004 0 . 192 0 . 312  df 1 1 1  Is .001 ns ns  1 1 1  .05 ns ns  67  Mean of  shots  34.638.  shooting The  for  The  per  averages  closeness  difference  ranged  difference  team's  graphically  game  of  when from  between  was  teams  the  to  the  output  are  low  a  low  most  of  27.089  and  least  to  a  high  frequent  7.549.  in  data  high  from  is  suggested  reduced  being  to  only  shots  2.5  rather  per  shots  period  —  the  a period  or  .5  goals. The goals  pattern, against  4.438.  The  averages  Mean  for  against Total mean  of  21  game  per  had teams  A42  or  the  about were  The  per  55  ranged  to  quite  a  65  of  against.  2.713  to  the  most  and  deviation  from  Mean  a high on  for  of  team  goals  1.745.  25.737  averages  was  to  5.875.  10.078  The  shots  period.  ranged  from  goals  exceeded  extreme  game  low  least  teams  shots  ranged  a  for  standard  game  most  3.4  game  (pages  between  per  the  similar  from  (76.2%)  against  between  was  ranged  goals.  mean g o a l s  NHL game suggest  game  1.745 16  per  shots  Table  per  shots  difference  expected,  difference  was  against  as  from  57.138  shots  6.275  to  to  8.913.  65.225.  and  7 or  homogeneous.  The  In  8 goals. data  are  Total  general, The  an  data  summarized  in  182-183). DISCUSSION  I.  Comparisons With The  result  results goals  of  and  of  this  previous shots  for  Other  Studies  study  did  not  studies.  The  periods,  games  differ  random and  greatly  from  sequences of  sets  of  games  the  wins-losses, agreed  with  68 the  randomness  Gilovich, outcomes  Vallone  outcomes  agreed  This  study  winning  and  look  doesn't The and  an  this  from:  methods same  and  Janssen's records, of  (1987)  wins  and  randomness  of  outcomes  implied  did  not  The  and  tie  in  reasons at  well  are  the  Cook  Mosteller's where  with  other  general,  the  by  Mosteller's twofold:  statistical data  research  linear  the  (1964).  probably  (Mosteller's  hockey  Haberman's  In  (1977)  by  multiple  and w i t h scores,  of  chance.  sport  study, this (1)  being  outcome  Mullet of  randomness  of  on d i s t r i b u t i o n  examination, come  the  found  (a)  likelihood  this of  suggested  dealt  homogeneity  research  of  with  college  opponents  often  occur.  data  in  elite  shooting  laws  scores  (b)  and  the  directly  losing  (1985),  Sequences  Simon  data  nonrandomness), football,  of  basketball  coaches'  the  scores.  not  Schutz  follow  with  study's  did  elite  Tversky  of  to  studies  football  of  analysis.  appear  baseball  on  analysis  football  results  and  s u g g e s t e d by  regression (1977)  quality  procedure  does  being  first  appear  seem t o  outcomes  to  examine  examined  found  that  while  (1971)  used  under hockey  Pollard  found  s c o r e s matched Mullet  outcomes,  not  employed  distributions;  football  at  different  (1977)  Benjamin  may  of  that  at  being the  literature  The  examined;  scores  the  goals,  different  and  (3)  Poisson  1986),  hockey,  binomial  closer  the  conditions.  fit  1985,  On  variations  (2)  outcome;  different  mean  the  case.  same  soccer,  in  contradictory. the  (1973,  a negative  looked  be  both  family  Reep,  baseball  Pollard  and  distribution.  But  which  effect  had  the  the  69 of  insuring  the  basic  al.  looked  noting  that  rate  requirement at  that  Poisson  the  goals  if  the  of  for  per  distribution,  the  game  rate  scoring will  of  Poisson and  from  hence  game  binomial  distribution  may  negative  binomial  Compound P o i s s o n )  of  Poisson  (1909,  1915,  scores to  be  median  s c o r e s of  likely  to  p.  1)  to  batsmen  many  generate  stated  likely  that  increased  if  his  n+ltfi  is  dependent  score  on  the  goals,  Pollard viewed a  in  found  geometric  a  et  by  of  the  negative noted  that  from  a  the  mixture  shots  across  This time  whatever  cricket  n+3  study  (at  distribution  1,  found 2,  shots  (except  goals  for  (1945,  equally  value It  of  n  is  s c o r i n g of  run.  (some  the  Cricket  losing  10  win  n+l  total)  was  dependent  that  goals,  total  against  all  fitted  a  in  (for,  minute  the  or  found  finding  5 or  is  the  condition  Wood  n+4).  nth  a  that  streaks.  study  a  he  scores,  s c o r e d the  and  close,  the  or  (winning,  distribution,  Wood n o t e d  n runs  also  total  cricket  distributions.  n+2,  in  found  very  Again,  shots  al.  were  distribution. This  uniform  a  arise  (1945)  made  n+l,  streaks  n.  et  to  sense,  of  binomial  has  with  occurrence for,  batsmen  on h a v i n g  that  a geometric  negative  findings  (1973)  can  Pollard  parameter  game,  geometric.  s c o r e s by  that  runs,  study  the  score  their  realize  followed  to  a n d Wood  a batsman  to  This  the  Pollard  primarily of  important  batsmen  1927)  similar  increase  run  their  constant,  distributions.  Elderton batsman's  (or  arise.  relatively  distribution.  explained  scoring,  varies  be  last  agreement against, intervals) 1 or  with total) all  2 minutes).  fitted This  70 held  for  individual  against,  and  contradict within  the  very  whereas  many of  the  this  or  binomial  was  likely  (a  and  this  goals  across  1+1+1 is  or  did  goals  not  counting 60  measured  score  for  This  involved  goals  a game"  for  combined.  outcomes final  of  (e.g.,  or  once  the  times  less,  time  events  minutes)  sequential  of  4-3  is  for  the  loser).  evidently  a result  of  The  "how  a different  etc.)  c a s e where seem t o  goals,  a game  spaces between  between  goals  followed  distribution.  the  event-rate  found  less or  outcomes  varying  against  (e.g.,  winner  study  negative  Hockey  teams,  since  mentioned scores  3 minutes  most  and  frames  the  total  kind  probabilities.  1 minute  less,  for  each minute  of  Finally,  or  time  1+1+1+1 f o r in  as  findings  earlier  counting  all  other  streaks,  goals  well  goals  long  all  counting: adding  for  as  there  both  goals  were,  follow  shots)  two  the either  commences as  a result  from  of  a  this  the  game  within  and  converge.  binomial:  varying  minutes  24-25,  distributions  negative  2  a geometric  As s u g g e s t e d on pages these  (adding  to  game  game  outcomes. II.  Model Schutz  Building (1982,  deterministic system and  the  is  exactly  series  of  change  over  5)  models  forces  conceived  p.  noted is  determined  acting  differential  of  time. as  that  The  being  on  that  the  "the by  it."  future  present  Calculus,  words  a moving  entire  the  equations, key  assumption  are  space,  of  a  system  provides  a  precise  status.'  'present  of  the  example,  predicting  'present then  behavior  status  for  usually  underlying  If  status'  time  is  itself  is  continually  change  that  The  real  model  changing second  the  present  difference  (Schutz,  everything model;  if  1982)  about  study  by  may b e  between is  second.  primarily we  we d o n o t  know  everything  chance  dealing  and if  can d e s c r i b e X with  factors  or  continual  we m u s t  a  we a  (especially  not),  this  with.  perceptual:  then  by  is  a deterministic  X,  influenced  It  stochastic know  deterministic  whether  use  a  X  is  stochastic  model. If  we  same  assume c h a n c e and  thing,  stretching  we may from  chance...pure parts  we  operates early  can in  stage  (defined The  as  conceive of  show  to  be  of  theoretical  being  axiomatic  model  inappropriate  seems  to  characterize  teams,  (Dickey,  occur  1895  with  Washington had  the  the  longest  1982)  elite  (Klein  winning  road  to  one  & Reif,  the  of  streak  of  the  continuum  ever  c o u l d be  use  in the  an  that  best  at  chance this  axiomatic  balanced  model  league  first  poor  pro are  cited  games).  basketball likely  The  1974-75  earlier.  NHL h i s t o r y  that  earliest  most  teams.  and  stage  basketball's  were in  the  'predictive').  Streaks  (37  p l a c e d on  developmental  1987) ever  being  than  extremely  percentage  winless  to  straight.  good or  parts  on a  perhaps,  sports:  Germans, 111  it  reasonably  most  extremely  is,  rather  applied  won  But  It  if  Buffalo  Capitals  lowest  assumes a  being  'chance'  development,  'descriptive'  be  the  label  ways.  as  really  determined...mostly  determined.  deterministic  would  to  the  are  events  determined...partly  chance with  days,  determinism  (.131)  They and  The  following  established main 1.  is  hockey  the  axiomatic  league.  model also  of a  an  It  is  of  outcomes w i l l  elite,  summary  well-  of  this  study's  findings. In  general,  the  pattern  across  time  (e.g.,  the  exceed  that  expected  pattern  for  a  of  team  be  outcomes  with  team  primarily for  A's  team  "random"  A will  not  win-loss  percentage). 2.  Variations the  pattern  games, 3.  and  Patterns that  a  and  of  measurement  outcomes  sets).  outcomes  repeat  Except  to  a  game  for will  final  distributed  across  outcomes  (2 period  be  e v e n more  of  play,  across  fairly  artificial  goals  time  enough  is  closely  total  affect  periods,  sufficiently  1 period  evenly  appreciably  occurs  s e a s o n outcome  minute  not  themselves  b a s e d on  outcomes w i l l  the be  real  will  (randomness  four-game  s e a s o n outcome  real  teams  unit  of  of  comparable  4.  in  correlated). for  all  (uniformly  distributed). 5.  The  frequency  shots),  distribution  however,  distribution  will  most  (suggesting  of  outcomes  likely  that  fit  rates  (e.g., the  of  goals  negative  outcomes  and binomial  fluctuate  randomly). 6.  7.  When t i m e  between  is  examined,  if  r  The is  =  1,  outcomes  a negative  a geometric  probability no b e t t e r  of  than  binomial  from  after  expected  one  goal  distribution  distribution  a win that  (e.g.,  will  a win, by  a  or  also a  team's  to  will  the  next)  emerge  and  emerge.  loss  after  won-loss  a  loss  record.  73 Game-to-game 8.  9.  outcomes w i l l  Upsets  seem t o  league  (a  There  but  no more  six-team  may  hockey  be  be  to  independent  probable  eight-team  a difference  appears  soccer  or  be  have  in  a  small  than  a  21-team  between  more  and b a s k e t b a l l  sports  upsets  do n o t  variables.  than  in  than  appear  to  large  NHL).  rate  soccer  a  of  upsets:  and  differ  basketball, in  rate  of  upsets. These  nine  different III.  sport  Final  noted  to  that  of  more  future there  distribution: by  Mullet,  Poisson  the  used  in  this  were  in  bases.  two  or  to  a  totally  baseball).  If  the  members  distribution  fit of  of  testing  test the  different  detecting  this  and  for the  a  to  (1967,  be  p.  237)  Poisson  variance  test  (used  population  actually  follow  means,  variance  test  than  the  the  goodness of  fit  is  test  that  the  case.  Zar  variance  equals  distributions also  employed  notes to  mean  c o u l d be  that  test  the  for  another a  in  a  examined  Poisson to  see  procedure  Poisson  fit.  precise  b e e n met  methods  with  p r o c e d u r e s may n e e d  S n e d e c o r and C o c h r a n  goodness of  c h i - s q u a r e may b e  The  adapted  football  statistical  Questionable  distribution  have  are  notes  distribution.  using  be  study.  (1984)  such  (e.g.,  complex  distributions  sensitive  if  hockey  data  1977).  more  Zar  than  may h o p e f u l l y  Comments  A number applied  postulates  conditions in  this  assumes:  for  study.  the  Poisson Zar  distribution  (1984)  notes  that  may a  not  Poisson  74 1)  a random d i s t r i b u t i o n of o b j e c t s i n s p a c e / t i m e i n which e a c h p o r t i o n o f t h e s p a c e h a s t h e same p r o b a b i l i t i t y of c o n t a i n i n g an o b j e c t  2)  t h e o c c u r r e n c e o f an o b j e c t i n any p o r t i o n o f space/time i n n o way i n f l u e n c e s t h e o c c u r r e n c e o f a n y o t h e r o f the o b j e c t s i n any p o r t i o n o f space/time  but: a if  (a)  the  face-off the  at  which  example  a goal  is  practically  goal  has  any  thinking  has  a  when  down b y  is  of  a n of  tend  to  average  may  be  a distortion  Poisson  in  the  first  zero  and  influence  on  team b e i n g  two  or  few  seconds  (b) the  'fired'  it  is  after unknown  scoring  of  up by  goal  a  three.  about  100  with  4 goals of  the  in  a p of 12  0.01.  units  requirements  of for  The  present  5 minutes an  each,  adequate  distribution.  Perhaps, be  of  the Poisson d i s t r i b u t i o n approaches the binomial d i s t r i b u t i o n when n i s l a r g e a n d p i s v e r y s m a l l . Thus, the P o i s s o n d i s t r i b u t i o n i s important in d e s c r i b i n g binomially d i s t r i b u t e d events having low probability  Zar's data  apart'  ice  one  Popular  'coming 3)  center  s c o r i n g of  another. or  probability  most  remembered  importantly,  it  (Lindgren,  1968,  p.  147)  should  that:  p r o b a b i l i t y d i s t r i b u t i o n s are idealizations... i m p l y i n g c o n d i t i o n s t h a t c a n n o t r e a l l y be met i n p r a c t i c e . . . o n e s i m p l y c a n n o t know w h e t h e r t h e c o n d i t i o n s a r e o r a r e n o t met i n p r a c t i c e . Zar  (1984,  difference a  number  variance  p.  test  of for  ways  419) may of  suggests be  to  analyzing  repeated  autocorrelation  used  measures  procedures  that test time and  the for  mean runs.  series the  (correlating  square  data:  successive  Schutz using  (1970)  analysis  associated trend a  time  series  lists of  analysis;  with  itself)  and  analysis  Tversky  based  (1985,  percentages estimates  p.  to  of  percentage:  on Markov 302)  determine  the one  based  percentages  player's  overall  runs  scored  time. could  in  Since be  and  to  compare  Jones  (1954)  hypotheses  could  of  requiring and  input  20  The goals  period,  data of  facilitate  units  shots,  two  while  periods,  defined  employed.  passes,  controlling checks  puck  attempted,  other  an  input  time  to  all  of  in  and,  in  was  game  units  of  this  four  recovered  pucks  end,  as  ratio  recovered,  Fiske  would  the  wins  segments It  is  c o u l d be  boards, of  problems  Using  seconds of  off  procedures  need  to  etc.  were  games.  real  analysis  span  times,  measurement  Such measures  elapsed  Such  remove  into  of  sequential-  study).  study  the  sports.  20-year  divided  and  from  time-related  and p e n a l t y  player's  number  testing  perhaps,  shooting  from  the  sampling.  a  the  Abelson's  of  this  over  game  two  games).  game  timed  complex (as  of  estimating  a means  economy  opponent's  loose  of  per  derived  across  shooting  (comparing  deviation one  and  player's  chance  a baseball  suggest  Vallone  player's  and  'non-timed'  rebounds in  of  a non-timed.sport,  goal  one  that  completed  of  measured  conceivable and  a means  sampling  of  each  game,  research  years  response  of  pre-testing  procedure  total  and  in  extensive  Jones'  obviously  value  with  from  percentage  a half-inning is  ratio  standard  each  suggests  oriented be  the  for  baseball  used  Fiske  on  Gilovich,  Lexis  error  shooting  (1989)  the  deviations  standard  shooting  Abelson  used  chains.  and of  losses,  one  quite operationally  possession,  seconds  checks  intercepted  completed passes,  to etc.,  76 could that  be  used.  reflected  outcome would  would  still  effects its  the  record.  In  wins  underlying  this  and  operating  as  fundamental  deterministic  insufficient  of  p.  even  to  future  course  hockey  teams  does  not.  God p l a y s  purely  the  with  that  random  with  may the  have  In  there  and  both  is  is  as  "we  can  of  universe;  at  considered  discovery are  a group  and  about  from  of the  research,  disorder  partly other  of  random  conclude  present  only  series  the  models  anything  been  goals  an a  Heisenberg's  order  to  partly  aspect  the  not  measures.  structure  certainty  of  completion  a game,  behavior  60%  would  applied  was  process,  Ironically,  Einstein  passes  deterministic  atom."  "chance"  that  these  the  average  individual  dice  of  of  complex  pass  a period,  The  physical  assert  Sometimes  study  a  .600  to  accordance with  cannot  "purpose".  a  deterministic  but  have  apply  uncovered  team X c o m p l e t e d  team w i t h  partly  atoms,  to  this  that  atoms.  if  is  study  such  limiting  to  only  an  within  same  be  prediction  structure  In  11)  that  same p o s t u l a t e s  would  models  are  a  functioning  aspect.  of  by  behind  the  possibly  complete/incomplete  the  deterministic we  the  characteristics.  to  1978,  extent Units  follow  losses  season that  its  the  could  investigation:  words,  mathematical a  to  expected  concept  in  (Olinick,  to  sequence  other  basic  and  in  measures  accurate.  expected  the  of  ability  fairly  pattern  shots,  games  be  outlined  exceed  The  team  be  passes,  and  A complex  seem  correct.  times,  God  77  APPENDIX  Table  Al  C h i - s q u a r e A n a l y s i s of U n i f o r m , P o i s s o n and Normal D i s t r i b u t i o n s o f A l l Team G o a l s f o r A c t u a l P l a y i n g T i m e (One M i n u t e D i v i s i o n s )  1st Min 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 T  ND UD PD  Obs 70 109 77 92 109 101 80 105 97 98 123 102 99 88 110 106 98 96 109 85 1954  ND 32 42 54 68 83 98 112 123 132 137 138 135 127 116 103 89 74 60 47 35  2 X df 139.591 19 16.633 19 754.284 19  Period UD 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98  PD 0 3 9 24 52 92 141 188 223 239 232 207 170 130 93 62 39 23 13 7  Is .001 n. s . .001  2nd Min 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 T  Obs 85 117 99 109 100 130 115 130 106 105 126 115 117 113 122 97 108 127 105 104 2230  ND UD PD  ND 37 49 64 80 96 113 129 142 15.2 157 157 153 144 131 116 100 83 67 52 39  Period UD 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112 112  2 X df 155.785 19 12.434 19 i8 5 8 . 6 4 1 19  PD 1 3 11 29 62 110 166 220 259 274 264 233 190 144 102 67 42 25 14 7  Is .001 n. s . .001  Table  Al  C h i - s q u a r e A n a l y s i s of U n i f o r m , P o i s s o n and Normal D i s t r i b u t i o n o f A l l Team G o a l s F o r A c t u a l P l a y i n g T i m e (One M i n u t e Divisions) (continued) 20  Min 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 T  ND UD PD  Minutes:  Obs 70 92 90 108 110 101 98 122 91 94 101 91 90 101 89 95 103 83 108 213 2050  3rd  ND 33 43 54 68 81 95 109 120 130 135 138 136 131 122 111 98 84 70 57 45  2 X df 2 1 4 . ' 746 5 4 . 579 9 1 1 . 756  Period  UD PD 103 0 103 2 103 7 20 103 103 44 103 81 128 103 103 178 103 219 243 103 103 245 103 226 103 . 193 103 153 103 113 78 103 103 51 103 31 103 18 103 10  19i 19I 19i  ls . 001 i . 001 i . 001 i  First  19  Min 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 T  Minutes:  Obs 70 92 90 108 110 101 98 122 91 94 101 91 90 101 89 95 103 83 108 1837  ND UD PD  ND 33 44 58 72 88 102 116 126 133 136 134 127 117 104 89 74 59 46 34  3rd  UD 97 97 97 97 97 97 97 97 97 97 97 97 97 97 97 97 97 97 97  2 X df 136 . 0 7 6 18 12 . 1 7 4 18 694 . 7 3 4 18  Period  PD 1 4 13 34 68 113 163 205 229 230 210 176 136 98 66 41 24 14 7  ls .001 n. s . .001  80 Table  A2  Chi-square A n a l y s i s of Uniform, Poisson, Negative N o r m a l D i s t r i b u t i o n s o f A l l Team G o a l s f o r A c t u a l (Two M i n u t e D i v i s i o n s )  Min Sc Obs 179 1-2 1 3-4 2 169 3 5-6 210 7-8 4 185 9-10 5 195 11-12 6 225 13-14 7 187 15-16 8 216 17-18 9 194 1 9 - 2 0 10 194 T 1954  ND UD PD NBD 3rd  Period  ND 73 123 181 235 270 273 244 192 134 82  UD 195 195 195 195 195 195 195 195 195 195  2 df X 136.498 6.745 279.010 198.771 Period:  Obs Min Sc 1-2 1 162 3-4 2 198 5-6 3 211 7-8 4 220 9-10 5 185 11-12 6 192 13-14 7 191 15-16 8 184 17-18 9 186 1 9 - 2 0 10 3 2 1 T 2050  ND UD PD NBD  1st  ND 75 122 178 231 268 277 254 209 153 99  2 X df 206.542 35.361 381.836 251.760  NBD 62 165 254 296 290 252 200 151 106 71  Sc 1 2 3 4 5 6 7 8 9 10  Obs 202 208 230 245 211 241 230 219 235 209 2230  ls .001 n. s . .001 .001  ND UD PD NBD  Minutes  3rd  9 9 9 9  20  PD S c 41 0 114 1 212 2 296 3 332 4 309 5 247 6 7 173 8 108 60 9  2nd  UD 205 205 205 205 205 205 205 205 205 205  9 9 9 9  PD S c 37 0 106 1 204 2 295 3 341 4 328 5 6 271 195 7 125 8 72 9  Is .001 .001 .001 .001  NBD 63 164 253 297 295 261 212 165 119 82  Period UD 223 223 223 223 223 223 223 223 223 223  2 X df 153.327 4.645 315.388 212.583 Period:  Sc Obs 1 162 198 2 3 211 4 220 185 5 6 192 7 191 8 184 186 9 T 1729  ND UD PD NBD  ND 86 143 210 272 310 311 276 216 149 90  ND 77 133 197 248 269 249 197 134 78  B i n o m i a l and P l a y i n g Time  1st  PD S c NBD 48 0 75 134 1 196 248 2 295 344 3 340 381 4 330 352 5 284 6 224 278 193 7 169 119 8 118 79 66 9  9 9 9 9  ls .001 n.s. .001 .001  18  Minutes  UD 190 190 190 190 190 190 190 190 190  2 X df 118.939 3.967 194.328 17.949  PD S c NBD 75 57 0 144 1 186 240 2 267 3 289 300 300 4 262 250 5 210 179 6 153 112 7 106 62 8 68  8 8 8 8  ls .001 n.s. .001 .001  81 Table  A3  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) Both  Goal Type Bos  Buf  Cai  NB.  Dist'n  P P G UD PD ND  Home 2 X  3.001 11.316 5.852"  Games n  Is  77 — —  ns ns ns  Team Away 2 X  Goals Games  7.766 18.798 11.959""  n  Is  74 — —  ns ns ns ns .001 ns  7.833 55.703 25.217  195  ns .001 .01  5.106 45.422 19.053  194  T G UD PD ND  6.505 64.907 26.317  272  ns .001 .01  4.258 64.319 25.659  268  P P G UD PD ND  2.257 18.811 7.548  98 — —  ns ns ns  NPPG UD PD ND  2.183 34.856 11.776  207  ns .001 ns  T G UD PD ND  2.217 51.699 17.824  305  ns .001 ns  95 — —  ns ns ns  8.498 17.287** 10.543+  7.943<< 5.378@@ 3.027>>  Total  Games 2  NPPG UD PD ND  P P G UD PD ND  Poisson Time  X  n  Is  8.530 26.572 12.665  151  ns .01 ns  7.343 97.709 38.537  389  ns .001 .001  ns 5.771 .001 1 2 6 . 6 4 4 .01 48.273  540  ns .001 .001  65 — —  ns ns ns  5.873 20.727 8.241  163  ns .05 ns  8.096 46.507 22.511  214  ns .001 .05  5.260 77.588 30.891  421  ns .001 .01  7.783 49.799 21.203  279  ns .001 .05  6.435 99.127 36.388  584  ns .001 .001  85 — —  ns ns ns  17.686 24.921" 14.283*  180  ns .01 ns  13.467< 11.276>> 9.848++  NPPG UD PD ND  5.071 50.034 19.613  205  ns .001 ns  3.591 40.848 15.393  187  ns .001 ns  5.995 86.214 35.584  389  ns .001 .001  TG UD PD ND  7.068 62.346 29.684  300  ns .001 .01  4.531 45.746 18.187  272  ns 001 ns  8.185 105.692 44.471  572  ns .001 .001  Number o f c e l l s w i t h * = 1, " = 2, + = 4, @@ = 12  expected counts l e s s than < = 5 , " " = 7 , ++ = 9 , <<  5: = 10,  >>  =  11,  82 Table  A3  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , Poisson and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g Time ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Both  Goal Type Chi  Dist'n  P P G UD PD ND NPPG UD PD ND T G UD PD ND  Det  P P G UD PD ND NPPG UD PD ND T G UD PD ND  Edm P P G UD PD ND  NB.  Home 2 X  Games n  9.483 100 17.585** — 9.945< —  Is  Team  Goals  Away Games 2 X n  Total  Games 2  Is  X  n  Is  ns ns ns  8.321 24.823+ 12.287"  113  ns .01 ns  11.005 35.298 15.969  213  ns .001 ns  9.645 26.409" 9.872  217  ns .01 ns  12.661 60.776 30.785  197  ns 001 L 01  8.684 77.568 31.283  414  ns 001 001  13.112 35.935 14.556  317  ns .001 ns  10.653 76.030 33.130  314  ns 001 001  12.155 108.918 40.451  627  ns .001 .001  73 - —  ns .05 ns  78  ns ns .02  15.026 37.773" 21.731*  151  ns .001 .05  12.099 223 45.821 12.317** —  ns .001 ns  4.314 54.189 21.902  251  ns 001 .05  10.809 95.283 41.037  474  ns .001 .001  5.922 59.159 23.706  ns .001 .02  4.824 60.188 24.593  329  7.056 114.303 44.884  625  —  ns .001 .02  ns .001 .001  86 — —  ns ns ns  13.472 23.835 13.850  159  ns .02 ns  6.647" 22.268!! 12.025""  10.585** 10.989<< 9.016++  296  73 — —  ns ns ns  11.458+ 17.719"' 23.304  6.766* 16.228>> 9.810""  —  NPPG UD PD ND  2.961 50.354 18.201  247  ns .001 ns  7.762 62.808 27.522  218  ns .001 .01  7.336 110.133 43.334  465  ns .001 .001  T G UD PD ND  4.944 57.226 20.758  320  ns .001 .05  6.955 73.554 29.667  304  ns 001 .01  8.038 128.322 49.230  624  ns .001 .001  Number o f c e l l s w i t h * = 1, " = 2, + = 4 , << = 1 0 , >> = 11  e x p e c t e d c o u n t s o f l e s s t h a n 5: < = 5, * * = 6, " " = 7, ! ! = 8 , ++  =  9,  83 Table  A3  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Both  Goal Type Har  LA  Min  Dist'n  P P G UD PD ND  Games n  4.188 81 20.250II— 9.043+ —  ls ns .05 ns  Away 2 X  Goals Games  5.060< 21.971!! 11.228<  Total  Games 2  n  ls  X  n  ls  76 — —  ns .05 ns  4.076 38.038 15.472  157  ns .001 ns  NPPG UD PD ND  3.723 46.187 18.230  217  ns .001 ns  5.448 210 51.406 20.654>> —  ns .001 .05  4.904 96.091 36.256  427  ns .001 .001  T G UD PD ND  3.280 65.118 23.443  298  ns .001 .02  5.211 70.077 26.277  ns 3.348 .001 131.430 .01 47.957  584  ns .001 .001  85 — —  ns ns ns  158  ns .01 ns  P P G UD PD ND  7.509~ 13.876** 6.338**  6.656~~ 17.123++ 9.088<<  286  73 — —  ns ns ns  7.227 26.753* 13.075  NPPG UD PD ND  8.700 72.999 33.256  293  ns .001 .001  7.380 51.153 22.254  253  ns 14.581 .001 122.633 .05 53.570  546  ns .001 .001  T G UD PD ND  5.144 84.850 34.759  378  ns .001 .001  7.840 61.495 25.257  326  ns 11.815 .001 148.344 .01 59.233  704  ns .001 .001  3.914 84 1 9 . 9 8 4 | | ~ 9.767+ —  ns .05 ns  4.607 43.739* 17.888  160  ns .001 ns  P P G UD PD ND NPPG UD PD ND T G UD PD ND  NB.  Home 2 X  Team  Poisson Time  7.728< 26.387! 13.802+  76 — —  ns .01 ns  7.168 34.766~ 15.301*  191  ns .001 ns  3.961 50.808 20.236  184  ns .001 .05  6.420 80.312 32.474  375  ns .001 .001  7.123 51.724 23.533  275  ns .001 .02  5.034 71.405 28.220  260  ns 8.490 .001 121.329 .01 48.200  535  ns .001 .001  Number o f c e l l s w i t h e x p e c t e d c o u n t s l e s s t h a n 5 : * = 1 , - = 2 , ! = 3 , + = 4 , < = 5 , * * = 6 , ~~ = 7 , ++ = 9 , << = 1 0 , >> = 11  !!  =  8,  84 Table  A3  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s for Actual Playing ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Both  Goal Type Mon  NJ  NYI  NB.  Home 2 X  Dist'n  P P G UD PD ND  Games n  9.283xx 21.9870® 13.645xx  Is  65 — —  ns .05 ns  Team Away 2 X  Poisson Time  Goals Games  9.166"" 9.605@@ 7.040>>  n  Is  73 — —  ns ns ns  Total 2 X  Games n  Is  10.386 22.3751 12.558"  138  ns .05 ns  N P P G UD PD ND  8.319 42.506 20.088  199  ns .001 .05  2.500 35.848 13.369  194  ns .001 ns  5.273 73.908 27.560  393  ns 001 .01  T G UD PD ND  5.303 53.370 22.523  264  ns .001 .05  4.445 39.481 14.287  267  ns .001 ns  5.190 90.625 31.237  531  ns 001 .01  7.963 25.544 12.890*  102  ns .01 ns  5.099 26.601 18.295  96  ns .01 ns  8.564 49.155 20.369  198  ns 001 .05  N P P G UD PD ND  5.133 40.184 18.295  188  ns .001 ns  5.133 63.413 27.047  215  ns .001 .01  9.589 99.945 42.835  403  ns ,001 .001  TG UD PD ND  5.738 58.905 24.287  290  ns .001 .02  8.168 71.052 27.473  311  ns 001 .01  8.922 139.765 55.092  601  ns 001 001  92 — —  ns ns ns  95 — —  ns ns ns  5.166 25.757 8.600  187  ns .01 ns  P P G UD PD ND  P P G UD PD ND  5.365* 10.443 4.624"  8.108* 17.360 8.473+  NPPG UD PD ND  9.762 62.630 28.504  196  ns .001 .01  4.960 35.282 14.055  201  ns .001 ns  10.377 94.970 40.661  397  ns 001 .001  T G UD PD ND  6.453 69.184 28.756  288  ns .001 .01  7.849 50.242 18.890  296  ns .001 ns  9.046 117.027 45.793  584  ns 001 001  >>,  12  =  1,  =  2,  3 =  7  =  11  =  =  13  = xx  85 Table  A3  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s for Actual Playing ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Both  Goal Type NYR  Phi  Pit  NB.  Dist'n  P P G UD PD ND  Home 2 X  9.128~~ 11.336@@ 8.046@@  Games n  ls  76 — —  ns ns ns  Team  Poisson Time  Goals  Away Games 2 X n 7.050 17.175++ 9.678**  Total  Games 2 n  ls  X  93 — —  ns ns ns  9.583 27.692 14.484  169  ns .01 ns  ls  NPPG UD PD ND  8.880 58.366 26.568  230  ns .001 .01  3.784 42.167 16.490  216 —  ns .001 ns  5.995 94.976 36.817  446  ns 001 001  T G UD PD ND  6.852 64.789 26.062  306  ns .001 .01  3.753 53.900 20.324  309  ns .001 05  5.791 113.516 41.534  615  ns 001 001  92 — —  ns .01 ns  87 — —  ns ns ns  8.449 35.514 16.666  179  ns 001 ns  P P G UD PD ND  8.409* 25.402~~ 14.055**  4.221 13.866++ 6.952~~  N P P G UD PD ND  2.568 39.225 13.982  203  ns .001 ns  10.790 56.548 27.951  204  ns .001 .01  5.470 87.588 35.006  407  ns 001 .01  T G UD PD ND  2.852 61.321 22.742  295  ns .001 .02  11.312 68.546 32.393  291  ns .001 .001  8.003 127.216 30.233  586  ns 001 ,001  8.236 25.811! 13.749"  115  ns .01 ns  3.809 25.389 10.322  116  ns .01 ns  7.603 48.875 10.727'  231  ns 001 ns  NPPG UD PD ND  8.997 63.695 28.777  229  ns .001 .01  3.433 47.784 19.715  233  ns .01 .05  7.575 106.910 43.784  462  ns 001 001  TG UD PD ND  6.081 79.007 32.002  344  ns .001 .001  4.564 69.351 26.919  349 —  ns .001 .01  7.280 146.900 57.159  693  ns 001 001  P P G UD PD ND  Number * = 1,  of c e l l s with ~ = 2, ! = 3,  expected counts * * = 6 , ~~ = 7 ,  l e s s t h a n 5: ++ = 9 , @@ =  12  86 Table  A3  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Both  Goal Type Que  StL  Tor  NB.  Dist'n  P P G UD PD ND  Home Games 2 X n Is  11.839<< 18.279<< 12.522++  77 — —  ns ns ns  Team  Poisson Time  Goals  Away Games 2 X n 8.290* 18.840** 12.729  Total  Games 2  Is  89 — —  ns ns ns  X  n  Is  14.615 33.370! 18.737  166  ns .001 ns  NPPG UD PD ND  6.512 49.236 21.266  232  ns .001 .02  3.351 55.659 21.049  210  ns .001 .05  5.539 103.707 39.358  442  ns 001 001  TG UD PD ND  8.541 63.728 27.576  309  ns .001 .01  2.598 69.461 26.477  299  ns .001 .01  7.152 130.658 49.568  608  ns 001 001  ns ns ns  12.603* 12.685!! 8.444!!  157  ns .05 ns  P P G UD PD ND  4.832xx 8.507< 4.401>>  63 — —  94  ns ns ns  14.408 19.955< 10.767"  N P P G UD PD ND  7.915 62.530 26.268  199  ns .001 .01  5.533 46.261 19.556  200  ns .001 ns  8.591 107.287 42.347  399  ns 001 001  T G UD PD ND  5.916 67.363 26.110  262  ns .001 .01  5.039 57.254 22.572  294  ns .001 .05  8.342 122.181 46.994  556  ns 001 ,001  72  ns ns ns  16.945 21.252' 14.783'  153  ns .01 ns  P P G UD PD ND  13.606! 12.993 10.382 ! !  81 —  ns ns ns  7.734* 14.865< 8.965**  NPPG UD PD ND  7.249 65.877 28.315  216  ns .001 .01  12.075 33.513 16.426  227  ns .001 ns  8.517 92.219 36.140  443  ns .001 .001  T G UD PD ND  9.007 73.694 30.299  297  ns .001 .01  12.673 42.187 17.323  299  ns 001 ns  13.255 104.345 41.703  596  ns .001 .001  Number o f c e l l s w i t h * = 1, " = 2, i = 3, x x = 13  expected counts l e s s than < = 5 , * * = 6 , ! ! = 8 , ++  5 =  9,  <<  =  10  87 Table  A3  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Both  Goal Type Van  Was  Win  NB.  Dist'n  P P G UD PD ND  Home Games 2 X n ls  6.238< 6.393!! 4.167!|  73 — —  ns ns ns  Team  Poisson Time  Goals  Away Games 2 X n 9.846|! 17.846<< 11.948++  70 — —  Total  Games 2  ls ns ns ns  X  n  ls  11.871 24.080+ 12.7661  143  ns .02 ns  NPPG UD PD ND  1.974 44.052 16.849  156  ns .001 ns  6.269 46.008 19.734  199  ns .001 .05  5.479 85.749 35.834  355  ns .001 .001  T G UD PD ND  2.622 47.344 19.278  229  ns .001 ns  3.273 58.169 23.371  269  ns .001 .02  3.050 103.561 37.738  498  ns .001 .001  86 — —  ns ns ns  82 — —  ns ns ns  7.419 21.321" 7.994  168  ns .05 ns  P P G UD PD ND  2.133 16.775** 6.102<  12.713< 8.768++ 7.297!I  NPPG UD PD ND  7.990 42.525 19.770  188  ns .001 ns  3.326 46.499 19.177  202  ns .001 ns  -5.177 84.446 34.219  390  ns .001 .001  TG UD PD ND  6.724 55.142 23.901  274  ns .001 .02  5.468 50.917 19.914  284  ns .001 .05  6.836 100.280 38.099  558  ns .001 .001  83 — —  ns ns ns  78 - —  ns ns ns  9.769 27.178 14.440  161  ns .01 ns  5 . 091 66.609 26.267  254  ns .001 .01  7.387 120.770 45.840  486  ns .001 .001  5.015 82.851 31.157  332  ns .001 .01  5.278 147.103 54.604  647  ns .001 .001  P P G UD PD ND  7.822* 15.673>> 9.381++  N P P G UD PD ND  6.966 57.606 23.852  232  ns .001 .02  TG UD PD ND  4.991 68.442 28.678  315  ns .001 ns  Number o f c e l l s w i t h * = 1, ~ = 2, i = 3, << = 1 0 , >> = 11  5.498* 14.927<< 6.553!1  e x p e c t e d c o u n t s l e s s t h a n 5: + = 4, < = 5, * * = 6, II = 8,  ++  =  9,  88 Table  A4  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) Goals  Goal Type Bos  Buf  Dist'n  P P G UD PD ND  n  Is  Away 2 X  Games  41  n  Is  44  ns —  Total 2 X  Games  4.892 19.840!! 9.091**  n  Is 85 — —  ns .05 ns  5.487 28.715< 13.598*  98 - —  ns .01 ns  7.269 28.149 13.032"  103  ns .01 ns  5.947 53.750 23.851  201  ns 001 .02  T G UD PD ND  5.232 37.535* 17.130  139  ns .001 ns  6.740 41.333* 19.392  147  ns .001 ns  4.614 76.908 31.246  286  ns 001 .01  P P G UD PD ND  TG UD PD ND  T G UD PD ND Number * = 1,  25  52  5.450 17.237+ 7.223+  114  ns ns  6.043 23.047 9.143  166  ns .02 ns  P P G UD PD ND NPPG UD PD ND  NB.  Games  For  N P P G UD PD ND  N P P G UD PD ND  Cai  Home 2 X  Poisson Time  8.524 14.177++ 8.134!! 7.381 16.535+ 7.659"  61  77  98 — —  ns ns ns  8.833 23.876 9.880  212  ns .02 ns  123  ns ns ns  9.560 35.519 13.361  289  ns 001 ns  —  14.431'  102  ns  41  4.600 34.004* 14.582  137  ns .001 ns  6.669 26.178" 15.476"  110  ns .01 ns  7.862 60.811 27.231  247  ns 001 .01  4.514 46.425 19.868  198  ns .001 .05  7.894 34.027 17.350  151  ns .001 ns  8.736 77.342 33.812  349  ns 001 001  of c e l l s with " = 2, + = 4,  expected counts l e s s than < = 5 , * * = 6 , i i = 8 , ++  5: = 9  89  Table  A4  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) Goals  Goal Type Chi  Det  Dist'n  Home Games 2 X n ls  For  Away 2 X  Games  P P G UD PD ND NPPG UD PD ND  49  7.058 16.958! 8.159"  115  ns ns ns  10.260" 33.000+ 16.281"  TG UD PD ND  13.686 26.068" 13.461"  164  ns .01 ns  8.139 37.699! 19.322  P P G UD PD ND NPPG UD PD ND T G UD PD ND  n  ns .01 ns  4.397 36.190 14.859  156  ns .001 ns  Games ls  n  ns  13.405  91  ns  89 — - -  ns 001 ns  8.909 42.356 20.867  204  ns 001 .05  131 — —  ns .001 ns  14.810 57.720 26.142  295  ns 001 .01  32  --— —  73 22.455 — 1 2 . 7 4 4 | | ~  41  115  Total 2 X  ls  42  7.654 24.853* 14.227  Poisson Time  .05 ns  4.640 29.905* 12.588  122 - —  ns .01 ns  6.384 49.921 21.300  237  ns .001 .05  5.008 30.023 13.688  154  ns .01 ns  4.740 62.381 25.303  310  ns .001 .01  39  —  11.720<  82  ns  Edm P P G UD PD ND NPPG UD PD ND  3.873 26.292 10.686  128  ns .01 ns  10.787 33.6431 19.039  111  ns 001 ns  7.745 53.822 24.323  239  ns .001 .02  T G UD PD ND  4.645 28.195 11.939  171  ns .01 ns  9.315 37.764" 17.948  150  ns .001 ns  8.898 62.949 26.212  321  ns .001 .01  NB.  Number = 2,  43  of =  c e l l s with 3, < = 5,  expected  counts  less  than  5:  90 Table  A4  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Goals  Goal Type Har  Dist'n  P P G UD PD ND NPPG UD PD ND T G UD PD ND  LA  Min  Games n  Is  Away 2 X  For Games  115  5.684 42.532 17.942  156  Is  46  41  6.836 31.253" 16.305"  n  Total 2 X  ns .01 ns ns .001 ns  23.975* 11.009 4.821 35.127 15.509  6.250*  n  Is  87  ns  96 —  ns .02 ns  4.721 54.109 23.312  211  ns .001 .02  142  ns .001 ns  5.489 72.275 29.399  298  ns 001 .01  79  ns  6.589 37.304 17.051  159  ns .001 ns  1.927 23.422" 8.705  132  ns .02 ns  5.744 61.018 25.337  291  ns 001 .01  T G UD PD ND  5.905 45.368 18.091  210  ns .001 ns  3.573 29.500* 12.388  160  ns .01 ns  6.560 72.275 28.576  370  ns 001 .01  P P G UD PD ND NPPG UD PD ND  51  Games  PPG UD PD ND NPPG UD PD ND  TG UD PD ND NB.  Home 2 X  Poisson Time  28  45  4.441 21.868 ! 9.532" 3.649 30.192 12.189  78  33  96  ns .05 ns  141  ns .01 ns  Number o f c e l l s w i t h = 1, " = 2, 1 = 3  7 .132'  84  ns .01 ns  6.573 52.749 21.828  180  ns 001 .05  117  ns .001 ns  6.398 68.445 27.802  258  ns 001 .01  4.979" 29.620* 14.863" 6.011 40.595 18.036  expected  counts  less  than  5:  91  Table  A4  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Goals  Goal Type  Dist'n  Home Games 2 X n ls  Away 2 X  Poisson Time  For Games  Total  Games 2  n  ls  X  n  ls  80  ns  Mon P P G UD PD ND NPPG UD PD ND  4.720 29.390 12.871  123  ns .01 ns  4.053 21.727! 11.346*  110  ns ,05 ns  5.287 49.915 20.326  233  ns .001 .05  T G UD PD ND  2.638 34.864 14.542  160  ns .001 ns  4.134 21.153* 10.182  153  ns .05 ns  4.442 58.871 21.827  313  ns .001 .05  46  ns  39  ns  9.192'  85  ns  97  ns  7.024 28.424" 14.609*  98 — —  ns ,01 ns  7.326 49.453 20.911  195  ns 001 .05  143  ns .01 ns  6.182 41.832 18.435  137  ns .001 ns  7.990 69.621 29.847  280  ns .001 .01  84 — —  ns ns ns  NJ  PPG UD PD ND NPPG UD PD ND T G UD PD ND  NYI  NB.  37  4.217  43  9.765' 5.152 30.192 12.621  P P G UD PD ND  43  6.641*  41  10.709" 6.785 4.911  NPPG UD PD ND  5.325 32.606 17.220  96 — —  ns .001 ns  3.340 17.209 7.273  82  ns ns ns  6.954 44.042 20.601  178  ns .001 .05  T G UD PD ND  6.386 29.189 13.288  139  ns .01 ns  4.871 17.029 7.455  123  ns ns ns  7.223 45.443 18.697  262  ns .001 ns  Number * = 1,  of c e l l s with " = 2, ! =3  expected  counts  less  than  5:  92  Table  A4  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Goals Home Games Goal Type  Dist'n  NYR P P G UD PD ND N P P G UD PD ND T G UD PD ND Phi  P P G UD PD ND NPPG UD PD ND T G UD PD ND  Pit  NB.  P P G UD PD ND  X  11.318  n  ls  39  —  121  16.304 6.693 33.241 15.876  ns • ns  160  ns 001 ns  54  ns  3.762 28.091" 11.876*  111  ns .01 ns  3.528 34.919 13.799  165  ns .001 ns  For  Away 2 X  Games  Total  2.630  n  ls  X  9.422  ls  9.428'  84  ns  ns — ns  7.284 50.098 21.887  225  ns 001 .05  149  ns .02 ns  5.399 61.222 23.130  309  ns 001 .02  45  ns  7.685 12.149  99  ns ns  96  ns  207  ns  4.325 57.263 23.448  ns 001 .02  ns 001 .05  6.370 68.953 28.687  306  ns 001 .01  9.655  119  ns  20.306 8.111 37.026 19.997  n  104  10.201* 2.717 30.850 12.257  Games 2  45  141  60  59  — — 14.190  N P P G UD PD ND  8.991 39.914 20.919  125 — —  ns .001 .05  10.691"  T G UD PD ND  5.311 45.682 18.281  185  ns .001 ns  5.118 28.958 12.954  Number * = 1,  Poisson Time  of =  cells 2  with  4.942  expected  ns  101  ns ns ns  4.157 51.811 21.042  226  ns 001 .05  160  ns .01 ns  5.600 70.386 27.940  345  ns 001 .01  counts  less  than  5:  93  Table  A4  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Goals Home Goal Type Que  Dist'n  P P G UD PD ND NPPG UD PD ND T G UD PD ND  StL  Tor  NB.  X  Games n  For Games  44  6.831  105  10.057 7.408 25.660* 12.304  149  4.769 31.064* 13.375  113  T G UD PD ND  5.769 33.373* 15.492  146  —  P P G UD PD ND NPPG UD PD ND  17.142  TG UD PD ND  4.476 34.831 14.476 of c e l l s " = 2  98  n  Is  X  41  ns  6.192 24.573  ns .01 ns  6.043 34.450* 15.397  33  85  77  ns ,02  5.693 39.932 16.353  182  ns 001 ns  118  ns .001 ns  5.822 53.862 21.319  267  ns 001 .05  41  126  ns .01 001  with  5.733 48.705 19.860  198  ns 001 .05  M I S S I N G 272 58.714 23.499  ns ,001 .02  20  ns  ns .001 ns  ns  74  — — 5.890 37.026" 36.365  Is  19.654  ns .01 ns ns .001 ns  n  —  55  8.914  105  ns  5.086 45.062 18.604  203  ns 001 ns  7.884 21.880" 11.253  125  ns .05 ns  5.648 48.423 19.868  258  ns 001 .05  ns 133  Games 2  35  5.642  Total  ns  P P G UD PD ND NPPG UD PD ND  Number * = 1,  Is  Away 2 X  Poisson Time  expected  counts  less  than  5:  94 Table  A4  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Goals  Goal Type Van  Dist'n P P G UD PD ND  44  NPPG UD PD ND  77  T G UD PD ND Was  TG UD PD ND  121 - —  TG UD PD ND Number * = 1,  Away 2 X  9.908 31.532 16.882"  104  7.381 43.064 19.296  159  — —  3.157 16.092 7.230'  ns .01 ns  2.279 27.133" 10.285  104  5.115 44.254 19.547  149  of c e l l s " = 2  with  Games  Total  n  Is  X 7.982'  78  ns  4.180 37.274 16.350  171  ns .001 ns  128  ns .01 ns  2.411 50.768 18.054  249  ns 001 ns  4.881  95  ns  ns .001 ns  5.026 55.030 22.053  208  ns .001 .05  ns .001 ns  6.317 70.758 29.847  303  ns .001 .01  79  ns  104  ns .001 ns  7.834 37.752 19.182  144  —  34  6.019*  111  ns .01  ns 4.157 145 .001 29.422* ns 12.137 expected  Is  ns ns  5.910 31.696 15.665  3.960 25.820" 11.763*  n  94  ns .01 ns  ns .001 ns  Games 2  40  45  7.987 39.196 18.804  For  34  55  P P G UD PD ND NPPG UD PD ND  NB.  4.596 28.400* 12.012  P P G UD PD ND NPPG UD PD ND  Win  Home Games 2 X n Is  Poisson Time  counts  4.790 59.053 24.788  ns 4.866 .01 69.412 ns 27.054 less  than  5:  215  294 '  ns .001 .01 ns .001 .01  95 Table  A5  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s for Actual Playing ( F i v e M i n u t e D i v i s i o n s : d f = 11) Goals Home Goal Type Bos  Dist'n P P G UD PD ND  NPPG UD PD ND T G UD PD ND Buf  T G UD PD ND  8.379' 31.936' 16.945  Away 2 X  6.174 32.435" 13.794  ns 001 ns  3.001  133  ns .001 ns  3.322 25.824" 10.691  46  2.613 22.677 9.866" 5.260 35.667 17.464  Games 2  n  ls  X  n  ls  7.083  66  ns  91  ns  5.786 42.268 15.950  188  ns 001 ns  121  ns .01 ns  6.044 51.664 21.576  254  ns 001 .05  3.449  86  ns  40  ns .02 ns  8.421 42.858 20.600  116  ns .001 .05  3.449 62.004 26.318  209  ns 001 .01  139  ns .001 ns  5.266 37.411 16.822  156  ns .001 ns  6.352 71.179 28.077  295  ns 001 .01  68  of c e l l s " = 2  Total  93 — —  NPPG UD PD ND 5.181  Games  30  97  34  Number * = 1,  ls  Against  36  P P G UD PD ND  T G UD PD ND NB.  n  P P G UD PD ND NPPG UD PD ND  Cal  X  Games  Poisson Time  102  with  44  3.640"  ns  5.318  expected  78  77 — —  ns — —  5.014 32.885" 12.656  145  ns .001 ns  121  ns —  9.099 32.138* 13.533  223  ns .001 ns  counts  less  than  5  96 Table  A5  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Goals  Goal Type Chi  Det  Home 2 Dist'n  X  NPPG UD PD ND  8.114  TG UD PD ND  11.163  102  145  9.874  Games  Total  ns  6.584  ns ns  5.194 43.319 17.769  Games 2  n  ls  X  71  32  n  ls  6.010 23.137" 10.746  122  ns .02 ns  210  ns 001 ns  332  ns 001 .05  108  ns  —  ns  6.128 36.563 14.940  179  ns .001 ns  7.325 55.762 21.992  46  78  8.726 25.795" 14.933*  108  ns .01 ns  4.796 27.993" 13.614*  129  ns .01 ns  9.265 50.364 23.527  237  ns 001 .02  6.988 28.683 14.437  140  ns .01 ns  8.594 35.210 17.731  175  ns 001 ns  9.595 58 . 9 8 2 26.597  315  ns 001 .01  Edm P P G UD PD ND  NB.  ls  Away 2 X  14.222*  P P G UD PD ND  T G UD PD ND  n  Against  51  P P G UD PD ND  NPPG UD PD ND  Games  Poisson Time  30  47  77  NPPG UD PD ND  3.900 28.005" 12.828  119  ns .01 ns  3.050 32.958 13.211  107  ns 001 ns  3.158 58.285 23.366  226  -ns 001 .02  TG UD PD ND  3.056 31.219* 12.346  149  ns .01 ns  2.865 36.287 15.304  154  ns 001 ns  3.179 68.521 25.944  303  ns 001 .01  with  expected  Number * = 1,  of c e l l s " = 2  counts  less  than  5;  97 Table  A5  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Goals Home Goal Type Har  Dist'n P P G UD PD ND  NPPG UD PD ND T G UD PD ND LA  Min  NB.  X  Games n  Is  Against  Away 2 X  40  3.865  102  7.919" 4.490 30.102 12.118  PPG UD PD ND  142  Poisson Time  Games n  Is  Total 2 X  30  Games n  Is  70  114  ns .01 ns  7.958 47.527 21.545  216  ns  7.623 30.999" 15.850"  ns 001 .05  ns .01 ns  4.287 37.918 15.292  144  ns .001 ns  6.025 65.222 26.144  286  ns .01 .01  4.764  79  ns  ns  34  45  NPPG UD PD ND  6.365 40.574 18.709  134  ns .001 ns  9.854  121  ns  14.194 68.010 32.630  255  ns 001 001  T G UD PD ND  4.096 44.808 19.871  168  ns .001 .05  8.449 31.626* 16.563  166  ns .001 ns  8.943 79.318 35.033  334  ns 001 ,001  6.634  82  ns  PPG UD PD ND  39  43  NPPG UD PD ND  7 . 539'  95  ns  4.658  100  ns  5 . 936 34.718 16.049  195  ns 001 ns  TG UD PD ND  7.553 25.645" 13.574"  134  ns .01 . ns  2.771 34.502 13.548  143  ns .001 ns  6.694 57.418 24.107  277  ns 001 .02  with  expected  Number * = 1,  of c e l l s " = 2  counts  less  than  5:  98 Table  A5  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , Poisson and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g Time ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Goals  Goal Type  Dist'n  Home 2 X  Games n  Mon P P G UD PD ND  28  NPPG UD PD ND  76  T G UD PD ND NJ  NYI  NB.  9.092  104  13.954  P P G UD PD ND  ls  Against  Away 2 X  Games  Total  Games 2  n  ls  X  30  n  ls  58  2.182  84  ns  6.073 28.784 12.143  160  ns .01 ns  ns  4.350  114  7.387"  6.664 36.752 13.847  218  ns  ns — ns  ns 001 ns  57  - —  3.594 22.577* 9.091  113  ns .05 ns  56  N P P G UD PD ND  6.840  91 — —  ns — —  5.716 37.767 17.419  117  ns .001 ns  8.077 57.708 26.117  208  ns 001 .01  T G UD PD ND  5.365 33.332 14.551  147  ns .001 ns  3.476 45.373 17.917  174  ns .001 ns  7.147 75.993 31.380  321  ns 001 001  —  3.498  103  ns  —  10.631'  P P G UD PD ND  49  54  ns  NPPG UD PD ND  5.747 34.857 17.193  100  ns .001 ns  6.404 23.629 11.718  119  ns .02 ns  8.365 55.094 24.637  219  ns 001 .02  TG UD PD ND  4.273 42.783 19.016  149  ns .001 ns  6.752 35.961 15.585  173  ns .001 ns  6.914 78.225 30.887  322  ns 001 .01  counts  less  Number o f c e l l s * =1, " = 2  with  expected  than  5:  99 Table  A5  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Goals  Goal Type  Dist'n  Home Games 2 X n Is  N P P G UD PD ND - T G UD PD ND Phi  Pit  NB.  Against  Away 2 X  37  NYR P P G UD PD ND 6.323 37.074* 17.895  109  6.787 39.449 16.181  146  P P G UD PD ND 4.277  T G UD PD ND  4.603 31.650 13.760  92  Games  ns .001 ns  4.072  n  Is  X  ns 001 ns  4.935 26.915 10.905  7.714  ns 001 ns  7.460 34.489 17.117  Is  85  221  ns  ns .001 .05  ns ,01 ns  6 .062 56.817 22.898  306  ns .001 .02  6.969'  80  ns  200  ns  4.151 31.098 13.299  ns .02 ns  150  ns 001 ns  3.469 59.875 22.484  280  ns .001 .05  57  — -—  2.892 25.072 10.713  112  ns .01 ns  160  ns  42  ns  n  4.608 50.063 21.268  112  8.854  55  P P G UD PD ND  Games 2  108  13.792" 130  Total  45  38  NPPG UD PD ND  Poisson Time  ns  NPPG UD PD ND  5.248 27.551 14.118  104  ns .01 ns  4.429 33.162 14.966  132  ns .001 ns  6.870 57.608 25.528  236  ns .001 .01  TG UD PD ND  5.423 36.722 17.042  159  ns 001 ns  4.683 44.974 18.844  189  ns .001 ns  7.159 78.087 31.842  348  ns .001 .001  with  expected  Number * = 1,  of  cells = 2  counts  less  than  5:  100 Table  A5  Individual Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Goals  Goal Type Van  Was  Win  NB.  Dist'n  Home Games 2 X n Is  P P G UD PD ND NPPG UD PD ND  5.689"  TG UD PD ND  4.780 25.901" 13.206*  P P G UD PD ND  Against  Away 2 X  6.304*  T G UD PD ND  4.335 17.574" 6.660"  Total  Games 2  n  Is  X  n  Is  169  ns  ns  3.414  93  ns  9.583  79  ns  6.672  105  ns  184  __  14.685  ns  6.411 52.873 23.079  ns .001 .02  ns .01 ns  4.533 36.695" 14.999  ns .001 ns  4.597 55.964 22.957  249  ns .001 .02  108  84  115  141  42  ns  ns ns ns  3.359  98  9.398"  —  5.334 18.813" 7.586*  140  38  P P G UD PD ND  Games  29  31  NPPG UD PD ND  Poisson Time  73  ns .05 ns  4.758 32.018 14.111  182  ns .001 ns  ns ns ns  7.649 32.941 12.935  255  ns .001 ns  6.967  82  ns  44  NPPG UD PD ND  6.162 23.951 11.608  128  ns .02 ns  5.334 44.160 17.934  143  ns 001 ns  6.847 66.048 27.074  271  ns .001 .01  TG UD PD ND  3.688 27.291 11.288  166  ns .01 ns  4.814 56.028 22.060  187  ns .001 ns  3.609 78.631 29.124  353  ns .001 .01  with  expected  Number * = 1,  of c e l l s " = 2  counts  less  than  5:  101 Table  A5  Individual Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( F i v e M i n u t e D i v i s i o n s : d f = 11) (continued) Goals  Goal Type Van  Dist'n  P P G UD PD ND NPPG UD PD ND T G UD PD ND  Was  Win  NB.  Home 2 X  5.689'  Games n  ls  Against  Away 2 X  Games  P P G UD PD ND 6.304*  T G UD PD ND  4.335 17.574" 6.660"  P P G UD PD ND  Games  ls  n  X  n  ls  169  ns  29  ns  3.414  93  ns  9.583  79  ns  6.672  105  ns  184  ns  6.411 52.873 23.079  ns ,001 . 02  ns 001 ns  4.597 55.964 22.957  249  ns ,001 .02  108  ns .01 ns  4.533 36.695" 14.999  31  NPPG UD PD ND  Total 2  14.685 4.780 25.901" 13.206*  Poisson Time  84  115  141  73  42  ns  ns ns ns  3.359  98  9.398"  —  5.334 18.813" 7.586*  140  38  ns .05 ns  4.758 32.018 14.111  182  ns 001 ns  ns ns ns  7.649 32.941 12.935  255  ns 001 ns  6.967  82  ns  44  NPPG UD PD ND  6.162 23.951 11.608  128  ns .02 ns  5.334 44.160 17.934  143  ns .001 ns  6.847 66.048 27.074  271  ns 001 .01  TG UD PD ND  3.688 27.291 11.288  166  ns .01 ns  4.814 56.028 22.060  187 -  ns 001 ns  3.609 78.631 29.124  353  ns 001 .01  Number * = 1,  of c e l l s " = 2  with  expected  counts  less  than  5:  102 Table  A6  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s for Actual Playing ( T e n M i n u t e D i v i s i o n s : d f = 5) Both  Goal Type Bos  Buf  Cai  Dist'n  Home 2 X  Games  Team  n  Is  Away 2 X  Poisson Time  Goals Total 2 X  Games n  Is  Games n  Is  P P G UD PD ND  3.028 1.535 3.535  77  ns ns ns  5.933 6.535 9.199  74  ns ns ns  7.383 5.538 12.007  151  ns ns .05  NPPG UD PD ND  4.468 18.148 21.440  195  ns .01 001  2.540 12.647 15.715  194  ns .05 .01  4.151 27.583 34.620  389  ns .001 001  T G UD PD ND  3.614 16.074 23.815  272  ns .01 001  1.696 15.471 22.115  268  ns .01 001  3.417 31.461 43.882  540  ns 001 001  P P G UD PD ND  1.319 3.309 6.526  98  ns ns ns  7.139 0.437 1.162  65  ns ns ns  5.161 1.957 6.275  163  ns ns ns  NPPG UD PD ND  1.574 8.409 12.297  207  ns ns .05  0.895 11.392 15.336  214  ns ,05 ,01  1.537 19.095 26.410  421  ns .01 001  TG UD PD ND  1.493 10.553 17.277  305  ns ns .01  1.448 8.988 15.017  279  ns ns ,02  2.651 18.847 32.721  584  ns .01 001  P P G UD PD ND  4.326 3.279 6.446  95  ns ns ns  8.763 1.576 4.186  85  ns ns ns  10.703 3.499 6.918  180  ns ns ns  NPPG UD PD ND  1.324 15.006 18.936  205  ns ,02 .01  2.614 11.514 14.196  187  ns .05 ,02  3.268 27.053 32.690  392  ns ,001 001  TG UD PD ND  1.807 15.504 21.125  300  ns .01 001  2.989 8.971 15.365  272  ns ns .01  4.197 24.614 37.982  572  ns 001 001  103 Table  A6  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , P o i s s o n and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g Time ( T e n M i n u t e D i v i s i o n s : d f = 5) Both  Goal Type Chi  Dist'n  Home 2 X  Games  Team  n  ls  Away 2 X  Goals Games n  ls  Total 2 X  Games n  ls  P P G UD PD ND  4.604 2.669 4.254  100  ns ns ns  3.023 4.493 7.166  113  ns ns ns  4.844 4.965 9.360  213  ns ns ns  NPPG UD PD ND  5 . 597 5 . 817 8 . 855  217  ns ns ns  1.217 14.966 17.752  197  ns .02 .01  2.634 17.524 25.125  414  ns .01 001  TG UD PD ND  7.659 7.460 12.523  317  ns ns ns  1.350 17.452 23.989  310  ns .01 001  4.544 20.613 32.929  627  ns ,001 ,001  P P G UD PD ND  4.131 6.649 8.206  73  ns ns ns  4.085 3.009 4.794  78  ns ns ns  6.700 8.580 13.313  151  ns ns ,05  N P P G UD PD ND  8.186 16.063 21.099  223  ns .01 001  2.381 12.947 16.906  251  ns .05 ,01  8.467 27.228 35.587  474  ns ,001 ,001  T G UD PD ND  4.060 14.766 21.513  296  ns .02 001  2.529 11.963 18.971  329  ns ,05 ,01  5.787 26 . 7 1 3 40.804  625  ns 001 001  Edm P P G UD PD ND  4.033 0.525 2.505  73  ns ns ns  4.657 4.038 6.322  86  ns ns ns  7.742 3.425 8.879  159  ns ns ns  NPPG UD PD ND  1.359 11.921 15.885  247  ns .05 .01  3.916 21.073 23.089  218  ns ,001 001  2.861 31.403 37.728  465  ns ,001 ,001  T G UD PD ND  1.708 10.092 17.532  320  ns ns ,01  3.278 21.336 15.467  304  ns ,001 .01  2.436 30.550 43.745  624  ns 001 ,001  Det  104 Table  A6  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , Poisson and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g Time ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Both  Goal Type Har  LA  Min  Dist'n  Home Games 2 X n Is  Team Away 2 X  Goals Games n  Is  Total 2 X  Games n  Is  P P G UD PD ND  2.055 5.044 7.360  81  ns ns ns  0.557 4.354 4.837  76  ns ns ns  1.432 7.758 11.718  157  ns ns .05  NPPG UD PD ND  1.742 13.652 16.628  217  ns 02 01  1.573 15.216 17.628  210  ns .01 .01  2.265 28.394 33.440  427  ns 001 001  TG UD PD ND  0.812 17.083 22.660  298  ns .01 .001  1.844 18.941 23.107  286  ns .01 001  0.989 33.872 44.188  584  ns 001 001  PPG UD PD ND  4.398 3.215 5.886  85  ns ns ns  1.131 2.948 3 . 960  73  ns ns ns  2.923 4.203 8.638  158  ns ns ns  NPPG UD PD ND  7.115 26.973 30.143  293  ns .001 .001  5.760 15.870 20.244  253  ns ,01 ,01  12.042 42.475 50.316  546  .05 001 001  T G UD PD ND  4.101 26.682 32.747  378  ns .001 .001  6.221 17 . 7 7 6 23.996  326  ns .01 001  9 . 398 44.411 57.078  704  ns 001 001  PPG UD PD ND  1.519 6.710 7.469  84  ns ns ns  1.792 7 . 871 9.868  76  ns ns ns  2.128 13.704 15.901  160  ns .02 .01  NPPG UD PD ND  3.618 8.912 12.699  191  ns ns .05  3.167 17.790 19.704  184  ns .01 .01  4.412 24.767 30.671  375  ns ,001 ,001  T G UD PD ND  2.749 14.492 18.972  275  ns .02 .01  3.478 23.865 25.798  260  ns 001 001  4.949 37.314 45.370  535  ns 001 001  105 Table  A6  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Both  Goal Type  Dist'n  Home Games 2 X n ls  Team  Poisson Time  Goals  Away Games 2 X n  ls  Total 2 X  Games n  ls  Mon P P G UD PD ND  4.256 6.467 8.683  65  ns ns ns  6.643 2.714 4.774  73  ns ns ns  7.122 5.003 9.270  138  ns ns ns  N P P G UD PD ND  4.924 12.825 14.739  199  ns .05 .02  1.127 7.441 11.889  194  ns ns .05  2.831 16.759 23.933  393  ns .01 .001  T G UD PD ND  1.668 11.708 16.032  264  ns .05 .01  2.959 5.647 12.671  267  ns ns .05  3.192 16.137 28.045  531  ns .01 001  PPG UD PD ND  2.137 6 .010 7.433  102  ns ns ns  2.457 8.248 9.899  96  ns ns ns  2 . 847 12.516 16.290  198  ns .05 .01  N P P G UD PD ND  3.217 11.039 15.777  188  ns ns .01  6.037 24.459 26.001  215  ns ,001 001  6.281 33.619 38.809  403  ns 001 001  T G UD PD ND  3.224 14.996 21.499  290  ns .02 001  4 . 802 30.690 32.153  311  ns 001 ,001  6.454 44.148 53.354  601  ns 001 001  P P G UD PD ND  2.532 1 . 842 3.350  92  ns ns ns  3.953 2.269 4.988  95  ns ns ns  4.217 3.693 8.310  187  ns ns ns  NPPG UD PD ND  4 . 894 20.367 23.331  196  ns .01 001  3.730 7.140 11.201  201  ns ns ns  5.691 25.458 33.482  397  ns 001 001  TG UD PD ND  3.618 18.985 25.103  288  ns .01 001  5.583 8.064 15.644  296  ns ns .01  5.888 26.725 39.610  584  ns 001 001  NJ  NYI  — —  106 Table  A6  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Both  Goal Type  Dist'n  NYR P P G UD PD ND  Phi  Pit  Home Games 2 X n Is 7.281 1.926 4.527*  Team Away 2 X  Poisson Time  Goals Games n  Is  Total 2 X  Games n  Is  76 — —  ns ns ns  3.414 2.048 5.208  93  ns ns ns  9.583 3.577 8.978  169  ns ns ns  NPPG UD PD ND  1.871 16.090 19.618  230  ns 01 .01  1.383 10.002 14.378  216  ns ns .02  2.271 25.402 33.148  446  ns ,001 ,001  T G UD PD ND  1.278 13.012 19.778  306  ns .05 ,01  1.532 10.068 16.793  309  ns ns ,01  1.879 21.510 35.712  615  ns ,001 001  P P G UD PD ND  6.370 9.222 11.291  92  ns ns .05  4.055 3.199 6.923  87  ns ns ns  7.287 9.272 17.092  179  ns ns .01  N P P G UD PD ND  1.197 6.458 11.296  203  ns ns .05  3.508 17.394 21.600  204  ns .01 001  1.966 21.464 31.740  407  ns ,001 ,001  T G UD PD ND  1.775 12.412 20.885  295  ns .05 .001  5.145 19.529 28.258  291  ns . 01 001  3.985 30.233 47.003  586  ns 001 001  P P G UD PD ND  3.643 4.716 8.455  115  ns ns ns  1.377 5.192 7.485  116  ns ns ns  2.429 8.865 15.059  231  ns ns .02  NPPG UD PD ND  3.430 19.722 21.222  229  ns .01 .001  0.745 9.271 15.330  233  ns ns .01  1.283 26.940 35.264  462  ns 001 001  TG UD PD ND  1.524 19.622 25.968  344  ns .01 .001  0 .903 14.300 22.146  349  ns .02 .001  1.296 33.761 48.141  693  ns 001 001  107 Table  A6  I n d i v i d u a l Team C h i - s q u a r e ' A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s for Actual Playing ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Both  Goal Type Que  StL  Tor  * "  Dist'n  Home 2 X  Games  Team  n  Is  Away 2 X  Poisson Time  Goals Games n  Is  Total 2 X  Games n  Is  P P G UD PD ND  6.920 4.546 7.767  77 — —  ns ns ns  5.554 6.805 9.306  89 — —  ns ns ns  9.856 9.237 16.145  166  ns ns .01  NPPG UD PD ND  2.319 9.846 14.560  232  ns ns .02  1.242 15.901 19.536  210  ns .01 .01  1.532 24.435 32.853  442  ns .001 .001  TG UD PD ND  4.456 11.744 20.604  309  ns .05 .001  1.128 17.455 24.010  299  ns .01 .001  4.163 27.978 44.419  608  ns .001 .001  63 — —  ns ns ns  6.735 0.477 3.200  94  ns ns ns  9.157 2.656 6.875  157  ns ns ns  P P G UD PD ND  3.628 0.711* 2.477"  •  NPPG UD PD ND  2.143 17.691 19.634  199  ns .01 .01  3.023 12.607 14.842  200  ns .05 .02  3.172 30.291 34.1849  399  ns .001 .001  T G UD PD ND  0.869 14.602 9.806  262  ns .02 ns  1.925 10.903 17.855  294  ns ns .01  1.824 25.668 37.386  556  ns .001 .001  P P G UD PD ND  6.682 0.932 1.137  81 — —  ns ns ns  1.557 1.557 3.042  72 — —  ns ns ns  7.024 1.502 3.838  153  ns ns ns  NPPG UD PD ND  3.698 21.860 24.963  216  ns .001 .001  9.217 8.010 9.684  227  ns ns ns  3.268 19.679 27.549  443  ns .01 .001  TG UD PD ND  2.177 14.914 22.616  297  ns .02 .001  8.991 7.583 11.751  299  ns ns .05  5.513 17.511 28.831  596  ns .01 .001  1 c e l l with expected count l e s s than 5 2 c e l l s with expected counts l e s s than  5  108 Table  A6  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Both  Goal Type Van  Was  Win  *  Dist'n  P P G UD PD ND  Home Games 2 X n ls 4.277 0.874 1.786*  73 - —  ns ns ns  Team Away 2 X  Poisson Time  Goals Games n  3.047 5.231 6.734  ls 70  ns ns ns  Total 2 X  Games  4.409 3.482 7 . 801  n  ls  143  ns ns ns  NPPG UD PD ND  1.297 14.106 15.737  156  ns .02 .01  3.060 14.364 16.973  199  ns ,02 ,01  3.393 26.348 32.598  355  ns ,001 ,001  T G UD PD ND  0.979 10.933 15.525  229  ns ns .01  1.632 15.208 21.863  269  ns .01 001  2.110 26.093 37.073  498  ns 001 001  P P G UD PD ND  0.773 3.225 5.358  86  ns ns ns  9.113 3.006 2 . 806  82  ns ns ns  5.459 2.324 5.146  168  ns ns ns  NPPG UD PD ND  0.838 9.394 12.483  188  ns ns .05  1.856 15.309 17.201  202  ns ,01 ,01  1.667 22.675 29.554  390  ns ,001 ,001  T G UD PD ND  1.262 11.792 17.690  274  ns .05 .01  3.575 11.829 16.249  284  ns .05 .01  2.655 21.644 32.613  558  ns .001 .001  P P G UD PD ND  5 . 842 3.588 7.586  83  ns ns ns  2.426 1.471 4.481  78  ns ns ns  7.593 4.539 10.387  161  ns ns ns  NPPG UD PD ND  4.632 19.322 21.339  232  ns .01 001  2.639 20.582 24.000  254  ns 001 001  4.880 38.165 43.087  486  ns 001 001  TG UD PD ND  1.959 17.048 23.820  325  ns .01 001  1.858 20.436 27.332  332  ns .01 001  2.219 35.242 49.565  647  ns 001 001  1 cell  with  expected  count  less  than  5  109 Table  A7  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) Goals  Goal Type Bos  Buf  Cal  NB.  Dist'n  P P G UD PD ND  Home Games 2 X n ls 2.548 2.746: 3.930"  41 — —  ns ns ns  Poisson Time  For  Away 2 X  Games  3.499 5.179+ 6.735+  n  ls  Total 2 X  Games ls  n  44 - —  ns ns ns  4.079 5.769 8.305  85  ns ns ns  NPPG UD PD ND  3.084 9.229 11.601  98 ~ —  ns ns .05  3.424 9.159 9.455  103  ns ns ns  3.803 16.989 19.492  201  ns .01 .01  T G UD PD ND  2.016 10.375 13.621  139  ns ns .02  1.630 10.947 13.684  147  ns ns .01  2.429 21.553 27.472  286  ns .001 .001  52 — —  ns ns ns  2.354<< 0.792!! 1.323""  25 — —  ns ns ns  2.910 0.781 3.200  77  ns ns ns  P P G UD PD ND  1.951 1.651 2.665"  NPPG UD PD ND  2.564 3.341 4.793  114  ns ns ns  3.905 2.440 2.883  98  ns ns ns  5 . 855 4.882 4.793  212  ns ns ns  T G UD PD ND  3.093 3.621 7.168  166  ns ns ns  3.660 1.413 3.894  123  ns ns ns  6.327 5.316 10.768  289  ns ns ns  P P G UD PD ND  2.333 3.863 4.936  61 — - -  ns ns ns  41 — —  ns ns ns  5.432 4.493 6.918  102  ns ns ns  NPPG UD PD ND  2.553 12.431 15.200  137  ns .05 .01  4.668 9.580 11.189  110  ns ns .05  5.758 21.046 24.218  247  ns .001 .001  T G UD PD ND  2.681 14.430 17.774  198  ns .02 .01  4.345 9.354 12.376  151  ns ns .05  6.189 22.777 29.553  349  ns .001 .001  Number " = 2,  .  5.833" 3.52K 3.560**  of expected counts l e s s ! = 3, + = 4, < = 5, * *  than = 6,  5 i n d i c a t e d by f o l l o w i n g : " " = 7, ! ! = 8 , << = 10  110 Table  A7  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type Chi  Det  Dist'n  P P G UD PD ND  4.299 1.879' 2.482'  Games  For  Away 2 X  Games  49  ns ns ns  2.340 1.664 i  42  ns ns ns  3.557 2.021 3.872  89  ns ns ns  89  ns ns ns  0.915 8.055 13.106  204  ns ns .05  131  ns ns ns  2.551 8.628 16.078  295  ns ns .01  32 — —  ns ns ns  4.056 6.091 8.484  73  ns ns ns  115  ns ns ns  1.512 6.691 4.923  TG UD PD ND  3.903 4.029 7.066  164  ns ns ns  0.815 6.749 9.888  41 — —  ns ns ns  1.776* 1.106** 1.461**  4.900" 7.571! 8.499!  Games  Is  2.029 3.146 4.923  P P G UD PD ND  Total 2 X  n  NPPG UD PD ND  n  Is  n  Is  NPPG UD PD ND  5.217 9.649 10.216  115  ns ns ns  1.027 5.143 7.758  122 -  ns ns ns  4.619 13.861 17.742  237  ns .02 .01  T G UD PD ND  3.086 10.195 12.967  156  ns ns .05  1.086 4.837 8.812  154 —  ns ns ns  2.794 13.858 21.000  310  ns .02 001  43 — —  ns ns ns  39 — —  ns ns ns  4.677 3.380 6.119  82  ns ns ns  Edm P P G UD PD ND  NB.  Home 2 X  Poisson Time  1.938 6.195 1.215+  5.653" 5.946: 6.879+  NPPG UD PD ND  1.938 6.195 8.698  128  ns ns ns  7.650 14.790 14.516  111  ns .02 .02  3.676 16.945 18.864  239  ns .01 .01  T G UD PD ND  2.930 5.810 8.585  171  ns ns ns  5.550 14.217 15.467  150  ns .02 .01  4.584 17.736 22.119  321  ns .01 001  Number = 1,  of =  expected counts l e s s 3, + = 4, * * 2,  than = 6  five  denoted  by:  Ill Table  A7  Individual C h i - s q u a r e A n a l y s i s of Uniform, Poisson and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g Time ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type Har  LA  Min  NB,  Home Games 2 X n ls  Dist'n  3.502 3.083" 4.936!  P P G UD PD ND  Games n  ls  Total 2 X  Games ls  n  ns ns ns  1.065 2.081" 3.348!  46  ns ns ns  2.483 4.069 7.156  87  ns ns ns  1.811 7.173 9.766  96  ns ns ns  2.631 16.945 19.752  211  ns .01 .01  142  ns ns .05  1.172 18.641 24.832  298  ns .01 001  28 —  ns ns ns  3.818 3.555 5.438  79  ns ns ns  3.980 11.746 13.603  115  ns .05 .02  T G UD PD ND  2.320 12.695 15.148  156  ns .05 .01  51  ns ns ns  4.689 4.128' 5.669'  Away 2 X  41  NPPG UD PD ND  PPG UD PD ND  For  1.380 8.407 12.306 1.468 1.612++  N P P G UD PD ND  4.741 12.619 14.419  159  ns .05 .02  1.285 5.213 9.183  132  ns ns ns  3.862 17.420 22.552  291  ns .01 001  T G UD PD ND  3.525 11.853 15.793  210  ns .05 .01  2.164 7.304 10.524  160  ns ns ns  4.287 18.172 25.087  370  ns .01 001  1.549 4.260* 4.621*  45 — —  ns ns ns  33 — —  ns ns ns  2.016 7.166 8.113  78  ns ns ns  NPPG UD PD ND  1.317 4.302 6.249  96 — —  ns ns ns  2.326 10.364 11.321  84  ns ns ,01  1.984 15.381 17.011  180  ns .01 .01  TG UD PD ND  1.241 7.260 9.429  141  ns ns ns  3.093 15.328 15.207  117  ns .01 .01  2.735 21.082 23.271  258  ns 001 001  P P G UD PD ND  Number *  =  1,  of =  cells 2,  with 3,  i 4.885** 4.277**  expected counts 6 = 8 = i i I  I  r  l e s s than 9 = ++  5:  112 Table  A7  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type  Dist'n  Mon P P G UD PD ND  NJ  NYI  NB.  Home 2 X 3.839" 5.365+ 6.930+  Games  Poisson Time  For  Away 2 X  Games  n  Is  37 - —  ns ns ns  5.662" 3.785** 3.759<  n  Is  43 — —  ns ns ns  Total 2 X  Games n  Is  5.811 4.574 7.520  80  ns ns ns  NPPG UD PD ND  1.594 8.227 9.003  123  ns ns ns  1.506 5.159 7.544  110  ns ns ns  0.867 10.809 14.657  233  ns ns .02  T G UD PD ND  0.250 8.317 10.969  160  ns ns ns  2.697 3.200 7.641  153  ns ns ns  1.554 10.765 18.028  313  ns ns .01  3.073 5.162' 5.447'  46  ns ns ns  2.105 6.838" 6.823*  39  ns ns ns  2.126 8.929 9.141  85  ns ns ns  NPPG UD PD ND  1.317 4.123 6.867  97 — —  ns ns ns  3.483 11.170 11.620  98 — —  ns ns .05  3.147 14.737 18.283  195  ns .02 .01  T G UD PD ND  1.429 5.828 9.189  143  ns ns ns  3.389 15.743 17.347  137  ns .01 .01  3.089 21.429 25.445  280  ns .001 .001  43 — —  ns ns ns  5.338 1.348< 1.469<  41 — —  ns ns ns  84 — —  ns ns ns  P P G UD PD ND  P P G UD PD ND  4.845" 1.551! 1.978+  9.233 2.544 3.387*  NPPG UD PD ND  3.368 10.942 13.370  96 — - -  ns ns .05  1.878 3.998 5.544  82 — —  ns ns ns  3.803 14.185 17.299  178  ns .02 .01  T G UD PD ND  4.437 9.265 12.549  139  ns ns .05  4.640 3.205 6.347  123  ns ns ns  5.581 10.730 16.892  262  ns ns .01  Number " = 2,  of c e l l s with ! = 3, + = 4,  expected counts < = 5, * * = 6  less  than  5:  113 Table  A7  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type  Dist'n  NYR P P G UD PD ND  Phi  Pit  NB.  Home Games 2 X n ls 4.627" 5.474+ 6.582+  Poisson Time  For  Away Games 2 X n  39 — —  ns ns ns  1.527 1.424' 2.142'  Total ls  Games 2 X n  ls  45  ns ns ns  2.776 4.199 6.798  84  ns ns ns  NPPG UD PD ND  4.119 8.881 10.831  121  ns ns ns  0.468 6.521 7.662  104  ns ns ns  2.305 13.309 16.979  225  ns .05 .01  T G UD PD ND  2.100 8.465 11.549  160  ns ns .05  0.305 6.486 9.482  149  ns ns ns  1.179 14.096 20.223  309  ns .02 .01  54 — —  ns ns ns  45 — —  ns ns ns  5.891 3.096 6.686  99  ns ns ns  P P G UD PD ND  4.251 3.682" 5.986*  5.172 2.159+ 3.504+  NPPG UD PD ND  1.409 6.545 9.556  111  ns ns ns  5.717 15.675 15.832  96  ns .01 .01  1.914 18.666 21.414  207  ns .01 001  T G UD PD ND  1.640 7.132 11.981  165  ns ns ns  4.992 13.128 16.719  141  ns .05 .01  2.891 18.500 27.029  306  ns .01 001  60  ns ns ns  0.852 1.719 2.952  59  ns ns ns  3.039 3.510 7.406  119  ns ns ns  ns .02 .02  1.587 3.496 5.993  101  ns ns ns  1.068 14.746 17.638  226  ns .02 .01  ns .05 .01  2.245 5.148 8.980  ns ns ns  1.770 16.094 23.672  345  ns .01 001  P P G UD PD ND  3.333 3.208" 4.634'  NPPG UD PD ND  4.011 14.467 14.551  125  TG UD PD ND  2.086 12.576 15.175  185  Number * = 1 ,  of c e l l s with " = 2 , + = 4  expected  — 160  counts  less  than  5:  114 Table  A7  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type Que  StL  Tor  NB.  Dist'n  P P G UD PD ND  Home 2 X 5.651" 2.487+ 4.341+  Games n  Is  44 - —  ns ns ns  Poisson Time  For  Away 2 X  Games  Total  Games 2  n  Is  X  1.621 3.615! 4.616!  41  ns ns ns  4.680 4.630 7.849  n  Is  85  ns ns ns  NPPG UD PD ND  3.428 4.859 6.108  105  ns ns ns  4.298 8.658 9.490  77  ns ns ns  2 . 831 11.637 15.061  182  ns ,05 ,02  T G UD PD ND  3.863 5.248 9.922  149  ns ns ns  2.245 9.089 11.912  118  ns ns .05  3.520 12.954 19.961  267  ns , 05 .01  33 — —  ns ns ns  5.147" 0.053+ 1.357+  41 — —  ns ns ns  10.210 1.393' 1.953'  70  ns ns ns  2.865 4.784 5.075'  85  ns ns ns  1.889 12.724 16.118  198  ns ,05 ,01  126  ns ns ns  1.074 10.333 17.000  268  ns ns ,01  20 — —  ns ns ns  55  ns ns ns  P P G UD PD ND  6.412" 3.008* 3.148**  NPPG UD PD ND  1.041 8.277 11.560  113  ns ns .05  TG UD PD ND  0.780 6.483 9.806  146  ns ns ns  0.960 4.147 7.223  35 - —  ns ns ns  1.900>> 2.93.1<< 2.409<<  P P G UD PD ND  3.140 0.520+ 1.192+  2.958 1.021 1.494'  N P P G UD PD ND  3.548 13.232 14.061  98 — ~  ns .05 .02  6.265 6.061 6.684  105  ns ns ns  1.683 11.080 14.222  203  ns .05 ,02  T G UD PD ND  1.903 9.366 12.027  133  ns ns .05  5.640 5.111 6.179  125  ns ns ns  2.428 8.997 14.430  258  ns ns 02  Number " = 2,  of c e l l s with ! = 3, + = 4,  expected counts l e s s than * * = 6 , << = 1 0 , >> = 11  5:  115 Table  A7  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type Van  Was  Win  NB.  Dist'n  Home 2 X  Games  For  Away Games 2 X n  ls  3.277* 1.475+ 1.743+  44 — —  ns ns ns  1.8751 4.841+ 5.024+  34 — —  ns ns ns  N P P G UD PD ND  2.419 7.566 7.952  77  ns ns ns  1.232 4.460 5.933  94  ns ns ns  T G UD PD ND  1.805 4.262 7.768  121  ns ns ns  0.554 5.920 8.614  128  ns ns ns  1.062 9.536 15.431  P P G UD PD ND  0.266 2.926 4.115  55  ns ns ns  2.595* 1.2641 1.976+  40 -  ns ns ns  NPPG UD PD ND  1.777 8.280 10.165  104  ns ns ns  4.497 13.344 14.340  104  TG UD PD ND  0.807 9.667 12.347  159  ns ns .05  3.976 11.856 13.878  P P G UD PD ND  2.124 1.767 3.196  45  ns ns ns  NPPG UD PD ND  5.782 16.853 17.046  104  ns .01 .01  T G UD PD ND  3.433 15.129 17.254  149  ns .01 .01  Number ! = 3,  of c e l l s with + = 4, < = 5,  ls  Total 2 X  n  P P G UD PD ND  Poisson Time  Games n  ls  78  ns ns ns  171  ns ns ,02  249  ns ns .01  1.569 3.474 5.409  95  ns ns ns  ns .05 .02  1.983 17.325 19.094  208  ns ,01 ,01  144  ns .05 .02  1.012 18.222 23.756  303  ns .01 001  34 -  ns ns ns  4.328 0.679 3.550  79  ns ns ns  2.521 7.872 10.306  111  ns ns ns  3.055 19.209 22.587  215  ns .01 001  1.741 5.309 9.609  145  ns ns ns  2.367 17.878 25.058  294  ns .01 001  5.077' 1.087< 1.678**  expected ** = 6  counts  less  1.881 2.758 4.652 2.435 10.289 13.675  than  5  116 Table  A8  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s for Actual Playing ( T e n M i n u t e D i v i s i o n s : d f = 5)  Goals  Goal Type Bos  Buf  Cai  NB.  Dist'n  Home 2 X  Games n  Against  Away Games 2 X n  Is  Poisson Time  Total  Games 2  Is  X  n  Is  3.886+ 1.221** 1.975**  36 — —  ns ns ns  3.956+  30  ns ns ns  5.135 2.789 5.817  66  ns ns ns  NPPG UD PD ND  1.878 9.447 9.863  97  ns ns ns  0.992 4.463 6.735  91  ns ns ns  5.786 11.398 15.223  188  ns .05 .01  TG UD PD ND  2.326 6.890 10.283  133  ns ns ns  1.671 5.374 9.115  121  ns ns ns  2.059 10.157 17.190  254  ns ns 01  2.340 4.760* 5.259*  46 — —  ns ns ns  €.071" 1.034+ 0.674+  40 - —  ns ns ns  3.012 1.24.2 4.124  86  ns ns ns  NPPG UD PD ND  1.247 6.562 8.432  93 — —  ns ns ns  2.224 13.642 14.036  116  ns .02 .02  2.671 18.522 22.138  209  ns .01 001  T G UD PD ND  2.381 9.097 13.697  139  ns ns .02  0.812 8.836 12.500  156  ns ns .05  2.282 18.229 25.466  295  ns .01 001  5.401+ 3.054** 3.1461  34 — ~  ns ns ns  5.314*  44 —  8 .796 2.619 4.499  78  2.044+  ns ns ns  ns ns ns  NPPG UD PD ND  0.821 5.714 6.336  68 — —  ns ns ns  0.860 3.669 5.003  77  ns ns ns  0.412 7 . 552 10.186  145  ns ns ns  T G UD PD ND  1.249 2.969 5.827  102 - - -  ns ns' ns  2.887 2.052 5.460  121  ns ns ns  3.307 5.034 11.178  223  ns ns .05  cells = 2,  with = 3,  P P G UD PD ND  P P G UD PD ND  P P G UD PD ND  Number = 1,  of  expected + = 4,  counts = 6,  l e s s than = 8  5:  117 Table  A8  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type Chi  Det  Dist'n  P P G UD PD ND  2.925 2.208 3.017'  Against  Away Games 2 X n  Total  Games 2  ls  X  n  ls  51  ns ns ns  1.416 3.439 5.150  71  ns ns ns  2.305 3.793 6.826  122  ns ns ns  NPPG UD PD ND  5.325 3.655 4.330  102  ns ns ns  2.220 9.284 9.003  108  ns ns ns  4.498 10.907 13.485  210  ns ns .02  T G UD PD ND  7.140 5.409 7.132  153  ns ns ns  1.303 11.174 13.905  179  ns .05 .02  4.230 13.049 19.004  332  ns .05 .01  32 — - -  ns ns ns  46  ns ns ns  4.473 3.641 5.486  78  ns ns ns  P P G UD PD ND  1.422< 1.519** 2.236+  4.129* 3.085" 2.870"  N P P G UD PD ND  5.343 9.522 12.054  108  ns ns .05  2.333 8.116 10.528  129  ns ns ns  6.573 15.821 20.675  237  ns .01 .001  T G UD PD ND  4.421 8.411 12.470  140  ns ns .05  3.178 7.533 10.813  175  ns ns ns  6.373 15.827 22.752  315  ns .01 001  30 — —  ns ns ns  47 — —  ns ns ns  6.092 3.003 5.735  77  ns ns ns  Edm P P G UD PD ND  NB.  Home Games 2 X n ls  Poisson Time  2.778** 0.995"" 3.004**  3.585 1.743" 3.128+  NPPG UD PD ND  1.491 7.599 9.552  119  ns ns ns  1.628 11.227 12.532  107  ns .05 .05  0.692 16.304 19.564  226  ns .01 .01  T G UD PD ND  1.069 6.673 9.664  149  ns ns ns  0.978 9.535 13.170  154  ns ns .05  0.550 15.227 21.604  303  ns .01 001  Number " = 2,  of c e l l s with expected < = 5, * * = 6  counts  less  than  5:  118 Table  A8  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type Har  LA  Min  NB,  Dist'n  P P G UD PD ND  Home Games 2 X n Is 3.831* 6.448* 7.133*  40 — —  ns ns ns  Poisson Time  Against  Away Games 2 X n  4.029+ 3.545<  Total  Games 2  Is  X  n  Is  30 - —  ns ns ns  4.982 9.618 10.304  70  ns ns ns  NPPG UD PD ND  2.282 5.651 7.821  102  ns ns ns  1.375 8.464 10.093  114  ns ns ns  2.389 12.920 16.114  216  ns .05 .01  T G UD PD ND  3.618 10.060 12.124  142  ns ns .05  1.774 11.862 12.857  144  ns .05 .05  3.904 20.065 24.356  286  ns .01 001  34 — —  ns ns ns  45 — —  ns ns ns  1.869 2.081 3.696  79  ns ns ns  P P G UD PD ND  4.566! 2.079+ 2.151+  0.381 1.610* 2.196"  N P P G UD PD ND  4.813 15.832 17.971  134  ns .01 .01  8.165 11.882 12.993  121  ns .05 .05  11.397 26.851 30.412  255  .05 001 001  T G UD PD ND  2.579 16.023 18.626  168  ns .01 .01  6.788 12.853 17.492  166  ns .01 .01  6.973 27.696 33.125  334  ns 001 001  0.767 3.174* 4.017*  39 — —  ns ns ns  0.342 3.445 3.298  43  ns ns ns  0.658 6.713 7 .420  82  ns ns ns  NPPG UD PD ND  3.981 5.906 7.746  95 — —  ns ns ns  2.230 7.024 8.528  100  ns ns ns  4.423 10.950 14.779  195  ns ns .02  T G UD PD ND  3.065 8.497 11.043  134  ns ns ns  1.453 9.784 11.555  143  ns ns .05  3.516 17.032 21.987  277  ns .01 ,001  P P G UD PD ND  Number * =1,  of c e l l s with expected counts = 3, + = 4, < = 5, = 2,  less = 8  than  5:  119 Table  A8  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type  Dist'n  Away Games 2 X n  ls  Total 2 X  Games n  ls  28 — —  ns ns ns  4.015+ 0.433* 1.153*  30 — —  ns ns ns  2.295 1.670 2.475  58  ns ns ns  NPPG UD PD ND  4.986 6.041 7.525  76  ns ns ns  0.510 4.034 4.949  84  ns ns ns  3.796 8.418 9.927  160  ns ns ns  T G UD PD ND  3.922 6.396 7.389  104  ns ns ns  1.805 3.440 5.705  114  ns ns ns  4.248 8.087 12.450  218  ns ns .05  PPG UD PD ND  0.481 1.958 2.788  56  ns ns ns  1.866 3.159 3.910  57  ns ns ns  1.854 4.461 6.654  113  ns ns ns  NPPG UD PD ND  3.485 8.566 10.426  91  ns ns ns  2.821 12.921 14.124  117  ns .05 .02  4.001 19.547 22.908  208  ns .01 001  TG UD PD ND  2.859 10.260 12.428  147  ns ns .05  1.949 15.272 17.139  174  ns .01 .01  3.832 22.849 28.827  321  ns 001 001  49  ns ns ns  2.169 4.599' 6.344'  54  ns ns ns  0.943 6.425 7 .776  103  ns ns ns  NY I PPG UD PD ND  NB.  Against  2.614"" 2.511<< 3.230++  Mon P P G UD PD ND  NJ  Home Games 2 X n Is  Poisson Time  0.300 2.414 3.311*  -  NPPG UD PD ND  1.250 10.053 10.414  100  ns ns ns  3.165 4.567 6.884  119  ns ns ns  2.679 12.175 16.664  219  ns ,05 .01  T G UD PD ND  0.773 11.487 13.775  149  ns .05 .02  2.553 7.106 10.705  173  ns ns ns  1.862 17.151 23.827  322  ns .01 001  Number * = 1,  of c e l l s with " = 2, + = 4,  expected counts " " = 7 , ++ = 9 ,  l e s s than << = 10  5:  120 Table  A8  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type  Dist'n  NYR P P G UD PD ND  Phi  Pit  NB.  Home G a m e s 2 X n Is  12.110< 5.580** 4.514+  37 — —  ns ns ns  NPPG UD PD ND  1.437 10.963 11.712  99  ns ns .05  T G UD PD ND  1.127 6.533 9.637  146  4.103+ 7.421+ 7.456+  NPPG UD PD ND  Poisson Time  Against  Away 2 X  Games  Total  Games 2  n  3.692 1.601+ 3.198!  Is  X  n  Is  48  ns ns ns  9.792 1.423 3.304  85  ns ns ns  1.457 4.495 6.326  112  ns ns ns  1.554 13.204 16.482  221  ns .05 .01  ns ns ns  1.594 4.183 7.461  160  ns ns ns  1.954 8 .946 16.451  306  ns ns .01  38  ns ns ns  2.776 4.446' 6.511'  42  ns ns ns  5.610 11.538 12.725  80  ns ,05 ,05  1.744 2.173 3.749  92 — —  ns ns ns  2.281 5.481 9.119  108  ns ns ns  2.480 5.425 11.212  200  ns ns .05  T G UD PD ND  1.405 6.073 9.697  130  ns ns ns  2.249 8.023 12.384  150  ns ns .05  1.658 12.197 20.128  280  ns ,05 ,01  P P G UD PD ND  1.728 3.355 5.459  55  ns ns ns  2.498 6.153 6.870  57  ns ns ns  2.094 7.702 9.857  112  ns ns ns  N P P G UD PD ND  1.650 6.624 8.064  104  ns ns ns  0.870 8.002 10.624  132  ns ns ns  2.202 13.212 18.635  236  ns .05 ,01  TG UD PD ND  2.045 8.698 12.781  159  ns ns .05  1.518 11.802 14.889  189  ns ,05 02  3.162 19.730 26.767  348  ns .02 001  P P G UD PD ND  Number ii = _ 3,  of c e l l s with + = 4, < = 5,  expected ** = 6  counts  less  than  5:  121 Table  A8  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type Que  StL  Tor  NB.  Dist'n  P P G UD PD ND  Home 2 X  i  2.119! 3.697**  Games n  Against  33 — —  ns ns ns  Games 2 X n  Total  Away ls  Poisson Time  4.664 4.308! 5.339+  Games 2  ls  X  n  ls  48 ~ —  ns ns ns  6.970 5.953 8.548  81  ns ns ns  NPPG UD PD ND  0.542 6.283 9.678  127  ns ns ns  0.982 9.266 11.358  133  ns ns .05  1.400 15.449 30.946  260  ns .01 001  T G UD PD ND  1.689 7.728 11.552  160  ns ns .05  1.970 9.757 14.562  181  ns ns .02  3.499 16.975 25.972  341  ns .01 001  30 — —  ns ns ns  2.582 0.742' 1.546'  53  ns ns ns  3.246 1.326 3.920  83  ns ns ns  P P G UD PD ND  2.660+ 2.885** 3.538**  NPPG UD PD ND  2.113 10.424 10.244  86  ns ns ns  1.491 8.504 9.068  115 — —  ns ns ns  2 .385 18.225 19.332  201  ns ,01 ,01  TG UD PD ND  0.987 9.536 11.222  116  ns ns .05  4.454 3.202 6.596  174  ns ns ns  4.188 8.933 15.632  338  ns ns ,01  46 — —  ns ns ns  1.272 1.022 2.007*  52 — —  ns ns ns  4.265 0.820 2.469  98  ns ns ns  P P G UD PD ND  5.122 1.252! 1.765+  N P P G UD PD ND  1.427 9.975 10.904  118  ns ns ns  4.098 3.227 4.290  122  ns ns ns  2.417 10.424 14.670  240  ns ns ,02  TG UD PD ND  1.337 6.938 10.695  164  ns ns ns  4.454 3.202 6.596  174  ns ns ns  4.188 8.933 15.632  338  ns ns ,01  Number * = 1,  of c e l l s with " = 2, ! = 3,  expected counts + = 4, * * = 6  less  than  5:  122 Table  A8  I n d i v i d u a l Team C h i - s q u a r e A n a l y s i s o f U n i f o r m , and Normal D i s t r i b u t i o n s f o r A c t u a l P l a y i n g ( T e n M i n u t e D i v i s i o n s : d f = 5) (continued) Goals  Goal Type  Dist'n  V a n P P G UD PD ND  3 . 4 6 8 ! ! 29 2.037 ! 1 2.435! I  — —  NPPG UD PD ND  4.535 12.016 12.527  79  T G UD PD ND  3.466 9.554 11.308  Was P P G UD PD ND  2.373!! 2.334!1 2.616""  N P P G UD PD ND  1.238 3.044 4.687  T G UD PD ND  1.514 3.166 5.685  W i n P P G UD PD ND  NB.  Home Games 2 X n ls  5.019+ 2.433** 5.313**  Against  Away Games 2 X n 3 .491" 2 .882** 4 .160**  ns ns ns  Poisson Time  36  — —  Total  Games 2 X n  ls ns ns ns  3 .279 1 .516 2 .870  ns ns 05  5 .045 19 . 9 3 4 22 . 0 0 7  65  — —  ns ns ns  ns .05 .05  3 .073 9 .828 11 . 3 9 1  105  108  ns ns .05  2 .440 5 .098 8 .746  141  ns ns ns  4 .107 18 . 1 6 8 22 . 9 1 4  249  ns .01 .001  31  ns ns ns  8 .206+ 2 .504 + 1 .204+  42  ns ns ns  6 .209 0 .863 0 . 877  73  ns ns ns  ns ns ns  1 .950 5 .769 7 .544  ns ns ns  2 .316 8 .367 11 . 0 5 1  182  ns ns ns  — —  — — 84  — — 115  ns ns ns  38  — —  ,  — — 98  — -—  184  ls  •  -—  ns .01 .001  3 .773 3 .340 5 .751  140  ns ns ns  4 .708 5 .627 10 . 6 3 8  255  ns ns ns  ns ns ns  1 .643 4 .463 5 .861  44  ns ns ns  4 .363 4 .934 8 .559  82  ns ns ns  --  —  -—  NPPG UD PD ND  4.088 7 .468 9.297  128  ns ns ns  3 .504 15 . 5 0 4 15 . 6 0 2  143  ns 01 01  5 .327 21 . 5 1 6 23 . 9 7 7  271  ns .001 .001  TG UD PD ND  2.220 5.577 9.144  166  ns ns ns  2 .896 17 . 1 3 2 19 . 3 0 9  187  ns 01 01  2 .663 21 . 1 8 1 27 . 2 0 7  353  ns .001 .001  Number o f c e l l s w i t h e x p e c t e d 2, + = 4, * * = 6, 7,  ——— ^  counts ! ! =8  less  than  5:  123 Table  A9  T o t a l Team C h i - s q u a r e C o m p a r i s o n o f S h o t D i s t r i b u t i o n s with Theoretical Normal, Uniform, Poisson, Geometric and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s TOTAL Shots/Game / S c a l e Observed 31 - 4 0 / 1 5 41 - 5 0 / 2 103 51 - 6 0 / 3 296 61 - 7 0 / 4 323 71 - 8 0 / 5 95 81 - 9 0 / 6 18 1 91 - 1 0 0 / 7  SHOTS  Expected Normal Uniform P o i s s o n 9 140 86 93 140 153 302 140 180 316 140 159 140 113 107 12 140 67  Geometric 420 210 105 53 26 13  Chisquare Normal 3 .702 Uniform 362 . 2 9 0 Poisson 192 . 0 3 7 Geometric 766 . 7 7 0 Negative Binomial 5 .087  Scale  -0 1 2 3 4  df 5 5 5 5 4  Negative Binomial Obs/Exp 108/109 296/302 323/300 9 5 / 95 1 8 / 18  Is n. s . 001 001 001 n. s .  SHOTS FOR 12 - 1 6 / 1 17 - 2 1 / 2 22 - 2 6 / 3 27 - 3 1 / 4 32 - 3 6 / 5 37 - 4 1 / 6 42 - 4 6 / 7 47 - 5 1 / 8 52 - 5 6 / 9 57 - 6 1 / 1 0 62 - 6 6 / 1 1  22 131 370 472 359 203 92 19 7 0 1  33 131 319 466 411 218 70 13  209 209 209 209 209 209 209 209  101 215 304 323 275 195 118 63  Normal Uniform Poisson Geometric N e g a t i v e '.B i n o m i a l  834 417 209 104 52 26 13 7 Chisquare 14.158 559.127 142.035 1630.499 6.330  0 1 2 3 4 5 6 7 df 7 7 7 7 7  27 144 338 458 391 216 76 16 Is .05 .001 .001 .001 n. s .  Table Total with  Team C h i - s q u a r e C o m p a r i s o n o f S h o t Distributions T h e o r e t i c a l Normal, Uniform, Poisson, Geometric and N e g a t i v e B i n o m i a l Distributions (continued) SHOTS  Shots/Game /Scale 12-16/1 17-21/2 22-26/3 27-31/4 32-36/5 37-41/6 42-46/7 47-51/8 52-56/9 57-61/10 62-66/11  Expected Geometric c3 cl c2 8 3 5 838 839 417 4 1 9 420 2 0 9 210 210 104 1 0 5 1 0 5 52 52 52 26 26 26 13 13 13 7 7 7  Observed c2 cl c3 23 23 23 129 1 2 9 129 374 374 374 468 468 468 367 367 367 198 198 198 92 92 92 25 18 27  Normal  cl c2 c3  Poisson  cl c2 c3  Chisquare 13.121 15.526 16.461 145.012 135.216 132.604  AGAINST  Expected Normal c3 cl c2 32 34 34 132 132 132 3 2 0 317 317 468 4 6 3 462 411 412 412 2 1 7 222 224 69 73 74 18 15 15  Observed cl c2 c3 23 23 23 1 2 9 1 2 9 129 374 374 374 468 468 468 367 367 367 198 198 198 92 92 92 18 25 27 7 0 2  Shots/Game /Scale 12-16/1 17-21/2 22-26/3 27-31/4 32-36/5 37-41/6 42-46/7 48+ /8  df 7 7 7 7 7 7  Is n. s . . 05 .05 .001 .001 .001  Negative  cl c2 c3  = Scale = Scale = Scale  is is is  A9  1 to 1 to 1 to  8, 9, 11  Expected Uniform cl c2 c3 209 210 2 1 0 209 210 210 209 2 1 0 2 1 0 209 210 2 1 0 209 210 210 209 2 1 0 210 209 210 210 2 0 9 210 2 1 0  Scale 0 1 2 3 4 5 6 7  Expected Poisson cl c2 c3 102 102 102 216 2 1 5 214 3 0 5 3 0 5 305 324 3 2 5 3 2 5 2 7 5 277 277 1 9 5 197 197 118 120 120 63 64 64  Expected Negative Binomial cl c2 c3 27 27 28 144 145 145 338 339 338 455 460 456 392 391 390 215 219 220 75 80 81 16 18 19  Uniform  cl c2 c3  Geometric  cl c2 c3  Binomial  cl c2 c3  Chisquare df 7 563.662 7 548.480 544.148 7  Is .001 .001 .001  1631.871 1639.386 1642.801  7 7 7  .001 .001 .001  6.302 7.023 7.374  7 7 7  n. s n. s n. s  9 t o 11 n o t i n c l u d e d ( t o t a l n - 9) 10 t o 11 n o t i n c l u d e d ( t o t a l n - 2) ( b a s e d o n t o t a l n)  125 Table  A10  T o t a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s with T h e o r e t i c a l Normal, Uniform, Poisson, Geometric and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s (continued) TOTAL  GOALS  Goals/Game Expected / S c a l e Observed Normal Uniform 22 24 105 0-2 / 1 88 86 105 3-4 / 2 5-6 / 3 205 185 105 7-8 / 4 238 239 105 175 105 9-10/ 5 186 72 87 105 11-12/6 32 105 13-14/7 24 15-16/8 9 4 105  Normal Uniform Poisson Geometric Negative Binomial  GOALS Shots/Game / S c a l e Observed 45 0 154 1 2 283 3 340 314 4 238 5 6 149 7 82 51 8 15 9 7 10 11 2  Poisson 61 123 164 164 132 88 50 25  Chisquare 5 . 932 2 8 2 . 963 6 0 . 736 7 2 9 . 615 2 . 807  Geometric 421 210 105 53 26 13 7 3  df 7 7 7 7 7  Scale 0 1 2 3 4 5 6 7  Negative Binomial 21 97 197 232 174 86 28 6  Scale 0 1 2 3 4 5 6 7 8 9  Negative Binomial 41 152 282 348 323 239 148 80 37 15  ls n.s. .001 .001 .001 n.s.  FOR/AGAINST  Expected N o r m a l U n i f o r mi P o i s s o n 54 140 41 152 129 140 282 234 140 348 323 140 140 323 342 140 239 276 148 171 140 78 80 140 140 36 29 140 15 8 140 140  Chisquare Normal 21 . 6 4 2 Uniform • 685 . 3 7 8 Poisson 3 .088 Geometric 1556 . 3 8 9 Negative Binomial 2 .668  1  Geometric 836 418 209 104 52 26 13 7 3 2  df 9 11 9 9 9  Is .02 .001 n.s. .001 n.s.  126 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l Distributions w i t h T h e o r e t i c a l Normal, U n i f o r m , P o i s s o n , Geometric and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l Total Boston Time (min) 0-5 5-10 10-15 15-20 20-25 25+  2 Sc 1 2 3 4 5 6  Obs 218 126 59 28 17 17  Buffalo 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  1 2 3 4 5 6  245 147 63 28 14 12  244 130 65 38 7 16  Chicago 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  Detroit 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  ND 103 140 107 47 11 2  UD 78 78 78 78 78 78  PD 124 126 85 43 18 6  GD 233 116 58 29 15 7  Sc 0 1 2 3 4 5  NBD 212 130 66 31 14 6  85 85 85 85 85 85  143 138 88 43 16 5  255 127 64 32 16 8  0 1 2 3 4 5  83 83 83 83 83 83  138 135 89 43 17 6  250 125 63 31 16 8  161 149 92 42 16 5  157 148 93 44 17 5  ND UD PD GD NBD  70 182 34 5 6  X .579 .059 .594 .177 .203  df 5 5 5 5 5  Is .001 .001 .001 n. s . n. s .  243 145 69 30 13 5  ND UD PD GD NBD  65 232 31 2 3  .131 .024 .496 . 819 .267  5 5 5 5 5  .001 .001 .001 n. s . n. s .  0 1 2 3 4 5  236 141 69 31 14 6  ND UD PD GD NBD  69 218 36 7 8  .401 .083 .905 .052 .279  5 5 5 5 5  .001 .001 .001 n. s . n. s .  276 138 69 35 17 9  0 1 2 3 4 5  292 143 65 29 13 6  ND UD PD GD NBD  90 276 51 7 6  .622 .967 .138 .017 .599  5 5 5 5 5  .001 .001 .001 n. s . n. s .  275 137 69 34 17 9  0 1 2 3 4 5  273 153 71 31 13 5  ND UD PD GD NBD  73 269 41 7 7  .133 .098 .290 .184 .278  5 5 5 5 5  .001 .001 .001 n. s . n. s .  Sabres  Calgary 0-5 5-10 10-15 15-20 20-25 25+  Games  Bruins  125 168 114 38 7 1 Flames 119 160 113 42 8 1  Black  299 132 71 21 13 16  Hawks  142 180 116 38 6 1  92 92 92 92 92 92  Red Wings 273 156 69 27 8 16  140 184 119 38 6 0  92 92 92 92 92 92  127 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s w i t h T h e o r e t i c a l Normal, U n i f o r m , P o i s s o n , Geometric and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l (c'd) Total Edmonton Time (min) 0-5 5-10 10-15 15-20 20-25 25+  2 Sc 1 2 3 4 5 6  Obs 292 146 60 30 12 11  Hartford 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6 Los  0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  ND 146 187 114 33 5 0  1 2 3 4 5 6  254 137 60 28 17 13  0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  123 163 113 41 8 1  Angeles 335 175 70 31 10 10  PD 162 148 90 41 15 5  GD 276 138 69 34 17 9  Sc 0 1 2 3 4 5  NBD 288 149 67 28 12 5  85 85 85 85 85 85  143 138 89 43 17 5  225 127 64 32 16 8  0 1 2 3 4 5  249 140 67 30 13 6  189 169 101 45 16 5  316 158 79 39 20 10  0 1 2 3 4 5  333 174 75 30 11 4  123 123 82 41 16 5  228 114 57 29 14 7  0 1 2 3 4 5  124 123 81 40 14 5  227 114 57 28 12 7  0 1 2 3 4 5  80 279 39 2 2  X .621 .901 .837 .558 .759  df 5 5 5 5 5  ls .001 .001 .001 n.s. n.s.  76 227 37 1 3  .528 .724 . 839 .949 .634  5 5 5 5 5  .001 .001 .001 n.s. n.s.  ND UD PD GD NBD  79 341 42 6 2  .408 .948 .673 .149 .804  4 5 5 5 5  .001 .001 .001 n.s. n.s.  209 129" 65 30 13 6  ND UD PD GD NBD  68 183 30 2 4  . 369 .971 .408 .405 .390  4 5 5 5 5  .001 .001 .001 n.s. n.s.  202 137 68 29 13 4  ND UD PD GD NBD  50 194 21 3 3  .631 .074 .297 .499 .174  4 5 5 5 5  .001 .001 .001 n.s. n.s.  ND UD PD GD NBD  184 237 121 24 2  108 149 105 38 7  ND UD PD GD NBD  Kings  North  221 113 63 28 22 9  Montreal  UD 92 92 92 92 92 92  Whalers  Minnesota 0-5 5-10 10-15 15-20 20-25 25+  Games  Oilers  105 105 105 105 105 105 Stars 76 76 76 76 76 76  Canadiens  209 125 67 34 10 9  111 160 105 32 4  76 76 76 76 76 76  128 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s w i t h T h e o r e t i c a l N o r m a l , U n i f o r m , P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l (c'd) Total Time (min) 0-5 5-10 10-15 15-20 20-25 25+  New  Jersey  Sc 1 2 3 4 5 6  Obs 276 135 64 30 10 11  2  New 0-5 5-10 10-15 15-20 20-25 25+  York 1 2 3 4 5 6  ND 132 180 127 46 9 1  1 2 3 4 5 6  124 166 114 40 7 1  248 145 58 33 13 13  1 2 3 4 5 6  147 197 111 26 3  274 143 76 22 12 10  256 128 66 32 14 16  Pittsburgh 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  330 167 61 30 21 5  PD 153 142 87 40 15 5  GD 278 139 70 35 17 9  Sc 0 1 2 3 4 5  NBD 270 144 65 28 12 5  143 138 89 43 17 5  255 128 64 32 16 8  0 1 2 3 4 5  245 144 69 31 13 5  156 145 89 41 15 5  269 134 67 34 17 8  0 1 2 3 4 5  269 152 69 29 11 4  141 139 91 44 17 6  256 128 64 32 16 8  0 1 2 3 4 5  247 140 68 32 14 6  183 165 100 45 16 5  308 154 77 39 19 10  0 1 2 3 4  323 171 73 29 11  ND UD PD GD NBD  85 261 36 8 2  X .013 .270 .611 .871 . 861  70 229 34 2 4  df 5 5 5 5 5  Is .001 .001 .001 n. s . n. s .  85 85 85 85 85 85  ND UD PD GD NBD  .500 .248 .578 .919 .584  5 5 5 5 5  .001 .001 .001 n. s . n. s .  65 271 33 4 4  .637 .174 .921 . 501 .226  4 5 5 5 5  .001 .001 .001 n. s . n. s .  78 218 38 2 5  .130 .885 .949 .768 . 249  5 5 5 5 5  .001 .001 .001 n. s . n. s .  90 326 46 4 7  .697 . 899 .765 .878 .255  4 5 5 5 4  .001 .001 .001 n. s . n. s .  Rangers  Philadelphia 0-5 5-10 10-15 15-20 20-25 25+  UD 88 88 88 88 88 88  Islanders  New Y o r k 0-5 5-10 10-15 15-20 20-25 25+  Games  Devils  90 90 90 90 90 90  ND UD PD GD NBD  Flyers  121 160 115 45 9 1  85 85 85 85 85 85  ND UD PD GD NBD  Penguins 174 222 121 28 3  102 102 102 102 102 102  ND UD PD GD NBD  129 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s w i t h T h e o r e t i c a l N o r m a l , U n i f o r m , P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l (c'd) Total Quebec Time (min) 0-5 5-10 10-15 15-20 20-25 25+  2 Sc 1 2 3 4 5 6  St . 0-5 5-10 10-15 15-20 20-25 25+  ND 131 177 118 39 6 1  Obs 259 146 67 35 13 11  1 2 3 4 5 6  1 2 3 4 5 6  111 149 109 43 9 1  237 121 58 38 10 16  Maple  268 135 65 27 12 14  131 170 113 38 6 1  Vancouver 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  177 114 66 36 12 19  Washington 0-5 5-10 10-15 15-20 20-25 25+  UD 89 89 89 89 89 89  PD 149 144 92 44 17 5  GD 266 133 66 33 17 8  Sc 0 1 2 3 4 5  NBD 253 152 73 31 13 5  ND UD PD GD NBD  80 80 80 80 80 80  131 130 86 42 17 6  240 120 60 30 15 8  0 1 2 3 4 6  227 132 65 30 14  149 141 89 42 16 5  261 130 65 33 16 8  0 1 2 3 4 5  181 96 75 45 21 8  212 106 53 27 13 7  136 131 84 41 16 5  243 121 61 30 15 8  66 240 31 1 2  X .934 .951 .099 .712 .926  df 5 5 5 5 5  ls .001 .001 .001 n.s. n.s.  ND UD PD GD NBD  74 201 37 4 7  .273 .688 .896 .614 .208  5 5 5 5 5  .001 .001 .001 n.s. n.s.  262 141 66 29 13 5  ND UD PD GD NBD  75 247 39 2 4  .508 .006 .712 .933 .557  5 5 5 5 5  .001 .001 .001 n.s. n.s.  0 1 2 3 4 5  168 125 69 34 16 7  ND UD PD GD NBD  54 138 14 11 6  .079 .912 .550 .682 .945  5 5 5 5 5  .001 .001 .02 .05 n.s.  0 1 2 3 4 5  229 141 67 29 12 5  ND 63 . 4 6 8 219 . 5 3 9 UD 27 . 4 1 2 PD GD 1 .782 NBD 2 .456  4 5 5 5 5  .001 .001 .001 n.s. n.s.  Louis Blues  Toronto 0-5 5-10 10-15 15-20 20-25 25+  Games  Nordique  1 2 3 4 5 6  235 136 57 36 13 8  Leafs 87 87 87 87 87 87  Canucks 86 123 103 51 14 2  71 71 71 71 71 71  Capitols 124 170 108 31 4  81 81 81 81 81 81  130 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s w i t h T h e o r e t i c a l Normal, U n i f o r m , P o i s s o n , Geometric and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l (c'd) Total Time (min) 0-5 5-10 10-15 15-20 20-25 25+  Winnipeg  Jets  Sc 1 2 3 4 5 6  ND 158 212 119 28 3  Games 2  Obs 290 159 74 32 10 10  UD 96 96 96 96 96 96  PD 167 155 96 45 17 5  GD 288 144 72 36 18 9  Sc 0 1 2 3 4 5  NBD 286 165 75 31 12 4  ND UD PD GD NBD  67 287 34 3 2  X .195 .461 .285 .295 .911  df 4 5 5 5 5  Is .001 .001 .001 n. s . n. s .  Home Games Boston Bruins 1 51 0-5 110 2 69 5-10 63 10-15 3 29 55 4 25 15-20 16 20-25 5 8 7 25+ 6 10 1 Buffalo 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  139 68 34 16 6 5  Calgary 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  130 71 33 17 3 9  Chicago 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  62 64 44 23 9 3  118 59 30 15 7 4  0 1 2 3 4 5  106 65 34 16 8 4  ND UD PD GD NBD  37 88 19 3 3  .732 .171 .487 .080 .055  5 5 5 5 5  .001 .001 .001 n. s . n. s .  45 45 45 45 45 45  78 72 44 21 8  134 67 34 17 8  0 1 2 3 4  133 78 35 14 5  ND UD PD GD NBD  35 129 15 0 3  .954 . 840 .701 .482 .198  4 5 4 4 4  .001 .001 .001 n. s . n. s .  44 44 44 44 44 44  74 71 46 22 9 3  132 66 33 16 8  0 1 2 3 4 5  128 73 35 16 7 3  ND UD PD GD NBD  34 121 21 0 4  .873 .245 .323 .905 .731  4 5 5 4 5  .001 .001 .001 n. s . n. s .  ND 53 . 8 7 5 UD 150 . 2 4 2 PD 31 . 4 5 9 GD 7 .746 NBD 8 .067  4 5 5 5 5  .001 .001 .001 n. s . n. s .  Sabres 72 95 56 15 2  Flames 68 92 58 17 12  Black  162 60 32 8 11 5  39 39 39 39 39 39  •  Hawks  78 96 54 14 2  46 46 46 46 46 46  84 74 44 19 7  139 70 35 17 9  0 1 2 3 4  155 71 30 13 5  131 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s w i t h T h e o r e t i c a l N o r m a l , U n i f o r m , P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l (c'd) Home Games Detroit Time (min) 0-5 5-10 10-15 15-20 20-25 25+  2 Sc 1 2 3 4 5 6  Obs 118 79 33 14 4 9  Edmonton 0-5 5-10 10-15 15-20 20-25 25+  Red Wings  1 2 3 4 5 6  1 2 3 4 5 6 Los  0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  154 68 35 16 5 4  131 70 28 16 9 7  1 2 3 4 5 6  80 103 55 12 1  PD 71 70 46 22 9 3  GD 129 64 32 16 8 4  Sc 0 1 2 3 4 5  NBD 119 74 36 16 7 3  ND UD PD GD NBD  30 116 18 5 4  X .319 .222 .465 .437 .242  47 47 47 47 47 47  84 75 45 20 _7  141 71 35 18 9  0 1 2 3 4  147 80 34 13 5  ND UD PD GD NBD  40 147 17 0 2  74 71 45 21 _8  131 65 33 16 8  0 1 2 3 4  126 75 35 15 _6  ND UD PD GD NBD  108 90 51 21 7  172 86 43 22 11 5  0 1 2 3 4  193 96 37 13 4  ND UD PD GD NBD  66 64 41 20 8  118 59 30 15 7  0 1 2 3 4  108 73 34 14 5  df 4 5 5 5 5  Is .001 .001 .001 n. s . n. s .  .315* .983 .983 .640 .587  4 5 4 4 4  .001 .001 .001 n. s . n. s .  42 115 19 1 5  .441 .746 .632 .441 .595  4 5 4 5 4  .001 .001 .001 n. s . n. s .  44 210 23 11 1  .550+ .689 .982 .566 .747  4 5 4 5 4  .001 .001 .001 .05 n. s .  4 5 4 4 4  .001 .001 .02 n. s . n. s .  Whalers 65 88 58 19 3  Angeles 195 95 32 14 2 6  Minnesota 0-5 5-10 10-15 15-20 20-25 25+  UD 43 43 43 43 43 43  Oilers  Hartford 0-5 5-10 10-15 15-20 20-25 25+  ND 65 91 58 17 2  113 63 36 13 8 3  111 135 56 8 0  44 44 44 44 44 44 Kings 57 57 57 57 57 57  North Stars 60 83 53 15 2  39 39 39 39 39 39  ND 27 . 4 9 2 UD 106 . 0 9 1 PD 11 . 5 6 8 GD 1 .712 NBD 3 .184  132 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s w i t h T h e o r e t i c a l N o r m a l , U n i f o r m , P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l (c'd) Home Montreal Time (min) 0-5 5-10 10-15 15-20 20-25 25+  2 Sc 1 2 3 4 5 6  New 0-5 5-10 10-15 15-20 20-25 25+  ND 54 78 54 18 3  Obs 101 67 29 19 7 4  1 2 3 4 5 6  67 88 53 15 2  132 61 34 13 8 4  1 2 3 4 5 6  1 2 3 4 5 6  60 86 58 19 3  GD 114 57 28 14 7  73 68 42 19 J7  26 92 9 3 2  X .349 .983 .310 .148 .883  df 4 5 4 4 4  Is .001 .001 n. s . n. s . n. s .  ND UD PD GD NBD  36 120 16 1 3  .146 .701 .778 .244 .966  4 5 4 4 4  .001 .001 .01 n. s . n. s .  109 78 38 16 _6  ND UD PD GD NBD  30 103 11 2 3  .558 .904 .725 .483 .720  4 5 4 4 4  .001 .001 .02 n. s . n. s .  0 1 2 3 4  132 82 35 13 4  ND UD PD GD NBD  28 144 15 4 3  .408 . 859 .726 .729 .770  4 5 4 4 4  .001 .001 .001 n. s . n. s .  0 1 2 3 4  131 72 33 14 6  44 . 2 9 8 ND 122 . 4 0 7 UD 22 . 2 2 7 PD 3 .963 GD 5 .471 NBD  5 5 4 4 4  .001 .001 .001 n.s. n. s .  Sc 0 1 2 3 4  NBD 97 71 36 15 _6  ND UD PD GD NBD  1 2 3 4 5 6  133 81 35 8 5 5  135 70 26 13 7 9  42 42 42 42 42 42  126" 63 32 16 8  0 1 2 3 4  125 72 33 13 5  42 42 42 42 42 42  68 68 45 22 _9  125 63 31 16 8  0 1 2 3 4  79 72 43 19 7  134 67 33 17 8  75 70 44 20 8  130 65 33 16 8  Rangers  Philadelphia 0-5 5-10 10-15 15-20 20-25 25+  PD 62 61 41 20 _8  Islanders  114 72 31 21 7 5  New Y o r k 0-5 5-10 10-15 15-20 20-25 25+  UD 38 38 38 38 38 38  Jersey Devils  New Y o r k 0-5 5-10 10-15 15-20 20-25 25+  Games  Canadiens  76 102 53 11 1  45 45 45 45 45 45  Flyers 68 88 55 17 2  43 43 43 43 43 43  133 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s w i t h T h e o r e t i c a l Normal, U n i f o r m , P o i s s o n , Geometric and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l (c'd) Home Games Pittsburgh Time (min) 0-5 5-10 10-15 15-20 20-25 25+  2 Sc 1 2 3 4 5 6  Quebec 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6 St.  0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  1 2 3 4 5 6  ND 85 106 60 15 2  Obs 171 72 32 14 11 4  UD 51 51 51 51 51 51  PD 91 81 48 21 8  GD 152 76 38 19 10  Sc 0 1 2 3 4  NBD 164 81 35 14 6  ND UD PD GD NBD  51 159 27 3 4  45 45 45 45 45 45  77 73 46 22 8  135 68 34 17 8  0 1 2 3 4  124 84 39 15 5  ND UD PD GD NBD  29. 126. 11. 0. 2.  60 61 41 21 8  113 56 28 14 7  0 1 2 3 4  113 56 34 15 7  ND UD PD GD NBD  72 70 45 22 8  129 65 32 16 8  0 1 2 3 4  120 77 37 15 6  ND UD PD GD NBD  47 52 38 21 9  97 48 24 12 6  0 1 2 3 4  68 62 36 17 7  129 77 35 20 5 4  70 98 59 16 2  Louis  Blues  109 51 29 22 4 9  51 72 53 21 4  126 68 33 17 4 10  Maple 64 88 58 19 3  38 38 38 38 38 38  ls .001 .001 .001 n.s. n.s.  896 117 065 891 460  4 5 4 4 4  .001 .001 .05 n.s. n.s.  35.976 84.870 16.146 4.325 6.423  4 5 4 4 4  .001 .001 .01 n.s. n.s.  613 885 456 659 241  4 5 4 4 4  .001 .001 .001 n.s. n.s.  .171 .741 .965 .911 .087  4 5 4 4 4  .001 .001 n.s. .05 n.s.  Leafs 43 43 43 43 43 43  Vancouver  Canucks  1 2 3 4 5 6  39 60 50 22 5  0-5 5-10 10-15 15-20 20-25 25+  df 4 5 4 4 4  X .822 .826 .112 .363 .641  Nordique  Toronto 0-5 5-10 10-15 15-20 20-25 25+  Penguins  73 55 34 14 7 10  32 32 32 32 32 43  ND UD PD GD NBD  35. 111. 15. 1. 4.  21 56 7 10 5  134 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l Distributions w i t h T h e o r e t i c a l N o r m a l , U n i f o r m , P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l D i s t r i b u t i o n From Time o f F i r s t G o a l (c'd) Home Washington Time (min) 0-5 5-10 10-15 15-20 20-25 25+  2 Sc 1 2 3 4 5 6  Obs 107 73 30 16 6 4  Winnipeg 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  ND 59 85 54 15 2  UD 39 39 39 39 39 39  PD 66 64 41 20 8  GD 118 59 30 15 7  Sc 0 1 2 3 4  NBD 104 75 35 14 5  ND UD PD GD NBD  47 47 47 47 47 47  80 76 48 22 _8  140 70 35 18 9  0 1 2 3 4  133 84 39 16 6  ND UD PD GD NBD  139 74 39 15 7 6  73 99 61 17 2  Away  1 2 3 4 5 6  1 2 3 4 5 6  Calgary 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  df 4 5 4 4 4  ls .001 .001 .05 n.s. n.s.  35 130 15 1 3  .817 .132 .374 .215 .369  4 5 4 4 4  .001 .001 .01 n.s. n.s.  33.693 93.458 15.431 4.105 5.296  4 5 4 4 4  .001 .001 .01 n.s. n.s.  .424 .950 .827 .967 .256  4 5 4 4 4  .001 .001 .01 n.s. n.s.  31 . 8 6 6 98 . 6 2 2 12 . 3 9 8 1 .956 4 .167  4 5 4 4 4  .001 .001 .02 n.s. n.s.  Games  Bruins  108 63 30 12 9 7  Buffalo 0-5 5-10 10-15 15-20 20-25 25+  26 105 9 2 2  X .092 .467 .601 .479 .235  Jets  Boston 0-5 5-10 10-15 15-20 20-25 25+  Games  Capitals  106 79 29 12 8 7  55 76 53 18 3  38 38 38 38 38 38  63 62 41 20 8  115 57 29 14 7  0 1 2 3 4  103 68 33 15 6  ND UD PD GD NBD  40 40 40 40 40 40  66 65 43 21 8  121 60 30 15 8  0 1 2 3 4  106 75 37 15 6  ND UD PD GD NBD  40 40 40 40 40  65 64 42 21 8  119 59 30 15 7  0 1 2 3 4  106 72 35 15 6  Sabres 59 84 56 18 3  30 103 14 5 5  Flames 114 59 32 21 4 7  57 80 55 18 3  ND UD PD GD NBD  135 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s w i t h T h e o r e t i c a l Normal, U n i f o r m , P o i s s o n , Geometric and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l (c'd) Away Chicago Time (min) 0-5 5-10 10-15 15-20 20-25 25+  Black  Games  Hawks 2  Sc 1 2 3 4 5 6  Detroit 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  Obs 137 72 39 13 2 11  ND 72 97 59 16 2  PD 79 74 46 22 _8  GD 137 69 34 17 9  Sc 0 1 2 3 4  NBD 131 82 37 15 _6_  ND UD PD GD NBD  87 78 47 21 _8  146 73 37 18 9  0 1 2 3 4  150 84 36 14 5  79 72 44 20 _8  135 67 34 17 8  0 1 2 3 4  41 41 41 41 41 41  71 67 42 20 8  124 62 31 16 8  48 48 48 48 48 48  82 77 49 23 9  144 72 36 18 9  UD 46 46 46 46 46 46  34 131 15 1 3  X .966 .833 .783 .549 .542  df 4 5 4 4 4  Is .001 .001 .01 n. s . n. s .  ND UD PD GD NBD  38 153 18 1 2  .644 .895 .215 .255 .658  4 5 4 4 4  .001 .001 .01 n. s . n. s .  136 76 34 14 _5  ND UD PD GD NBD  41 133 20 4 5  .795 .655 .083 .047 .647  4 5 4 4 4  .001 .001 .001 n. s . n. s .  0 1 2 3 4  118 73 34 14 6  ND UD PD GD NBD  35 112 15 2 3  .477 .519 .537 .322 .757  4 5 4 4 4  .001 .001 .01 n. s . n. s .  0 1 2 3 4  135 87 40 16 6  34 . 0 9 9 ND UD 134 . 7 7 0 PD 13 . 848 GD 0 .876 NBD 2 .450  4 5 4 4 4  .001 .001 .01 n. s . n. s .  Red Wings 155 77 36 13 4 7  83 107 58 13 1  49 49 49 49 49 49  Edmonton O i l e r s 1 2 3 4 5 6  0-5 5-10 10-15 15-20 20-25 25+  138 78 25 14 7 7  Hartford 0-5 5-10 10-15 15-20 20-25 25+ Los 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  123 67 32 12 8 6  72 95 56 15 2  45 45 45 45 45 45  Whalers 63 86 54 16 2  Angeles Kings 1 2 3 4 5 6  140 80 38 17 8 4  75 103 62 17 2  136 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s w i t h T h e o r e t i c a l N o r m a l , U n i f o r m , P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l (c'd)  Minnesota Time (min) 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6 New  0-5 5-10 10-15 15-20 20-25 25+  0-5 5-10 10-15 15-20 20-25 25+  Obs 108 50 27 15 14 6  ND 49 67 51 22 5  Games  UD 37 37 37 37 37 37  PD 58 60 40 21 _8  GD 110 55 28 14 7  Sc 0 1 2 3 4  NBD 98 63 32 15  64 61 39 19 _7  114 57 28 14 7  0 1 2 3 4  81 73 44 20 _7  137 69 34 17 9  43 43 43 43 43 43  76 70 43 20 7  58 82 51 14 1  Jersey  45 45 45 45 45 45  78 73 45 21 8  38 38 38 38 38 38  Is .001 .001 .001 n.s. -n.s.  . 837* .911 .667 .678 .791  4 5 4 4 4  .001 .001 n.s. n.s. n.s.  37 142 16 0 2  .083* .824 .133 .481 .209  4 5 4 4 4  .001 .001 .01 n.s. n.s.  38 127 20 3 5  .920 .626 .178 .208 .041  4 5 4 4 4  .001 .001 .01 n.s. n.s.  ND 38 . 8 3 0 UD 128 . 4 9 3 PD 17 . 4 5 9 GD 2 .031 NBD 4 .698  4 5 4 4 4  .001 .001 .01 n.s. n.s.  40 80 22 6 8  101 72 34 13 5  ND UD PD GD NBD  23 102 8 1 2  0 1 2 3 4  140 80 34 13 5  ND UD PD GD NBD  130 65 33 16 8  0 1 2 3 4  131 74 33 14 5  ND UD PD GD NBD  135 68 34 17 8  0 1 2 3 4  132 79 36 15 6  _1_  Devils  1 2 3 4 5 6  144 74 30 17 2 7  77 100 55 13 1  New  York  Islanders  1 2 3 4 5 6  134 73 27 12 6 8  1 2 3 4 5 6  df 4 5 4 4 4  ND UD PD GD NBD  X .879 .292 .104 .487 .608  Canadiens  108 58 38 15 3 5  New Y o r k 0-5 5-10 10-15 15-20 20-25 25+  Away Stars  2 Sc 1 2 3 4 5 6  Montreal 0-5 5-10 10-15 15-20 20-25 25+  North  70 91 54 15 2  46 46 46 46 46 46  Rangers  141 62 41 14 7 5  71 95 58 16 2  137 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s w i t h T h e o r e t i c a l N o r m a l , U n i f o r m , P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l ( c ' d ) Away Philadelphia Time (min) 0-5 5-10 10-15 15-20 20-25 25+  2 Sc 1 2 3 4 5 6  Obs 121 58 40 19 7 7  Pittsburgh 0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  1 2 3 4 5 6 St.  0-5 5-10 10-15 15-20 20-25 25+  1 2 3 4 5 6  1 2 3 4 5 6  UD 42 42 42 42 42 42  87 114 63 14 1  52 52 52 52 52 52  Sc 0 1 2 3 4  NBD 111 76 38 17 7  ND UD PD GD NBD  92 84 50 23 8  156 78 39 20 10  0 1 2 3 4  158 91 39 15 6  ND UD PD GD NBD  44. 164. 21. 3. 4.  74 71 45 21 8  131 65 33 16 8  0 1 2 3 4  124 76 36 15 6  73 69 43 20 8  128 64 32 16 8  0 1 2 3 4  124 75 34 14 5  78 70 42 19 7  132 66 33 16 8  0 1 2 3 4  138 74 32 13 5  X 34.207 99.569 14.247 2.992 5 . 327  df 4 5 4 4 4  ls .001 .001 .01 n.s. n.s.  079 535 474 875 157  4 5 4 4 4  .001 .001 .001 n.s. n.s.  ND UD PD GD NBD  37.853 115.939 17.183 2.177 4.541  4 5 4 4 4  .001 .001 .01 n.s. n.s.  ND UD PD GD NBD  35 119 15 1 3  .248 .771 .378 .119 .631  4 5 4 4 4  .001 .001 .01 n.s. n.s.  ND 38.939 137.957 UD PD 19.722 2.450 GD NBD 3.676  4 5 4 4 4  .001 .001 .001 n.s. n.s.  Nordique 66 89 58 18 3  Louis  Blues  128 70 29 16 5 7  67 89 55 16 2  Maple  142 67 32 10 8 4  PD 68 68 45 23 9  GD 126 63 32 16 8  Penguins  130 69 32 15 8 7  Toronto 0-5 5-10 10-15 15-20 20-25 25+  ND 59 84 59 21 4  159 95 29 16 10 3  Quebec 0-5 5-10 10-15 15-20 20-25 25+  Games  Flyers  44 44 44 44 44 44  43 43 43 43 43 43  Leafs  74 95 52 12 1  44 44 44 44 44 44  138 Table  All  I n d i v i d u a l Team C h i - s q u a r e C o m p a r i s o n o f G o a l D i s t r i b u t i o n s w i t h T h e o r e t i c a l N o r m a l , U n i f o r m , P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s From Time o f F i r s t G o a l (c'd)  Time (min) 0-5 5-10 10-15 15-20 20-25 25+  PD 61 62 42 22 _9  GD 116 58 29 14 7  Sc 0 1 2 3 4  NBD 95 71 37 17  42 42 42 42 42 42  71 67 42 20 _8  125 62 31 16 8  0 1 2 3 4  49 49 49 49 49 49  88 79 47 21 8  148 74 37 18 9  0 1 2 3 4  Sc 1 2 3 4 5 6  ND 52 75 56 22 4  Obs 104 59 32 22 5 9  1 2 3 4 5 6  1 2 3 4 5 6  151 85 35 17 3 4  + Two c e l l s  UD 39 39 39 39 39 39  ND UD PD GD NBD  30 84 11 4 4  2 X .321 .062 .351 . 815 .817  121 72 33 14 6  ND UD PD GD NBD  39 115 16 1 3  .140 .151 .640 .138 .908  4 5 4 4 4  .001 .001 .01 n.s. n.s.  147 90 38 14 4  ND UD PD GD NBD  32 158 14 0 1  .149+ .439 .176 .986 .422  4 5 4 4 4  .001 .001 .01 n.s. n.s.  than  5  _1_  df 4 5 4 4 4  ls .001 .001 .05 n.s. n.s.  Capitols  128 63 27 20 7 4  Winnipeg 0-5 5-10 10-15 15-20 20-25 25+  Games  Canucks  Washington 0-5 5-10 10-15 15-20 20-25 25+  Away Vancouver  64 86 54 16 _2  Jets 85 113 57 11 1  with  expected  counts  less  Table Means  A12  a n d V a r i a n c e s f o r I n d i v i d u a l T e a m s H o m e , Away a n d T o t a l Games f o r F r e q u e n c y D i s t r i b u t i o n s From Time o f F i r s t G o a l Home  Away 2  Total  X  S  _ X  Bos  2.06  1.85  2.00  1.66  2.03  1.75  Buf  1.87  1.37  2.00  1.53  1.93  1.44  Cai  1.93  1.53  2.00  1.60  1.96  1.56  Chi  1.78  1.41  1.91  1.54  1.85  1.48  Det  1.96  1.51  1.82  1.31  1.89  1.41  Edm  1.80  1.25  1.87  1.45  1.83  1.35  Har  1.94  1.60  1.92  1.49  1.93  1.54  LA  1.69  1.06  1.90  1.33  1.79  1.19  Min  1.94  1.36  2.07  1.90  2.00  1.62  Mon  2.01  1.47  1.95  1.38  1.98  1.43  NJ  1.87  1.39  1.83  1.33  1.85  1.36  NYI  2.00  1.49  1.87  1.49  1.94  1.49  NYR  1.82  1.19  1.89  1.40  1.78  0.99  Phi  1.90  1.61  2.02  1.64  1.92  1.57  Pit  1.80  1.35  1.82  1.22  1.79  1.23  Que  1.91  1.30  1.94  1.56  1.93  1.43  StL  2.05  1.82  1.91  1.48  1.98  1.66  Tor  1.97  1.65  1.81  1.30  1.89  1.47  Van  2.26  1.94  2.10  1.79  2.17  1.86  Was  1.95  1.36  1.90  1.45  1.93  1.40  Win  1.91  1.41  1.81  1.14  1.86  1.27  Team  2 S  _ X  2 S  140  Table Total  Team C h i - s q u a r e C o m p a r i s o n o f W i n , L o s s a n d T o t a l Streak Frequencies with Normal, Uniform, Poisson, G e o m e t r i c and N e g a t i v e B i n o m i a l Distributions Conventional Winning  Streak Length 1 2 3 4 5 6 7  Observed 185 102 46 26 16 11 16  Normal 75 99 88 54 22 6 1  Method Streaks  Expected Uniform Poisson 58 58 58 58 58 58 58  Losing 239 93 57 29 18  116 151 91 25 3  89 89 89 89 89  Geometric  97 108 79 44 19 7 2  Normal Uniform Poisson Geometric Negative Binomial  1 2 3 4 5  A13  201 101 50 25 13 6 3 Chisquare 81 . 3 2 5 233 . 1 0 0 50 . 4 0 2 11 . 5 1 9 7 .296  Scale Negative Bionomial 0 179 1 102 2 56 3 30 4 16 5 9 5 6  df 6 6 6 6 6  Is .001 .001 .001 n. s n. s  Streaks 127 117 72 33 12  218 109 55 27 14  Chisquare Normal 7 2 . 452 Uniform 153 . 2 4 4 Poisson 33 . 4 5 7 Geometric 2 .643 Negative Binomial 8 .211  0 1 2 3 4 df 4 4 4 4 4  Is .001 .001 .001 n. s n. s  223 122 54 23 9  141  Table  A13  T o t a l Team C h i s q u a r e C o m p a r i s o n o f W i n , L o s s a n d T o t a l Streak Frequencies with T h e o r e t i c a l Normal, Uniform, P o i s s o n , G e o m e t r i c and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s (continued)  Total Scale 1 2 3 4 5 6 7  Observed 424 195 103 55 30 13 20  Normal 180 234 187 92 28 5 1  Uniform  Streaks Poisson  120 120 120 120 120 120 120  Geometric  223 227 154 79 32 11 3  420 210 105 53 26 13 7  Winning  Scale 1 2 3 4 5 6. 7 8 9 10 11 12 13  Observed 185 102 46 26 16 11 7 3 4 0 0 1 1  Normal 87 118 89 37 9 1  6 6 6 6 6  Is .001 .001 .001 n. s n. s  Geometric  Scale  193 97 48 24 12 6.  0 1 2 3 4 5  Negative Binomial 408 214 109 55 28 14 7  Method Streaks  Expected Uniform Poisson 64 64 64 64 64 64  0 1 2 3 4 5 6 df  Chisquare Normal 149 . 2 0 1 Uniform 424 . 6 9 0 84 . 6 5 7 Poisson Geometric 7 .154 Negative Binomial 7 .711 Unconventional  Scale  104 104 70 35 14 5  Normal Uniform Poisson Geometric Negative Binomial  Chisquare 59.827 152.737 27.493 2.413 3.756  df 5 5 5 5 5  Negative Bionomial 178 108 54 26 12 5  Is .001 .001 .001 n.s. n.s.  142 Table  A13  T o t a l Team C h i s q u a r e C o m p a r i s o n o f W i n , L o s s a n d T o t a l Streak Frequencies with T h e o r e t i c a l Normal, Uniform, P o i s s o n , Geometric and N e g a t i v e B i n o m i a l D i s t r i b u t i o n s (continued)  Losing 1 2 3 4 5 6 7 8 9 10 11  239 93 57 29 14 1 1 1 0 0 1  119 154 87 22 2  86 86 86 86 86  1 2 3 4 5 6 7 8 9 10 11 12 13  Observed 424 195 103 55 30 13 8 4 5 0 0 2 1  128 116 70 32 11  Normal Uniform Poisson Geometric N e g a t i v e :B i n o m i a l  Total Scale  Streaks  Normal 192 252 184 76 17 2 0  Uniform 118 118 118 118 118 118 118  216 108 54 27 14  0 1 2 3 4  Chisquare 68.914 158.271 31.093 2.236 7.182  df  224 121 53 21 8 ls n.s. .001 .001 n.s. n.s.  4 4 4 4 4  Streaks Poisson 228 224 147 72 28 9 3  Normal Uniform Poisson Geometric Negative Binomial  Geometric  Scale  414 207 104 52 26 13 6  Chisquare 134.040* 448.178 65.500 1.116 3.686  2 c e l l s w i t h e x p e c t e d v a l u e s l e s s than 5. N o r m a l D i s t r i b u t i o n w i t h d f = 5 was 5 9 . 8 2 7  Negative Binomial 406 220 108 51 24 11 5  0 1 2 3 4 5 6. df 6 6 6 6 6  ls .001 .001 .001 n.s. n.s.  Chisquare ( s i g n , at  for .001).  Table Chi-square Comparison Game P o i n t R e c o r d s f o r  A14  of B a c k - t o - B a c k and N o n - B a c k - t o - B a c k 1985-86 N a t i o n a l Hockey League Season  Bos  1st Night PG P L 16 22  2nd Night PG P L 23 15  Other Games PG P L 47 34  1 s t v 2nd 1 s t v OG 2 2 X Is X Is 2.581 ns 2.009 ns  2 n d v OG 1 v 2 v 0 2 2 X Is X Is 0.224 ns 2.939 ns  Buf  10  20  12  18  58  42  0.287  ns  5.628  .02  3.009  ns 7.093  .05  Cai  13  17  19  11  57  43  2.411  ns  1.734  ns  0.381  ns 2.635  ns  Chi  19  23  28  14  39  37  3.913  .05  0.400  ns  2.598  ns 4.224  ns  Det  12  24  7 29  21  67  1.787  ns  1.173  ns  0.285  ns 1.987  ns  Edm 19  11  25  5  75  25  3.068  ns  1.569  ns  0.903  ns 3.203  ns  Har  22  12  17  17  45  47  1.503  ns  2.487  ns  0.012  ns 2.591  ns  LA  14  20  12  20  28  66  0.093  ns  1.469  ns  0.655  ns 1.700  ns  Min  14  12  10  16  61  47  1.238  ns  0.059  ns  2.732  ns 2.739  ns  Mon  19  13  16  16  52  44  0.567  ns  0.264  ns  0.167  ns 0.571  ns  NJ  12  30  16  26  31  45  0.857  ns  1.743  ns  0.082  ns 1.771  ns  NYI  21  17  15  23  54  30  1.900  ns  0.899  ns  6.556  02  6.565  .05  NYR  20  22  16  26  42  34  0.778  ns  0.634  ns  3.190  ns 3.220  ns  Phi  29  11  29  11  52  32  0.000  ns  2.435  ns  2.435  ns 3.857  ns  Pit  21  23  15  29  40  32  1.692  ns  0.671  ns  5.047  05  5.047  .05  Que  21  11  14  18  57  39  3.090  ns  0.394  ns  2.372  ns 3.478  ns  StL  23  17  17  23  43  37  1.800  ns  0.152  ns  1.350  ns 2.028  ns  Tor  12  32  19  25  26  46  2.440  ns  0.969  ns  0.575  ns 2.441  ns  Van  14  22  11  25  34  44  0.551  ns  0.223  ns  1.751  ns 1.758  ns  Was  28  16  26  18  53  19  0.192  ns  1.290  ns  2.651  ns 2.887  ns  Win  11  23  10  24  38  54  0.069  ns  0.837  ns  1.489  ns 1.888  ns  PG = P o i n t s G a i n e d , P L = P o i n t s L o s s , OG = O t h e r Games 1 s t v 2 n d , 1 s t v O G , 2 n d v OG : : d f = 1 1 v 2 v OG : :  df=  2  Table Significance  Levels  Condition  W,T Home (n,40)  = W;  for  A15  Runs T e s t s  A L = L  Away (n,40)  If Total (n,80)  on I n d i v i d u a l  Teams  Condition B I f home, W = W; L , T = L away, W , T = W; L = L Home Total (n,40) (n,80)  Bos  .6688  .9437  . 8028  .6845  .6147  Buf  .6456  . 8569  .2194  .9815  .9820  Cai  .4548  .5953  .0774  .0217*  .9942  Chi  .1801  .5702  .9955  .2065  .6218  Det  .3232  .5218  .8359  . 8691  .6528  Edm  .7893  .1743  .0692  .9437  .1023  Har  .1360  .0099*  .6358  . 8403  .3683  LA  .6459  .0238*  .6311  . 2203  .5044  Min  .7974  .4766  .3392  .3993  .8864  Mon  .8974  .3993  .7213  .7557  .2460  NJ  .7957  .6114  .8263  .8691  .9816  NY I NYR Phi Pit Que  .3650 .8827 .9318 .5702 1.0000  .4305 .1206 .9872 . 5218 .6720  .1159 .1452 .8915 . 8572 .9816  .2662 .3232 .0465* .1995 .3498  .1867 .2801 .8263 .9276 .7187  StL  .7009  .6886  .5485  .2203  .9820  Tor  .2003  .4376  .2594  .1448  .4612  Van  .1995  .9467  .1166  .2639  .4405  Was  .1455  .6114  .4766 Win .9467 * Significant i n non-random  . 8028 .3552 direction  .6258 .7893  .7075 .4540  145 Table  A16  I n d i v i d u a l Team S i g n i f i c a n c e L e v e l s f o r Runs W i t h E a c h P e r i o d T r e a t e d a s a Game (W,T = W i n , L = L o s s )  Bos  Home AwayTotal  PI 9815x 9437x 0003*  Bu'f  Home Away Total  7974 1936 2594  Cai  Home Away Total  0149* 5493 0623  3606 9839x ,2149  Chi  Home Away Total  0851 5313 9951x  0905 5478 1867  8569 9437 2801  3993 2048 3267  1801 4766 7161  0927 5254 2809  Det  Home Away Total  3993 5254 2084  3232 2046 0058*  2853 0347* 1788  2065 5603 6311  5254 0549 2594  8827 5104 5855  Edm  Home Away Total  ,5702 0099* 3693  ,0668 ,5603 ,7576  1609 3993 6921  5702 2003 6055  ,3367 ,2046 7161  9437 5254 8819  Har  Home Away Total  ,1460 ,0404* 9795x  ,7592 6456 ,3614  ,2331 4766 3269  6978 1801 1893  3503 0927 8172  .3503 ,5104 ,7075  LA  Home Away Total  ,5493 6720 2256  7592 ,1033 ,9216  5254 9872x 3267  1385 6978 0491*  7777 6978 5736  Min  Home Away Total  8691 8403 2924  3467 ,5313 7161  4414 7603 0122*  2446 1360 1155  4766 5313 9594x  0493* ,7488 .1301  Mon  Home Away Total  7991 6666 0147*  7009 3993 4449  6590 0314* 7490  5422 2639 2288  7991 5702 2284  3808 3993 ,7609  NJ  Home Away Total  *  = sign,  ,7893 , 8569 ,7761  P2 .1801 .0851 .2376  Test  P3 .7991 .4305 .5377  P1+P2 ,7893 7974 3399  P1+P2 .5702 .7974 .0602  7974 4625 0588  8691 3367 0937  3503 7360 3693  1964 3436 8028  0394* 3808 7461  1848 5493 3662  3606 4305 5377  8974 ,1964 0476*  9815x 6720 8310  0827 7957 , 8001  nonrandom d i r e c t i o n ;  9318 2048 ,1746  0493* 2003 ,7103  x  in  = sign,  2582 9872x 2502  alternating  P2+P3 .3498 .0409* .5482  1801 0200* 0246*  6886 2190 6683 direction  146 Table  A16  I n d i v i d u a l Team S i g n i f i c a n c e L e v e l s f o r Runs W i t h E a c h P e r i o d T r e a t e d a s a Game (W,T = W i n , L = L o s s ) (continued)  Test  NYI  Home AwayTotal  PI .7360 .6688 .5044  P2 .7009 .0549 . 6396  P3 .6345 .3367 . 8608  P1+P2 .6886 .0450x .6683  P1+P2 .2048 .3006 .2629  P2+P3 4625 5256 1835  NYR  Home Away Total  .9467 .7777 .0719  .8403 .5953 .5897  .7777 .6720 .5525  9467 9484 8001  .7974 .1609 . 8080  .0691 .7957 .1452  Phi  Home Away Total  .9839 .9484 .2210  .3993 .4305 .9506x  .4073 .0958 .5194  6712 3467 3166  .0146* .5218 .3399  .4376 .1936 .5751  Pit  Home Away Total  1385 2582 8080  .3498 .6114 .1752  .2331 .0927 .6218  0827 4219 4540  4305 3006 3269  . 8403 .5313 .8001  Que  Home Away Total  2853 5603 5044  5493 8569 8041  .6345 .4625 . 8263  1095 5478 2199  .7957 . 5313 .6566  .2190 .4414 .8608  StL  Home Away Total  .4904 .3006 .9044  .8403 .9467 .1457  .1033 .1743 .0573  3993 5603 8001  .5478 .3275 .1592  .7777 .1743 .1460  Tor  Home Away Total  .7603 .0135* .0565  .8827 l.OOOOx .6147  l.OOOOx .2662 .7533  .5313 .0608 .6566  .5218 .2446 .6147  ,4766 ,5104 ,6485  Van  Home Away Total  .7592 .9839 .7359  .3232 .4904 .9795x  .1936 .3650 .8864  9389 ,7957 ,2799  .0493* l.OOOOx .3174  .9839x .1095 .3460  Was  Home Away Total  .8974 .5702 .9938x  .1995 .0958 .0672  1.0000 .4032 .5751  6666 ,1385 0766  1.0000 . 5953 .3746  .9389 .9437 .1299  Win  Home Away Total  .7893 .7603 .6147  .2853 .9872x .4074  9872x 8569 ,0679  .3467 .1995 l.OOOOx  * x  Significant Significant  in in  .9437 .2048 .7761  nonrandom d i r e c t i o n a l t e r n a t i n g W/L/W/L  direction  .5218 l.OOOOx .8220  Table  A17  S i g n i f i c a n c e L e v e l s f o r Runs T e s t s On N u m b e r o f S h o t s B y P e r i o d f o r I n d i v i d u a l T e a m s (Team w i t h M o s t S h o t s , X P e r i o d = W i n ) Team Bos  Period 1 . 9079  Period 2 . 1938  Period 3 .3344  Total Shots .9216  Buf  .2563  .1547  . 8043  .4863  Cai  .4745  .1965  .9815x  .1532  Chi  .2697  .6971  .9949x  . 2829  Det  •9688x  .4272  .5164  .4351  Edm  .1146  .7860  .6375  .4697  Har  .8787  .9087  .4674  .2144  LA  .3245  .7104  .2265  .3460  Min  .6260  .7249  .4517  .0124*  Mon  .6856  .9533  .6348  .2660  NJ  .4221  .1795  .6260  .1408  NY I  .9368  . 3014  .4697  .0708  NYR  .5770  .6280  .3437  .1773  Phi  * x  .2346  .0558  .6968  .0360*  Pit  .4468  .2475  .4008  .7808  Que  .4116  .2576  .3779  . 8136  StL  .8174  .5992  .0435*  .6438  Tor  .2371  .0973  .1626  .0035*  Van  .0958  .6442  .3487  .0595  Was  .4860  .1042  .1900  . 8905  Win  .3288  .6923  .1994  .1460  Significant Significant  in in  nonrandom direction a l t e r n a t i n g W/L/W/L  direction  148 Table  Runs  Home  Test  A18  I n d i v i d u a l Team R e s u l t s on T o t a l G o a l s Away a n d T o t a l G a m e s "  Away  Total  Home  Away  Total  Bos  .1647  .4701  .1348  NYI  .9166  .7361  .6491  Buf  .9174  .4714  .7423  NYR  .7846  .3136  . 5553  Cal  .5236  .1069  .7847  Phi  .5045  . 8301  .4328  Chi  .3726  .0295*  .2075  Pit  .6654  .0549  .4054  Det  .0802  ,7914  .3205  Que  .9303  .4757  .9110  Edm  .9395  .6093  .9070  StL  .7909  .7783  .5791  Har  .0016*  .0133*  .2364  Tor  .7001  .0927  .1601  LA  .2884  1339  .6331  Van  .4486  .4785  .1931  Min  .3386  2750  .0823  Was  .5532  .4809  . 3643  Mon  . 8645  2786  .7838  Win  .2049  .0351*  .6416  NJ  .9230  8967  .9012  G o a l s f o r (1) a n d g o a l s a g a i n s t (0) f r o m p e r i o d t o p e r i o d , game t o game *  F o r Home,  Denotes .05 direction.  level  of  significance  or  tracked  less  in  nonrandom  149 Table  A19  I n d i v i d u a l Team S i g n i f i c a n c e L e v e l s f o r R u n s T e s t s o n A b o v e / B e l o w Mean V a r i a t i o n s (P1G1. . . P 2 G 1 . . . P 3 G 4 0 )  GF  Home Games GA SF  SA  GF  Away Games GA SF  SA  Bos  .9262  .7250  . 8759  .1891  .0672  ,4523  .8259  .3595  Buf  .3445  .9262  .4556  .6335  ,5366  , 3752  .1390  ,2564  Cal  .0350*  .8617  .4919  .2825  ,0147*  ,8074  .0992  2152  Chi  .7267  .5255  . 8926  .6928  ,5999  .7339  .5290  .2244  Det  .9588x  .4575  .4556  .1041  ,8199  , 8470  .9410  ,4008  Edm  .2849  .0328*  .9143  .0992  9357  , 8520  .1494  .9477  Har  .0137*  .7300  9780x  .1984  , 8905  .2076  ,0000  LA  .2083  . 8059  9975X  .3175  ,1156  ,7321  Min  .2200  .9519x  .4705  .5824  3587  Mon  .2663  .3797  .6764  ,6335  NJ  .8211  .0357*  .1344  ,6007  NYI  .1621  .4931  .0733  ,0174*  6205  NYR  .4499  .0428*  .6192  ,4150  Phi  .3025  .9887x  .3595  Pit  .4322  .6545  Que  .4453  StL  9973x  .9780x  6148  9451  .0885  6005  6809  ,4008  .3578  ,2701  ,4914  , 8520  .6928  6005  9975x  .8926  5802  2577  4080  .0019*  8926  ,3175  3368  4914  .4705  2716  .6568  ,0159*  4499  7955  .4919  6928  .3797  .5084  ,3976  9037  7228  .4937  9410  .8134  .0586  .1163  6240  8751  .7570  9902  Tor  .4575  .1468  .6555  ,1457  6700  2663  .0929  1014  Van  .9519  .9391  .2152  ,5476  2641  1541  .7533  9608  Was  .3187  .0259*  .2764  7182  9685  1245  .5841  1390  Win  .1426  .6599  .4652  7267  8706  2716  . 4705  9030  * x  Denotes Denotes  probability probability  of of  0000X  .05 or .95 or  less, more,  150 Table  A20  I n d i v i d u a l Team S i g n i f i c a n c e L e v e l s f o r Runs T e s t s A b o v e / B e l o w Mean V a r i a t i o n s (P1G1...P2G1...P3G80) T o t a l Games  Bos  Goals  For .1704  Buf  .8200  .2715  .6106  . 3675  Cai  .0112*  .5787  .2327  .0432*  Chi  .9534x  .3752  .7992  . 8792  Det  .0777  .4615  •9517x  . 8754  Edm  .3008  .0396*  .8954  .1824  Har  .1878  . 8083  .1113  .9107  Against . 3135  Goals For .4487  G o a l s Agad .6907  LA  .0369*  .5834  .6106  .6196  Min  .0653  .4821  .0755  . 2482  Mon  .6823  .5715  .5673  .5063  NJ  .7345  .5294  .0509  .4486  NYI  .7134  .6794  .7609  . 8350  NYR  .0580  .4479  .0121*  .5643  Phi  .1693  .6265  .4210  .3987  Pit  * x  Goals  .7801  .7924  .6800  .4599  Que  . 5635  .0162*  .1246  .5239  StL  . 8295  .0669  .0391*  .1133  Tor  .9590x  Van  .7979  .3175  .6462  .3951  .0692  .0604 .7050  Was  .1910  .2300  .6383  .8245  Win  .1744  .3507  .3014  .8756  Denotes .05 Denotes .95 direction)  level level  of of  significance significance  or or  l e s s (nonrandom direction) greater (alternating  151 Table Runs T e s t L e v e l s and S e t - t o - S e t  Team Bos  Nb.  X is  Runs  A21  o f S i g n i f i c a n c e f o r I n d i v i d u a l Teams C o r r e l a t i o n s on Four-Game Sets Treated a s Games ( T i e s = Wins)  p  4G S e t  r  Teams  p  4G  Set  . 8250  .026  Buf  .1189  -.357  NYR  .2880  -.131  Cai  .7390  -.056  Phi  .1158  .321  Chi  .6096  -.169  Pit  .3766  -.218  Det  .1849  .186  Que  .6096  -.169  Edm  .7668  .050  StL  .3493  .186  Har  .5020  -.209  Tor  l.OOOOx  -.056  LA  .7402  -.149  Van  .3297  -.295  Min  .3297  -.295  Was  .3493  .050  Mon  .7390  -.056  Win  .3297  -.267  NJ  .6478  -.131  in  alternating  (nonstreak)  NYI  Runs  .3583  direction  of  -.267  significance.  Table  A22  E m p i r i c a l P r o b a b i l i t y of Repeating a Win, Loss or T i e C o n d i t i o n e d on t h e Outcome o f P r e v i o u s Game(s) P P P W:1W W:2W W:3W w/n w/n w/n Bos  P P P L:1L L:2L L:3L 1/n 1/n 1/n  P P P T:1T T:2T T:3T t/n t/n t/n  .444 16/36  .400 6/15  .333 2/6  .345 10/29  .300 3/10  .333 1/3  .143 2/14  .000 0/2  0/0  .459 17/37  .500 8/16  .500 4/8  . 514 18/35  .500 9/18  .444 4/9  .286 2/7  .000 0/2  0/0  .679 36/53  .686 24/35  .652 15/23  .059 1/17  .000 0/1  .000 0/0  .000 0/9  0/0  0/0  .269 7/26  .286 2/7  .500 1/2  .512 21/41  .714 15/21  .667 10/15  .167 2/12  .000 0/2  0/0  .353 12/34  .500 6/12  .667 4/6  .394 13/33  .333 4/12  .500 2/4  .083 1/12  .000 0/1  0/0  .395 15/38  .400 6/15  .667 4/6  .303 10/33  .400 4/10  .250 1/4  .125 1/8  .000 0/1  0/0  .459 17/37  .294 5/17  .200 1/5  .432 16/37  .500 8/16  .375 3/8  .000 0/5  0/0  0/0  .537 22/41  .476 10/21  .333 3/9  . 355 11/31  .364 4/11  .000 0/4  .143 1/7  .000 0/1  0/0  Min  .296 8/27  .500 4/8  .500 2/4  .389 14/36  .429 6/14  .500 3/6  .188 3/16  .333 1/3  .000 0/1  Mon  .604 32/53  .625 20/32  .650 13/20  .167 3/18  .000 0/3  .000 0/0  .125 1/8  .000 0/1  0/0  .308 8/26  .125 1/8  1.000 1/1  .512 .524 21/41 11/21  .455 5/11  .250 3/12  .000 0/3  .444 12/27  . 333 4/12  .250 1/4  .660 31/47  .645 20/31  .600 12/20  .000 0/5  0/0  0/0  .541 20/37  .600 12/20  .583 7/12  .529 18/34  .529 9/17  .500 4/8  .000 0/8  0/0  0/0  .472 17/36  .529 9/17  .555 5/9  .457 16/35  .375 6/16  .167 1/6  .125 1/8  .000 0/1  0/0  Buf  Cai  Chi  Det  Edm  Har  LA  NJ  NYI  NYR  Phi  0/0  153 Table  A22  E m p i r i c a l P r o b a b i l i t y of Repeating a Win, Loss or T i e C o n d i t i o n e d on t h e Outcome o f P r e v i o u s Game(s) (continued) P P P W:1W W:2W W:3W w/n w/n w/n Pit  P P P L:1L L:2L L:3L 1/n 1/n 1/n  .462 18/39  .412 7/17  . 571 4/7  .259 7/27  .143 1/7  .000 0/1  .344 11/32  .400 4/10  .333 1/3  . 400 14/35  .500 7/14  . 286 8/28  .125 1/8  .000 0/1  .511 23/45  .455 15/33  .400 6/15  .667 4/6  .439 18/41  .500 9/18  .240 6/25  Total n  Que  StL  Tor  Van  Was  Win  .424 14/33  P P P T:1T T:2T T:3T t/n t/n t/n  .429 6/14  .167 1/6  .143 1/7  1.000 1/1  .578 .600 26/45 15/25  .571 8/14  .143 1/7  .000 0/1  . 571 4/7  .083 1/12  .000 0/1  0/0  .500 11/22  .545 6/11  .000 0/6  0/0  0/0  .579 22/38  .476 10/21  .333 3/9  .125 1/8  .000 0/1  0/0  .778 7/9  .321 9/28  .333 3/9  .000 0/3  .100 1/10  . 000 0/1  0/0  . 333 2/6  . 500 1/2  .476 20/42  .450 9/20  .556 5/9  .083 1/12  .000 0/1  0/0  .439  .465  .556  .452  .491  .465  .119  .087  .000  322 733  147 316  80 144  331 733  160 326  73 157  23 193  2 23  0 1  0/0  0/0  Table  A23  I n d i v i d u a l T e a m I n t e r p e r i o d O u t c o m e a n d Game Outcome C o r r e l a t i o n s (W = 2 , T = 1 , L = 0 )  Bos  PI  v P2 .079  P I v P3 .393  Buf  .090  -.088  .037  ,352  .517  .421  Cai  .078  .092  .088  .437  .587  .328  Chi  .086  .104  .051  ,308  .435  .672  Det  .085  -.110  -.030  ,315  ,419  .424  Edm  .150  .098  .105  , 579  .469  .398  Har  .001  .157  .143  .441  ,454  .642  LA  .037  .049  .259  .363  ,536  .648  Min  .117  .168  .043  ,382  .383  .618  Mon  .232  .099  .008  ,441  ,306  .510  NJ  .129  -.014  .049  304  ,518  .475  NYI  .096  -.111  .024  ,215  .486  .401  NYR  022  .092  .025  380  ,425  .641  Phi  .177  .032  -.149  353  ,459  .360  Pit  ,047  .206  . 323  433  668  .577  Que  ,057  .083  .039  458  514  .468  StL  ,018  .017  .033  517  362  .536  Tor  ,121  .141  .125  543  420  .579  Van  024  .189  .012  564  403  .550  Was  019  .004  -.053  401  518  .405  Win  015  .043  .083  534  428  .434  period  is  Note:  Each  P2 v P3 .057  treated  as  a  PI  v GO ,624  separate  P2 v GO .370  game,  P3 v GO .628  Table  A24  P e r i o d to P e r i o d C o r r e l a t i o n s of Goals F o r , G o a l s A g a i n s t , S h o t s F o r and S h o t s A g a i n s t F o r I n d i v i d u a l Teams  PlvP2  For PlvP3  P2vP3  PlvP2  Against PlvP3 P2vP3  Bos  Goals Shots  .046 .049  233 142  .204 .144  .174 .069  021 084  031 195  Buf  Goals Shots  .083 .164  006 176  124 013  014 023  083 052  005 246  Cal  Goals Shots  .168 .068  257 141  .055 .205  .156 .070  015 043  063 206  Chi  Goals Shots  .172 .202  006 060  .061 .135  062 073  239 068  039 125  Det  Goals Shots  .109 .052  343 143  .088 .212  .056 .119  050 050  052 244  Edm  Goals Shots  .222 .028  050 097  .059 .040  .204 .057  122 001  072 069  Har  Goals Shots  .006 .241  067 114  .179 .126  .002 .121  236 061  129 061  LA  Goals Shots  150 030  107 097  049 010  144 098  058 024  052 123  Min  Goals Shots  .154 .148  096 038  037 ,283  199 146  052 083  200 135  Mon  Goals Shots  .031 .006  ,176 078  .071 .170  .049 .262  134 260  096 009  NJ  Goals Shots  .046 .066  ,153 020  .093 .071  .056 .091  002 195  131 142  NYI  Goals Shots  .120 .061  142 024  .001 .008  .029 .129  017 042  275 051  NYR  Goals Shots  109 324  069 121  .146 .011  .064 .093  002 117  146 139  Phi  Goals Shots  121 170  063 008  .226 .099  .032 .093  025 129  033 138  Table  A24  P e r i o d to P e r i o d C o r r e l a t i o n s of G o a l s F o r , G o a l s A g a i n s t , S h o t s F o r and S h o t s A g a i n s t f o r I n d i v i d u a l Teams (continued) For  Against  Pit  Goals Shots  .097 .059  .075 .101  .025 .075  -.069 .286  .072 .061  .242 .107  Que  Goals Shots  -.008 .170  -.004 .124  .027 .191  .072 .245  .099 -.114  -.091 .152  StL  Goals Shots  -.042 .293  .109 .172  .049 -.123  -.054 .119  -.004 -.029  .035 .145  Tor  Goals Shots  -.008 -.050  .231 .094  .094 .037  .148 .154  .087 -.049  .098 -.035  Van  Goals Shots  .102 .164  .143 -.055  -.013 .028  -.202 -.013  .154 .006  -.012 .165  Was  Goals Shots  -.042 -.058  .035 -.051  -.001 .032  .103 .100  .014 .077  -.068 .230  Win  Goals Shots  .046 .179  .216 .032  -.035 .105  .136 .017  -.034 -.045  -.014 -.115  Table Individual Total Team Bos  Goals  P I v P2 .042  A25  Team P e r i o d - t o - P e r i o d Between PI  v P3 064  Periods P2  v P3 .113  Goal  Total  and  Shot  Shots  PI  v P2 066  Correlations  Between PI  v P3 149  Periods P2 v P3 . 036  Buf  .000  .100  -.108  .044  .110  .090  Cal  .036  .161  .034  .107  .034  .297  Chi  -.177  .212  -.109  .195  .112  .061  Det  .063  .120  -.106  .133  .024  .151  Edm  .268  .065  -.052  .017  .127  .086  Har  .007  .062  .189  .223  .160  .143  LA  .049  .024  .015  .106  .122  .092  Min  -.086  .070  .111  .100  .062  .180  Mon  .121  .068  .138  .007  .032  .030  NJD  .030  .057  .116  .093  .075  .098  NYI  . 215  .102  -.193  .011  .065  .019  NYR  .138  .037  -.096  .118  .032  .049  Phi  -.065  .012  -.011  .057  .232  .162  Pit  .049  .029  -.073  .124  .077  .101  Que  -.074  .106  .019  .003  .043  .041  StL  -.012  .141  .019  .269  .062  .041  Tor  .024  .166  .040  .203  .278  .038  Van  .016  .121  .060  .153  .139  .254  Was  .068  .103  -.006  .026  .020  .242  Win  .189  .261  -.174  .070  .201  .123  Table  A26  I n d i v i d u a l Team C o r r e l a t i o n s o f Between P e r i o d s and w i t h T o t a l PI  v  P2  PI  v  P3  P2  v  P3  PI  v  Goal Goal  TGD  Differences Difference P2  v  TGD  P3  v TGD  Bos  -.150  .337  .122  .633  .494  .775  Buf  -.101  -.019  .145  .408  .658  .669  Cai  .068  .187  .118  .573  .670  .682  Chi  -.063  -.010  .092  .477  .609  .653  Det  -.002  -.183  -.046  .451  .617  .520  Edm  .117  .112  -.052  .626  .691  .496  Har  .002  .095  .136  .506  .615  .729  LA  -.085  .083  .071  .481  .509  .759  Min  -.267  .079  .061  .443  .504  .707  Mon  -.148  .210  -.063  .607  .423  .699  NJ  -.138  -.081  .113  .412  .625  .630  NYI  -.056  .024  -.075  .555  .578  .532  NYR  -.015  .087  .008  .568  .501  .698  Phi  -.104  .065  -.156  .516  .538  .552  Pit  -.031  .090  .302  .536  .674  .720  Que  .117  .191  -.051  .662  .561  .648  StL  -.136  -.051  .023  .508  .474  .646  TML  .169  .156  .199  .629  .718  .661  Van  -.133  .164  -.118  .529  .506  .578  Was  -.012  -.048  -.060  .543  .613  .502  Win  .040  -.093  .166  .539  .679  .578  -.036  .061  .051  Total  .535  .593  .646  159 Table Individual Between PI  v  P2  PI  A27  Team C o r r e l a t i o n s P e r i o d s and T o t a l v  P3  P2  v  P3  of Shot D i f f e r e n c e Shot D i f f e r e n c e  PI  v  TSD  P2  v  TSD  P3 v  TSD  Bos  .083  .002  .265  .527  .723  .672  Buf  .084  .053  .105  .551  .667  .643  Cal  .329  .036  .359  .614  .811  .682  Chi  .040  -.009  .097  .542  .587  .669  Det  -.069  -.116  .278  .429  .696  .659  Edm  .044  .145  -.064  .681  .518  .602  Har  .155  .039  -.049  .671  .647  .491  -.040  .109  -.182  .603  .532  .526  Min  .182  -.058  .040  .621  .662  .541  Mon  -.130  .167  .114  .481  .631  .691  NJ  -.156  .049  .104  .484  .535  .709  NYI  .110  .092  -.034  .648  .588  .590  NYR  .089  .037  .142  .522  .709  .640  Phi  .126  -.094  .075  .529  .623  .631  Pit  .372  .145  .161  .723  .666  .687  Que  .287  .000  .226  .630  .776  .600  StL  .156  .059  -.046  .696  .595  .534  Tor  .107  .020  .120  .550  .676  .640  Van  -.018  -.206  -.014  .499  .612  .477  Was  .074  -.002  .296  .582  .699  .650  Win  .248  -.150  -.077  .643  .675  .426  Total  .101  .015  .100  .584  .652  .616  LA  NB.  Total  shot  difference  correlation  with  Game O u t c o m e =  .142  160 Table Correlation Between PI Win/Ties/Losses  v  P2  PI  v  P3  P2  v  P3  .082  .060  For  .009  -.002  .075  Against  .014  .035  .073  Shots Shots  of W i n s , G o a l s and S h o t s P e r i o d s f o r A l l Teams C o m b i n e d  -.034  Goals Goals  A28  For  .118  .034  .124  Against  .077  .054  .106  Total  Goals  Both  Teams  .057  .052  .013  Total  Shots  Both  Teams  .098  .087  .141  Table  A29  I n d i v i d u a l Team Lagged C o r r e l a t i o n s of Wins, T i e s , Losses f o r P e r i o d s 1 , 2 a n d 3 B e t w e e n Games n a n d n + l  Bos  P1G1  v P1G2..n -.228  Buf  -.133  Cai  .102  Chi  P2G1 v P 2 G 2 . . n -.124 -.143  P3G1 v P 3 G 2 . . n .061  Gl v G2..n -.025  248  .041  .181  .024  -.091  -.034  -.183  .099  -.072  Det  -.035  -.248  .102  -.090  Edm  -.099  -.101  .087  -.200  Har  -.020  -.122  .083  -.041  LA  .142  -.062  .121  -.018  Min  .017  .047  .293  -.113  Mon  -.331  -.092  .030  -.164  NJ  -.122  .027  .168  -.038  NYI  -.096  .083  .112  .161  NYR  .034  .050  .169  .167  Phi  -.102  -.028  .108  .028  Pit  .000  -.106  .025  -.034  Que  -.040  -.098  .019  -.068  StL  .034  .185  .228  -.091  Tor  -.267  .022  .045  -.125  Van  .140  -.095  .098  .121  Was  -.065  .091  .059  -.122  Win  -.064  -.156  .087  -.132  162 Table  A30  I n d i v i d u a l Team C o r r e l a t i o n s o f G o a l s F o r , G o a l s A g a i n s t a n d T o t a l G o a l s B e t w e e n P e r i o d s f o r Game l . . n v s . Game 2...n  PI  Goals For Gl P2 G l  P3  Gl  Goals PI G l  Against P2 G l P3  Gl  Total PI  Goals P2  P3  Bos  -.070  -.278  .035  -.046  .115  -.002  .093  -.086  -.009  Buf  -.019  -.025  .145  -.150  .018  .190  -.014  .121  .033  Cal  -.091  .037  .086  .298  -.024  .085  .056  -.030  .094  Chi  -.144  -.132  .105  .093  -.031  -.030  -.013  .021  -.054  Det  .037  .117  -.046  -.170  -.054  -.027  .017  .206  -.055  Edm  .046  -.123  -.050  -.098  .078  -.001  -.007  .130  .027  -.045  .004  .124  -.187  -.307  -.016  -.173  -.205  -.086  .025  -.121  .050  -.027  .090  -.134  -.123  -.051  -.011  -.089  .046  -.232  .042  -.125  -.061  -.147  -.062  -.093  Mon - . 1 7 1  -.058  -.033  -.099  .044  -.024  -.006  .057  .030  -.168  .067  .217  -.179  -.126  -.165  -.245  -.031  .003  .012  -.066  -.055  -.048  .049  -.072  .023  -.073  -.068  NYR  -.052  .326  .115  -.030  -.039  -.200  -.041  .118  -.325  Phi  -.189  -.186  -.061  -.051  -.062  -.088  -.132  -.214  -.026  Pit  -.033  -.066  .027  -.097  .058  -.121  -.149  .039  -.100  Que  -.047  -.144  -.151  .084  -.112  -.061  .073  -.247  -.226  StL  .035  .030  -.083  .007  .044  -.042  -.095  -.004  .020  Tor  -.039  -.108  .091  -.074  -.160  -.036  .176  -.254  -.017  Van  -.108  -.162  -.236  .203  .073  .096  .035  -.073  -.083  Was  -.187  -.016  .082  .106  -.170  .025  -.021  -.152  .178  Win  -.068  .032  -.008  -.099  -.168  -.094  .018  -.045  -.046  Har LA Min  NJ NYI  163 Table  A31  I n d i v i d u a l Team C o r r e l a t i o n s o f S h o t s F o r , S h o t s A g a i n s t a n d T o t a l S h o t s B e t w e e n P e r i o d s f o r Game l . . n v s . Game 2...n Shots PI  Gl v  PI  G2  For  P2 G l v P2 G2  Shots P3 v P3  Gl G2  PI v PI  Against  Gl  P2  Gl  v G2  Total P3  v P2  G2  P3  Gl v G2  PI PI  Gl v G2  Shots P2  Gl v P2 G2  P3  Gl  P2  G3  Bos  .080  .080  -.094  ,135  .157  .154  .186  ,070  -.116  Buf  .103  .001  -.049  ,167  .061  .077  ,163  ,183  -.018  Cai  .016  .198  -.080  ,071  .090  .047  .026  202  .099  Chi  .008  .109  -.104  ,028  .084  -.110  ,075  021  -.099  Det  .030  ,110  -.112  066  ,053  -.017  077  024  -.021  Edm  .144  ,078  -.135  ,002  .029  -.087  .027  018  -.176  Har  .115  ,081  -.134  ,043  ,166  -.051  ,128  019  -.175  LA  .187  .029  .121  ,003  ,096  -.039  .081  165  .065  Min  .051  .127  .026  .116  ,093  .047  ,077  090  -.024  Mon  .045  ,053  .068  041  ,020  -.086  ,095  012  .081  NJ  .227  ,044  .156  ,023  ,002  .082  ,049  058  .155  NYI  .031  ,050  -.088  136  .075  .019  ,020  090  -.017  NYR  .094  106  .000  ,051  ,177  -.153  ,077  073  -.123  Phi  .174  035  -.061  115  ,100  .052  ,002  080  -.009  Pit  .025  ,108  -.039  153  ,139  -.020  015  006  -.067  Que  .149  054  -.067  016  ,047  -.033  009  135  -.047  StL  .112  ,034  -.066  073  053  -.007  141  073  .016  Tor  .098  ,186  .129  072  ,106  .118  052  094  .180  Van  .096  087  .001  235  ,015  -.141  077  057  -.036  Was  .006  019  .072  002  ,140  -.155  137  235  -.047  Win  .142  069  .062  067  .009  -.021  ,101  098  .018  Table  A32  Raw a n d B i n a r y I n d i v i d u a l T e a m C o r r e l a t i o n C o e f f i c i e n t s for Goals (P1G1..P2G1..P3Gn) Home GF  GF  Total GA  GF  GA  Bos  raw bin  -.027 -.012  160 029  .128 .154  Oil 053  .103 .086  .070 .064  Buf  raw bin  -.019 .078  .024 .012  026 053  035 ,091  .008 .010  081 073  Cai  raw bin  .037 .186  191 009  .165 .219  085 036  074 161  079 ,039  Chi  raw bin  -.101 -.041  .017 .053  026 044  .125 .022  .052 .009  .020 .054  Det  raw bin  .049 -.014  .109 .057  .023 .015  .125 .027  .015 .021  .090 .053  Edm  raw bin  -.053 .092  .152 .190  .055 .017  085 008  .018 .062  .063 .130  Har  raw bin  098 ,214  007 021  .031 .017  .007 .005  .038 .080  .016 .010  LA  raw bin  -.006 .107  .024 .028  046 135  089 046  .032 .130  071 031  Min  raw bin  -.111 -.116  .003 .018  .078 .071  .050 .004  .093 .121  ,010 051  Mon  raw bin  097 093  117 072  .122 .042  .002 .090  .001 .024  .027 .032  NJ  raw bin  -.068 -.032  092 202  047 059  .023 .008  .006 .017  .003 .045  NYI  raw bin  .113 .124  .001 .067  .096 .048  196 006  .008 .022  .092 .029  NYR  raw bin  .062 .063  082 190  ,183 098  .066 .085  .142 .120  049 052  .114 .092  .018 .059  .134 .094  .014 .029  Phi Raw Bin  Away GA  = =  raw -.198 054 bin -.104 005 raw s c o r e raw s c o r e s c o n v e r t e d t o (no g o a l s i n p e r i o d = 0 ;  0,1 s c o r i n g s y s t e m 1 o r more g o a l s i n  a  period  Table  A32  Raw a n d B i n a r y I n d i v i d u a l T e a m Correlation Coefficients for Goals (P1G1..P2G1..P3Gn) (continued) Home GF  Away GA  GF  Total GA  GF  GA  Pit  raw bin  -.080 -.082  .079 -.046  .129 . 063  -.012 .013  .030 .015  .025 .011  Que  raw bin  -.030 .059  -.028 .072  .045 .006  -.002 .023  .029 .031  .025 .151  StL  raw bin  -.042 .017  -.023 .165  .040 -.059  -.065 -.020  .008 -.020  -.031 -.120  Tor  raw bin  -.055 .057  .213 .127  .087 .036  .064 .093  .017 .002  .090 .060  Van  raw bin  -.091 -.018  -.003 -.013  .161 .090  -.108 -.133  .008 .010  -.068 -.062  Was  raw bin  -.034 .079  .164 .199  .010 -.008  -.113 -.160  .020 .077  .001 -.084  Win  raw bin  -.040 -.137  .023 .034  .094 -.020  .070 .092  -.004 -.090  .061 .057  Raw = Bin =  raw raw (no  score s c o r e s c o n v e r t e d t o 0,1 s c o r i n g s y s t e m g o a l s i n p e r i o d = 0; 1 o r more g o a l s i n  a  period  Table  A33  Raw a n d B i n a r y I n d i v i d u a l T e a m C o r r e l a t i o n C o e f f i c i e n t s for Shots (P1G1..P2G1..P3Gn) Home SF -.058 .006  SA -.125 -.129  Away SF .041 .009  SA .160 .076  Total SF SA_ .027 .045 .045  Bos  raw bin  Buf  raw bin  -.038 -.078  -.003 .035  .076 -.144  .180 .098  .031 .030  Cai  raw bin  .086 .053  .120 .089  .142 .143  .038 .105  .120 .074  Chi  raw bin  .162 .004  -.054 -.044  .067 .051  .094 .103  .085 .012  Det  raw bin  .084 -.078  .144 .141  .039 -.002  -.024 -.082  .050 .000  Edm r a w bin  -.065 .001  .055 .143  .101 .125  -.050 -.015  -.006 -.014  Har  raw bin  .215 -.012  -.037 -.126  .083 .107  -.020 -.008  .175 .098  LA  raw bin  -.043 -.006  -.048 -.100  -.107 -.012  -.022 .038  .005 .030  Min  raw bin  .127 .058  -.029 .042  .113 .147  -.043 .040  .143 .111  Mon r a w bin  .057 -.046  -.162 .035  .008 -.093  -.128 -.110  .047 -.042  NJ  raw bin  .066 -.147  -.142 -.059  -.015 -.046  .016 .040  .004 -.131  NYI  raw bin  .097 .157  .028 .210  -.094 .004  -.123 -.059  .026 .015  NYR r a w bin  .027 .039  -.140 -.082  .176 .277  .077 .004  .162 .159  Phi  raw bin  .167 .076  .014 .085  .093 .058  .037 .092  .138 .049  Pit  raw bin  -.007 .032  .197 .211  -.037 .056  .126 -.046  .052 .023  Table  A33  Raw a n d B i n a r y I n d i v i d u a l T e a m C o r r e l a t i o n C o e f f i c i e n t s f o r Shots (P1G1..P2G1..P3Gn) (continued) Home SF  raw bin  Away SA  SF  Total SA  SF  SA  Que  raw bin  .010 .053  .181 .069  .028 .054  .063 -.002  .131 .095  .083 .037  StL  raw bin  .085 .138  .037 -.008  .083 .020  .077 -.009  .101 .129  .120 .098  Tor  raw bin  -.042 -.051  .065 .125  -.042 -.163  .013 .142  .027 -.034  .065 .117  Van raw bin  -.030 .105  -.071 -.064  .064 -.041  .035 -.012  .063 .113  .046 .020  Was  raw bin  .147 .092  .130 .024  -.066 .044  .027 -.144  .037 .026  .086 .010  Win  raw bin  .204 .059  -.007 -.041  .030 .057  -.144 .005  .135 .063  -.038 -.014  = raw = raw  scores s c o r e s c o n v e r t e d t o 0/1 s c o r i n g no g o a l s i n p e r i o d = 0 1 o r more g o a l s i n p e r i o d = 1  system:  168 Table  A34  I n d i v i d u a l Team C o r r e l a t i o n C o e f f i c i e n t s f o r S h o t s and G o a l s F o r and A g a i n s t GF v  SF  GA v  SA  GF v  GA  SF v  SA  GA v  SF  Bos  Home Away Total  .351 .341 .322  .427 .207 .317  .024 -.002 .009  -.248 -.071 -.173  -.111 .116 -.003  Buf  Home Away Total  .375 .339 .371  .391 .312 .351  -.046 -.198 -.129  -.233 -.068 -.165  .082 -.060 .003  Cal  Home Away Total  .372 .390 .389  .324 .226 .270  -.002 .140 .048  -.219 -.248 -.227  -.139 .194 .017  Chi  Home Away Total  .388 .240 .344  .294 .242 .282  .023 .028 .013  -.268 -.246 -.280  -.025 .020 -.022  Det  Home Away Total  .207 .476 .349  .435 .295 .370  -.106 -.003 -.049  -.110 -.164 -.155  -.001 -.078 -.052  Edm  Home Away Total  .382 .349 .371  .278 .263 .270  .051 .030 .039  -.222 -.274 -.254  -.126 -.130 -.129  Har  Home Away Total  .392 .397 .395  .465 .240 .349  -.151 .130 -.028  -.236 -.115 -.179  -.265 .069 -.123  LA  Home Away Total  .403 .359 .411  .292 .347 .319  .011 -.081 -.029  -.156 -.209 -.182  -.206 .016 -.104  Min  Home Away Total  .336 .273 .312  .199 .112 .152  -.032 .052 .005  -.183 -.263 -.227  .082 .100 .087  Mon  Home Away Total  .394 .272 .333  .336 .262 .296  .030 -.025 -.100  -.194 -.198 -.217  .008 .038 .018  NJ  Home Away Total  .209 .374 .288  .363 .277 .330  .109 .060 .081  -.318 -.072 -.208  .088 .082 .077  169  Table  A34  I n d i v i d u a l Team C o r r e l a t i o n C o e f f i c i e n t s f o r S h o t s and G o a l s F o r and A g a i n s t (continued) GF v  SF  GA v  SA  GF v  GA  SF v  SA  GA v  SF  NYI  Home Away Total  .249 .424 .336  .168 .244 .209  .092 -.009 .031  -.215 -.362 -.300  -.024 -.087 -.067  NYR  Home Away Total  .283 .330 .304  .482 .341 .410  -.010 .134 .052  -.140 -.087 -.124  -.060 .144 .025  Phi  Home Away Total  .199 .320 .265  .277 .498 .406  -.026 -.016 -.028  -.096 -.231 -.191  .040 -.016 .001  Pit  Home Away Total  .157 .329 .247  .216 .411 .334  .018 -.173 -.087  -.216 -.225 -.243  .020 -.032 -.032  Que  Home Away Total  .374 .300 .362  .366 .270 .319  -.081 -.149 -.120  -.026 -.139 -.148  .036 -.064 -.038  StL  Home Away Total  .263 .341 .309  .300 .470 .408  -.145 .012 -.078  -.172 -.138 -.170  -.044 .001 -.047  Tor  Home Away Total  .417 .274 .341  .350 .337 .345  -.057 .132 .048  -.206 -.260 -.238  -.130 -.035 -.083  Van  Home Away Total  .186 .333 .257  .384 .263 .336  .168 .065 .116  -.072 -.157 -.145  .013 .016 -.004  Was  Home Away Total  .235 .355 .290  .316 .270 .304  .086 .035 .052  -.288 -.064 -.196  -.016 -.063 -.050  Win  Home Away Total  .423 .414 .418  .112 .351 .254  .064 -.045 .002  -.248 -.128 -.190  -.015 .028 .007  o  170 Table Individual Chi-square Analysis Games (Ties=Wins)  A35  Team T e s t s o f S t a t i o n a r i t y o f Mean V a r i a t i o n s on Four-Game Goals For  Goals Against  Shots For  Sets Shots Against 2  X  ls  ef  X  ls  X  ls  X  ls  X  ls  Bos  6.836  .05  U L  1.348 1.006  ns ns  0.954 0.954  ns ns  0.154 0.154  ns ns  0.477 0.619  ns ns  Buf  1.381  ns  U L  0.144 0.144  ns ns  0.144 0.144  ns ns  0.477 0.619  ns ns  0.477 0.619  ns ns  Cal  2.341  ns  U L  0.619 0.158  ns ns  1.145 0.650  ns ns  0.583 1.010  ns ns  0.477 0.619  ns ns  Chi  1.630  ns  U L  0.000 0.154  ns ns  0.650 1.418  ns ns  4.133* 4.669*  ns ns  0.154 0.154  ns ns  Det  2.930  ns  U L  0.000 0.154  ns ns  0.619 0.477  ns ns  0.158 0.619  ns ns  2.600 2.206  ns ns  Edm  4.548  ns  U L  0.000 0 .154  ns ns  4.248* 3.744*  ns ns  0.619 0.477  ns ns  0.477 0.619  ns ns  .001  U L  0.154 0.154  ns ns  0.619 0.158  ns ns  0.619 0.477  ns ns  0.154 0.154  ns ns  ns  U L  0.477 0.158  ns ns  0.158 0.619  ns ns  0.158 0.619  ns ns  1.145 1.142  ns ns  Har  14.849  LA  4.048  Min  6.245  .05  U L  1.145 1.418  ns ns  0.154 0.154  ns ns  0.144 0.440  ns ns  0.440 0.144  ns ns  Mon  0.709  ns  U L  0 .000 0.154  ns ns  1.145 1.418  ns ns  1.348 1.895  ns ns  0.000 0.154  ns ns  17.463  .001  U L  0 .144 0.144  ns ns  0 . 650 1.145  ns ns  0 . 477 0.158  ns ns  2.136 2.267  ns ns  NJ  NYI  2.969  ns  U L  1.171 1.171  ns ns  0.954 0.954  ns ns  0.144 0.144  ns ns  0.144 0.144  ns ns  NYR  0.288  ns  U L  0.000 0.154  ns ns  0.000 0.154  ns ns  0.440 0.144  ns ns  0.158 0.477  ns ns  Phi  2.401  ns  U L  1.145 0.650  ns ns  0.583 0.418  ns ns  0.000 0.154  ns ns  0.477 0.619  ns ns  171 Table Individual Chi-square Analysis  Games (Ties=Wins)  A35  Team T e s t s o f S t a t i o n a r i t y o f Mean V a r i a t i o n s on Four-Game Sets (continued) Goals For  Goals Against  Shots For  Shots Against 2  Is  X  ef  X  Is  X  Is  X  Is  X  Is  Pit  6.015  ,05  U L  1.115 1.418  ns ns  2.267 2.136  ns ns  2.206 1.529  ns ns  Que  5.044  ns  U L  0.158 0.477  ns ns  0.158 0.477  ns ns  0.154 0.154  ns ns  0.440 0.144  ns ns  StL  6.685  05  U L  0.154 0.154  ns ns  0.000 0.154  ns ns  0.619 0.477  ns ns  1.418 1.145  ns ns  Tor  0.282  ns  U L  0.154 0.154  ns ns  0.418 1.010  ns ns  3.844* 3.593*  ns ns  0.000 0.154  ns ns  Van  2.836  ns  U L  0.144 0.144  ns ns  0.158 0.477  ns ns  0.154 0.154  ns ns  Was  1.679  ns  U L  0 .477 0.619  ns ns  0 .477 0.619  ns ns  0.158 0.619  ns ns  0.158 0.477  ns ns  Win  9.169  02  U L  2.206 2.600  ns ns  0.583 0.418  ns ns  1.006 1.348  ns ns  0.158 0.477  ns ns  df  2  = 2 for  cells  all  with  cases  expected  counts  less  than  5.0  0.440 ns 0.144 ns  1.798 ns 1.622 ns  172 Table  A36  I n d i v i d u a l Team N o r m a l D i s t r i b u t i o n C h e c k s a n d Set-to-Set Correlations f o r f o u r game s e t s  Bos  goals shots  For ndc* .986 .990  Buf  goals shots  .995 .969  -.192 .291  .995 .973  -.192 .056  .992 .977  -.117 .458  Cai  goals shots  .990 .946  -.324 -.115  .979 .985  .078 .297  .977 .961  -.282 .489  Chi  goals shots  .989 .887  -.452 .224  .985 .995  .146 -.167  .989 .984  -.141 .178  Det  goals shots  .999 .965  .186 -.028  .995 .987  -.323 -.084  .987 .971  -.315 .329  Edm  goals shots  .958 .992  .335 -.124  .979 .981  -.254 -.073  .995 .992  .077 -.002  Har  goals shots  .981 .967  .004 .456  .989 .990  -.218 -.067  .957 .978  .051 -.144  LA  goals shots  .985 .976  -.213 -.037  .962 .978  .227 -.207  .991 .992  -.078 .455  Min  goals shots  .980 .987  -.035 -.206  .945 .965  -.039 -.149  .982 .980  -.183 -.075  Mon  goals shots  .992 .971  -.097 .083  .974 .979  -.226 -.194  .969 .984  -.315 -.073  NJ  goals shots  .994 .972  .010 .003  .953 .977  -.080 -.200  .961 .981  .039 .017  NYI  goals shots  .990 .982  -.066 .199  .984 .948  -.100 -.630  .992 .981  -.014 .066  NYR  goals shots  .987 .988  .137 -.133  .990 .988  .306 .114  .992 .983  .256 .190  Phi  goals shots  .994 .991  -.097 -.171  .980 .986  .302 -.277  .993 .987  .093 .218  Pit  goals shots  .986 .972  -.376 -.214  .985 .968  -.257 .171  .980 .970  -.530 -.045  r .173 .192  Against ndc .959 .995  r .253 .123  Total ndc .966 .985  r_ .184 .148  173 Table  A36  I n d i v i d u a l Team N o r m a l D i s t r i b u t i o n Checks and Set-to-Set Correlations f o r f o u r game s e t s (continued)  *  Que  goals shots  For ndc* .990 .980  StL  goals shots  ,991 984  Tor  goals shots  .996 .961  Van  goals shots  Was  Win  ndc  =  Against ndc 978 975  645 024 -.579 -.070  007 188  Total ndc 988 964  .106 .183  .985 .976  .151 -.072  .980 .948  -.235 .055  199 203  989 979  329 554  987 991  .010 .283  .985 .979  266 042  987 984  -.055 .161  975 975  -.031 .232  goals shots  985 959  031 241  978 976  -.241 .170  990 986  .310 .090  goals shots  .969 .966  .065 .111  994 986  960 979  .050 -.339  normal  distribution  check  -.026 -.228  174  Table Artificial W  Season Boston  Bruins  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  37 35 25 34 30 40 35  Calgary 88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3 Detroit  L  Pts  %  29 23 24 18 31 28 30  14 22 31 28 19 12 15  88 92 81 96 79 92 85  . 550 .575 .506 .600 .494 .575 .531'  Flames 54 34 43 45 47 47 53  Records  Season  W  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  17 23 19 13 20 19 16  9 23 18 22 13 14 11  117 91 104 112 107 108 117  .731 .569 .650 .700 .669 .675 .731  34 34 31 27 33 34 31  Hartford  Whalers  34 26 30 39 31 34 36  38 26 24 29 32 31 32  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3 Edmonton  12 20 19 14 16 12 13  80 88 81 68 82 80 75  .500 .500 .506 .425 .513 .500 .469  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3 Los  5 26 29 20 13 14 11  79 82 83 82 83 84 85  .494 .513 . 519 .513 .519 .525 .531  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  T  L  Pts  %  Sabres  38 23 37 30 34 30 37  Chicago  Red Wings  37 28 27 31 35 35 37  Season  Buffalo  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  T  and R e a l  A37  7 23 20 19 13 16 14  35 34 23 31 33 34 29 Black  27 30 26 23 30 30 25  83 69 94 79 81 76 88  .519 .431 .588 .494 .506 .475 .550  Hawks  41 29 30 43 33 36 48  12 21 24 14 17 14 7  66 81 76 60 77 74 57  .413 .506 .475 .375 .481 .463 .356  34 34 27 28 33 36 28  8 25 16 21 14 12 13  84 67 90 83 80 76 91  .525 .419 .563 .519 .500 .475 .569  91 79 87 81 84 81 86  .569 .494 . 543 .506 .524 .506 .538  Oilers 38 21 37 31 33 32 39  Angeles 42 28 32 34 36 33 38  31 29 25 33 32 32 32  Kings 7 23 23 13 12 15 10  175  Table Artificial  Season  W  Minnesota  North  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3 New  T  and R e a l Season Records (continued)  Pts  %  Stars  37 26 36 34 40 37 35  16 26 17 14 11 11 15  27 25 22 26 24 26 26  41 33 34 34 35 38 38  70 82 71 78 69 75 75  .438 .513 .444 .488 .431 .469 .469  12 22 24 20 21 16 16  37 26 30 38 28 36 35  Pittsburgh 88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  40 31 28 36 34 39 37  35 30 26 28 34 31 35  66 72 68 72 69 68 68  .413 .450 .425 .450 .431 .425 .425  53 43 29 40 47 51 41  York  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  8 24 24 14 18 13 10  82 76 84 90 74 85 80  . 513 .475 .525 .563 .463 .531 . 500  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3 Quebec  7 18 13 15 13 12 9  87 80 69 87 81 90 83  .543 .500 .431 .543 .506 .563 .519  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  L  T  Pts  %  Canadiens 18 17 23 19 16 20 19  9 20 28 21 17 9 20  115 106 86 101 111 111 102  .719 .663 .538 .631 .694 .694 .638  61 70 76 68 71 60 65  .381 .438 .475 . 425 .444 .375 .406  8 21 23 22 19 13 15  80 81 91 90 89 85 91  . 500 .506 .569 .563 .556 .531 .569  7 21 19 18 11 17 14  61 71 65 60 61 65 60  .381 .444 .406 .375 .381 .406 .375  Islanders 28 24 27 25 29 21 27  Philadelphia  Penguins 33 31 39 29 33 29 34  W  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3 New  York Rangers  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  Season Montreal  J e r s e y ]D e v i l s  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3 New  27 28 27 32 29 32 30  L  A37  36 30 34 34 35 36 38  47 34 31 37 38 41 42  5 22 22 18 13 18 11  Flyers 36 29 23 24 26 31 27  Nordigue 27 25 23 21 25 24 23  46 34 38 41 44 39 43  176  Table Artificial  Season  W  St.  Blues  L o u i si  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  33 30 25 28 32 31 30  L  35 30 29 31 34 37 36  T  12 20 26 21 14 12 14  and Real Season (continued)  Pts  78 80 76 77 78 74 74  %  .488 . 500 .475 .481 .488 .463 .463  Vancouver • Canucks 88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  33 30 29 27 29 31 28  Winnipeg  Jets  88-89 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  26 21 21 25 26 25 27  A37 Records  Season  W  Toronto  Maple  88 - 8 9 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  28 22 26 23 30 22 26  Washington  39 23 26 35 30 35 31  8 27 25 18 21 14 21  74 87 83 72 79 76 77  .463 .544 .519 .450 .494 .475 .481  42 37 35 33 42 40 40  12 22 24 22 12 15 13  64 64 66 72 64 65 67  .400 .400 .413 . 450 .400 .406 .419  L  88 - 8 9 P 1 P 2 P 3 P 1+2 P 1+3 P 2+3  41 35 28 31 36 39 35  46 36 37 35 41 43 41  T  Pts  %  Leafs 6 22 17 22 9 15 13  62 66 69 68 69 59 65  .388 .413 .431 .425 .431 .369 .406  92 96 80 84 92 96 89  .575 .600 . 500 .525 .575 .600 . 556  Capitals 29 19 28 27 24 23 26  10 26 24 22 20 18 19  Table Correlations  Outcomes  f o r Outcomes Based on A r t i f i c i a l Seasons as Compared t o R e a l Season Outcomes  1  P  2  P 3  Pl+2  Pl +3  P2+3  Wins  .642  .675  .871  .921  . 887  .917  Losses  .731  .648  .816  . 863  .923  .877  Ties  -.034  .164  .066  .260  -.377  .191  Points  .717  .724  .883  .926  .943  .930  .569  .693  . 849  . 846  .916  . 891  Standings*  *  P  A38  Spearman r a n k c o r r e l a t i o n s . moment c o r r e l a i t o n s .  Remainder  are  Pearson  product-  178  Table Upsets  A39  Comparisons: 37-38, 46-47, 88-89 N a t i o n a l Hockey League Seasons Pre-Game  Rank  Season  Rank  2 U 312  NU 409  %U 43. 3  228 163 61 53  325 255 90 96  41. 39. 40. 35.  163  255  39. 0  30 27  48 61  38. 5 0 .008 30. 7 2 .143  61  90  40. 4  v . 50% 4 6 - 4 7 NHL v . 1 0 0 % 3 7 - 3 8 NHL  30 53  48 96  38 . 5 0 . 0 8 0 35. 6 0 .742  100%  3 7 - 3 8 NHL  53  96  35. 6  50% 3 7 - 3 8 NHL  27  61  3 0 . 7 0 .591  8 8 8 - 8 9 NHL  46  55  45. 5  312 228 163 53 27  409 325 255 96 61  22  28  v . 1 0 0 % 8 8 - 8 9 NHL v . 75% 8 8 - 8 9 NHL  312 228  409 325  43. 3 0 .010 41. 2 0 .145  50% 8 8 - 8 9 NHL  163  255  39. 0  v . 1 0 0 % 4 6 - 4 7 NHL v . 50% 4 6 - 4 7 NHL  61 30  90 48  40. 4 0 .201 38 . 5 0 . 3 8 7  50% 4 6 - 4 7 NHL  30  48  38. 5  v.  27  61  30.7  100%  8 8 - 8 9 NHL  v . 75% v . 50% v.100% v.100%  88-89 88-89 46-47 37-38  NHL NHL NHL NHL  50% 8 8 - 8 9 NHL v. v.  50% 4 6 - 4 7 NHL 50% 3 7 - 3 8 NHL  100%  v. Top  4 6 - 4 7 NHL  v.100% v . 75% v . 50% v.100% v . 50% Top  88-89 88-89 88-89 37-38 37-38  NHL NHL NHL NHL NHL  6 8 8 - 8 9 NHL  50% 3 7 - 3 8 NHL  43. 41. 39. 35. 30.  2 0 4 6  3 2 0 6 7  X  2 Is  2 .016 n . s . 7 . 4 1 5 .01 0 . 422 n . s . 3 .008 n . s .  0 0 1 2 4  .186 .653 .451 .504 . 382  n.s. n.s.  n.s. n.s.  n.s.  n.s. n.s. n.s. n.s. .05  44. 0  1.110  n.s. n.s.  n.s. n.s.  n.s.  U 274  NU 460  %U 37 . 3  200 142 51 47  353 272 103 104  36 34 35 31  144  272  34 . 6  28 24  50 51  35 . 9 32 . 0  51  103  33 .1  28 47  50 104  35 . 9 31 .1  47  104  31 .1  24  51  32 . 0  40  67  37 . 4  274 200 142 47 24  460 353 272 104 51  18  35  34 . 0  274 200  460 353  37 . 3 36 . 2  144  272  34 . 6  51 28  103 50  33 .1 35 . 9  28  50  35 . 9  24  51  32.0  37 36 34 31 32  .2 .6 .9 .1  .3 .2 .6 .1 .0  X  0 3 0 2  .183 .024 .974 .085  1.:s .  n. n. n. n.  s. s. s. s.  0 .048 0 .193  n. s. n. s.  0 .178 0 .139  n. s. n. s.  0 .018  n. s .  0 0 0 1 0  n. n. n. n. n.  .000 .057 .356 .097 .560  s. s. s. s. s.  0 .240 0 .101  n. s. n. s .  0 .013 0 .052  n. s. n. s .  0.259  n.s.  179  Table  Based  Chi-Square Comparisons of Upsets on Pre-Game v s . S e a s o n Rank P o s i t i o n Pre-Game  League  A40  Season  U's  NU's  % U's  U's  NU's  % U's  X  l.s.  NHL 100%  88-89  312  409  43.3  274  460  37.3  5.342  .05  75%  88-89  228  325  41.2  200  353  36 . 2  2.988  n. s.  50%  88-89  163  255  39.0  144  272  34.6  1.719  n.s,  100%  46-47  61  90  40.4  51  103  33.1  1.739  n.s,  50%  45-47  30  48  38.5  28  50  35.9  0.110  n.s,  100%  37-38  53  96  35.6  47  104  31.1  0.667  n.s,  50%  37-38  27  61  30.7  24  51  32.0  0.033  n.s.  Top  8 88-89  46  55  45.5  40  67  37.4  1.427  n.s.  Top  6  22  28  44.0  18  35  34.0  1.091  n.s,  1  88-89  Div  Soccer  87-88  100%  3  pt  104  171  37 . 8  81  198  29.0  4.806  .05  50%  3  pt  46  136  25.2  52  105  33.1  2.525  n.s,  100%  2  pt  79  124  38.9  72  194  27.1  7.404  .01  50%  2  pt  46  85  35.1  31  105  22.8  4.935  .05  177  351  33.5  165  363  31.3  0.623  n.s  NBA 50%  88-89  180  Table Cross  Sport  A41  Chi-Square  Comparisons  Pregame  Season 2  Us 100%  88-89  100% 100% 50% 75% 50%  X  2 l.s.  Us  NUs % U s  43.3  Soc 2 p t  79  124  38.9  1.232  ns  76  194  28.1  7.328  .01  Soc 3 p t  104  171  37.8  2.436  ns  81  198  29.0  6.112  .02  NBA  177  351  33.5  12.164  165  363  31.3  5.004  .05  228  325  41.2  200  353  36.2  177  351  33.5  6.848  .02  165  363  31.3  2.919  ns  NBA  .001  460  l.s.  409  NHL  274  X  312  88-89  NHL  NUs % U s  37.3  100%  Soc 2 p t  79  124  38.9  0.330  ns  76  194  28.1  5.233  .05  100%  Soc 3 p t  104  171  37.8  0.890  ns  81  198  29.0  4.220  .05  50%  Soc 2 p t  46  85  35.1  1.649  ns  31  136  22.8  18.241  50%  Soc 3 p t  46  136  33.8  14.908  .001  52  105  33.1  0.495  ns  163  255  39.0  144  272  34.6  50%  88-89  NHL  .001  50%  Soc 2 p t  46  85  35.1  0.637  ns  31  136  22.8  6.615  .01  50%  Soc 3 pt  46  136  25.2  10.515  .01  52  105  33.1  0.070  ns  50%  NBA  177  351  33.5  3.035  ns  165  363  31.3  0.092  ns  61  90  40.4  51  103  33.1  100%  46-47  100%  Soc 2 p t  79  124  38.9  0.079  ns  76  194  28.1  1.154  ns  100%  Soc 3 p t  104  171  37.8  0.273  ns  81  198  29.0  0.781  ns  NBA  177  351  33.5  2.438  ns  165  363  31.3  0.192  ns  30  48  38.5  28  50  35.9  50% 50%  46-47  NHL  NHL  50%  Soc 2 p t  46  85  35.1  0.237  ns  31  105  22.8  4.262  .05  50%  Soc 3 pt  46  136  25.2  0.466  ns  52  105  33.1  0.179  ns  50%  NBA  177  351  33.5  0.737  ns  165  363  31.3  0.676  ns  181'  Table Cross  Sport  A41  C h i Square (continued)  Comparisons  2 U s NUs % U s 100%  37-38  100% 100%  NHL  2 l.s.  53  96  35.6  Soc 2 pt  79  124  38.9  0.410  Soc 3 p t  104  171  37.8  177  351  33.5  27  61  30.7  50% NBA  50%  X  37-38  NHL  U s NUs % U s  X  l.s.  47  104  31.1  ns  76  194  28.1  0.415  ns  0.209  ns  81  198  29.0  0.205  ns  0.217  ns  165  363  31.3  0.001  ns  24  51  32.0  50%  Soc 2 p t  46  85  35.1  0.465  ns  31  105  22.8  2.126  ns  50%  Soc 3 p t  46  136  25.2  0.879  ns  52  105  33.1  0.029  ns  50%  NBA  177  351  33.5  0.275  ns  165  363  31.3  0.312  ns  177  351  33.5  165  363  31.3  50%  NBA  100%  Soc 2 p t  79  124  38.9  1.874  ns  76  194  28.1  0.815  ns  100%  Soc 3 pt  104  171  37.8  1.467  ns  81  198  29.0  0.424  ns  50%  Soc 2 p t  46  85  35.1  0.119  ns  31  105  22.8  3.717  ns  50%  Soc 3 p t  46  136  25.2  4.274  .05  52  105  33.1  0.196  ns  182 Table I n d i v i d u a l Team and T o t a l G o a l s  A42  Means a n d S t a n d a r d D e v i a t i o n s F o r , A g a i n s t a n d F o r , A g a i n s t a n d T o t a l S h o t s P e r Game For  Against  Total  Bos  Goals Shots  X 3.675 31.375  sd 2.127 7.359  X 3.138 26.763  sd 1.589 6.226  X 6.813 58.138  sd 2.586 8.914  Buf  Goals Shots  3.638 27.900  1.844 6.742  3.700 29.750  2.040 6.883  7.338 57.650  2.470 8.577  Cal  Goals Shots  4.425 34.638  2.293 7.656  2.838 25.737  1.522 6.016  7.262 60.380  2.836 8.990  Chi  Goals Shots  3.687 32.713  1.811 7.594  4.213 31.538  2.017 7.787  7.900 64.250  2.617 9.330  Det  Goals Shots  3.912 28.875  1.780 6.879  3.963 31.187  1.958 7.492  7.875 60.000  2.582 9.410  Edm  Goals Shots  4.062 27.825  2.172 6.550  3.800 30.413  1.977 6.290  7.863 58.237  2.984 7.631  Har  Goals Shots  3.725 31.050  2.068 7.525  3.162 28.925  2.126 6.035  7.338 59.970  2.908 9.320  LA  Goals Shots  4.700 31.750  2.178 7.041  4.213 33.475  1.992 6.042  8.913 65.225  2.834 8.475  Min  Goals Shots  3.213 31.437  1.791 7.529  3.487 32.450  1.869 6.422  6.700 63.888  2.664 8.689  Mon  Goals Shots  3.950 30.850  1.848 5.715  2.713 26.663  1.624 5.571  6.662 57.513  2.619 6.910  NJ  Goals Shots  3.525 31.200  1.849 6.235  4.062 29.544  2.021 6.544  7.588 60.937  2.924 7.959  NYI  Goals Shots  3.325 30.275  1.847 6.475  4.050 30.813  1.698 6.432  7.375 61.088  2.572 7.264  NYR  Goals Shots  3.875 33.950  1.912 7.092  3.838 31.200  2.040 7.099  7.713 65.150  2.829 9.550  Phi  Goals Shots  3.850 29.937  1.751 6.530  3.563 30.538  1.875 6.864  7.512 60.475  2.584 8.800  Pit  Goals Shots  4.338 28.513  2.105 6.555  4.363 35.825  2.223 7.410  8.700 64.338  2.711 8.576  183 Table  For,  A42  I n d i v i d u a l Team Means a n d S t a n d a r d Deviations T o t a l G o a l s a n d F o r , A g a i n s t and T o t a l Shots A g a i n s t and (continued) For X  Against sd  X  Total sd  X  sd  Que  Goals Shots  3.362 28.450  1 884 7 289  4.238 32.500  1.957 6.707  7.600 60.950  2 309 8 172  StL  Goals Shots  3.437 28.862  1. 7 8 5 6 092  3.563 28.275  1.967 6 . 547  7.000 57.138  2 619 8 422  Tor  Goals Shots  3.237 27.089  2. 0 2 0 5, 938  4.275 34.127  2 256 7. 2 3 5  7.512 61.215  2 968 8 882  Van  Goals Shots  3.112 30.513  1 779 7 135  3.162 28.212  642 ,103  6.275 58.720  2 600 9 980  Was  Goals Shots  3 . 812 31.175  1 910 6 207  3.227 27.550  1.817 7.099  7 .050 58.725  2 815 8 392  Win  Goals Shots  3.750 29.519  2 072 6, 867  4.438 32.215  2 .116 6.162  8.188 61.734  3 011 8 , 847  184 REFERENCES Abelson,  R.  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