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Computer-aided recording and mathematical analysis of team performance in volleyball Eom, Han Joo 1989

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Computer-aided Recording and Mathematical Analysis of Team Performance i n V o l l e y b a l l By Han Joo Eom B.P.E., and M.P.E., Sung Kyun Kwan University, Seoul, Korea A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF PHYSICAL EDUCATION In THE FACULTY OF GRADUATE STUDIES SCHOOL OF PHYSICAL EDUCATION We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1989 © Han Joo Eom, 1989 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 of Physical Education The University of British Columbia Vancouver, Canada Date September, 1989  DE-6 (2/88) i i ABSTRACT The purpose o f t h i s study was t o develop and t e s t a method t o analyze and e v a l u a t e team performance i n v o l l e y b a l l i n terms of i n d i v i d u a l s k i l l performance as w e l l as s e q u e n t i a l s k i l l performances. Seventy-two sample games from the F.I.V.B Cup i n t e r n a t i o n a l men's v o l l e y b a l l c o m p e t i t i o n were v i d e o taped, computer recorded, and s t a t i s t i c a l l y a n alyzed. Games were grouped i n t o two c a t e g o r i e s a c c o r d i n g t o the team s t a n d i n g and game s t a t u s : Top 4-Bottom 4 teams and Winning-Losing games. MANOVAs and d i s c r i m i n a n t f u n c t i o n a n a l y s i s were used t o i n v e s t i g a t e the p l a y i n g c h a r a c t e r i s t i c s of i n d i v i d u a l s k i l l performance and t o s e l e c t the best p r e d i c t o r ( s ) of team success among the s k i l l components. L o g - l i n e a r procedures were used t o examine the dependencies ( f i r s t - and second-order t r a n s i t i o n p a t t e r n s ) among the s e q u e n t i a l p l a y i n g a c t i o n s . R e s u l t s showed t h a t : 1) the s i g n i f i c a n t d i f f e r e n c e s between the groups were due t o b e t t e r performances on those s k i l l s which took p l a c e i n the Counterattack Process ( i . e . , Block, Dig, Set, and S p i k e ) , demonstrated by the Top 4 teams and i n Winning games. Among these the Block and Spike were the most ( r e l a t i v e l y ) important s k i l l s d e t e r m i n i n g team success; 2) Success i n s p i k i n g performance was more dependent upon the g i v e n outcomes of the set ( l s t - o r d e r ) than those of the r e c e p t i o n (2nd-order); and 3) the p a t t e r n s of 1 s t - and 2nd-o r d e r t r a n s i t i o n s were s t a b l e and c o n s i s t e n t r e g a r d l e s s o f the i i i Team, Game an d P r o c e s s S t a t u s . B o t h t h e m e t h o d o l o g y a n d s u b s e q u e n t r e s u l t s p r o v i d e a v i a b l e a i d f o r e f f e c t i v e c o a c h i n g i n v o l l e y b a l l . I n a d d i t i o n , t h i s t o o l may a l s o b e a p p l i c a b l e t o o t h e r s p o r t i n g c o n t e x t s . i v TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES v i LIST OF FIGURES v i i i ACKNOWLEDGEMENTS i x CHAPTER I. INTRODUCTION 1 Statement o f the Problems 5 D e l i m i t a t i o n s 6 I I . REVIEW OF LITERATURE 7 2.1 Sport A n a l y s i s 7 2.2 Q u a n t i t a t i v e A n a l y s i s i n V o l l e y b a l l 13 2.3 A n a l y s i s of S e q u e n t i a l Events i n Sport . . . 20 2.3.1 S t o c h a s t i c p r o c e s s e s 21 2.3.2 L o g - l i n e a r a n a l y s i s 25 I I I . METHOD AND PROCEDURE 2 9 3.1 Subject of Ob s e r v a t i o n 29 3.2 S k i l l Components of Ob s e r v a t i o n 30 3.3 O b s e r v a t i o n C r i t e r i a 31 3.4 V a l i d i t y o f O b s e r v a t i o n C r i t e r i a 31 3.5 I n t r a - O b s e r v e r R e l i a b i l i t y 34 3.6 Computer Program 35 3.6.1 Input program 36 3.6.2 Output program 38 3.7 S t a t i s t i c a l A n a l y s i s 43 IV. RESULTS AND DISCUSSION 4 6 4.1 A n a l y s i s o f I n d i v i d u a l S k i l l 4 6 4.1.1 MANOVA mixed model d e s i g n 4 6 4.1.2 MANOVA f o r randomized groups d e s i g n . 53 4.1.3 D i s c r i m i n a n t f u n c t i o n a n a l y s i s . . . . 59 4.2 A n a l y s i s of S e q u e n t i a l S k i l l s 65 4.2.1 F i r s t - o r d e r t r a n s i t i o n from the r e c e p t i o n t o s e t 66 4.2.2 F i r s t - o r d e r t r a n s i t i o n from the set to s p i k e 75 4.2.3 T r a n s i t i o n p a t t e r n among the o f f e n s i v e p l a y s 79 4.2.4 Second-order t r a n s i t i o n from the r e c e p t i o n t o s p i k e 82 V. SUMMARY AND CONCLUSIONS 8 9 C o n c l u s i o n s 90 Recommendations 93 REFERENCES 94 APPENDIX A. Types of Set 100 B. O b s e r v a t i o n C r i t e r i a 101 C. L e t t e r t o v o l l e y b a l l E x p e r t s I l l D. Keyboard Layout 114 E. An Example of the Computer Screen D i s p l a y and Data F i l e 115 F. P l a y i n g P a t t e r n s of I n d i v i d u a l S k i l l 117 G. Decomposition of 1?- f o r T r a n s i t i o n from Set t o Spike 123 H. Decomposition of 1?- f o r T r a n s i t i o n from R e c e p t i o n t o Spike 124 v i LIST OF TABLES Table 2- 1. T r a n s i t i o n M a t r i x 23 3- 1. Number of Games Per Team P l a y e d i n the P r e l i m i n a r y Round 2 9 3-2. Percentage of Agreement between the C r i t e r i a and the Coaches i n the C l a s s i f i c a t i o n o f the S k i l l s 33 3-3. Comparison between the C r i t e r i o n and Coach C i n Spike 34 3-4. R e l i a b i l i t y C o e f f i c i e n t s f o r the S e l e c t e d S k i l l s 35 3-5. An Example of S t a t i s t i c a l Output f o r S e t t i n g Performance 3 9 3-6. An Example of T r a n s i t i o n M a t r i x between Set and Spike 4 0 3- 7. O p e r a t i o n a l D e f i n i t i o n s and Equations 42 4- 1. Means and Standard D e v i a t i o n s f o r Set and Spike. 4 6 4-2. R e s u l t s o f MANOVA and U n i v a r i a t e Follow-ups . . 48 4-3. Means and Standard D e v i a t i o n s , Averaged over the Game Status 4 9 4-4. Observed Frequency and P r o p o r t i o n f o r Set and Spike 51 4-5. D e s c r i p t i v e S t a t i s t i c s f o r the E i g h t S k i l l s . . 53 4-6. R e s u l t s o f MANOVA and U n i v a r i a t e ANOVA Follow-ups 55 4-7. R e s u l t s o f D i s c r i m i n a n t F u n c t i o n A n a l y s i s . . . 61 4-8. W i t h i n C o r r e l a t i o n M a t r i x 62 4-9. C l a s s i f i c a t i o n R e s u l t s w i t h D i s c r i m i n a n t F u n c t i o n 63 4-10. Decomposition o f f o r T r a n s i t i o n from R e c e p t i o n t o Set 68 v i i 4-11. Decomposition of f o r the T r a n s i t i o n from R e c e p t i o n t o Set wi t h Set b e i n g t r e a t e d as the Dependent Measure 7 0 4-12. T r a n s i t i o n P a t t e r n from the R e c e p t i o n t o the Set 72 4-13. Decomposition of f o r the T r a n s i t i o n from Set t o Spike w i t h Spike b e i n g t r e a t e d as the Dependent Measure 7 6 4-14. T r a n s i t i o n P a t t e r n from the Set t o the Spike . . 77 4-15. T r a n s i t i o n M a t r i c e s f o r the Three O f f e n s i v e P l a y s 80 4-16. Decomposition of 1?- f o r the Second-Order T r a n s i t i o n from Reception t o Spike w i t h Spike b e i n g t r e a t e d as the Dependent Measure 83 4-17. T r a n s i t i o n P a t t e r n from the R e c e p t i o n t o the Spike 84 LIST OF FIGURES gure 1. A Flow Diagram of the Game o f V o l l e y b a l l i x ACKNOWLEDGEMENTS T h i s t h e s i s r e p r e s e n t s the combined e f f o r t s o f many i n d i v i d u a l s t o whom I am g r a t e f u l l y a p p r e c i a t i v e . I would l i k e t o express my most s i n c e r e a p p r e c i a t i o n t o the members of my committee: Drs. Ian Franks, Robert Mosher and Robert Schutz f o r t h e i r guidance and support d u r i n g a l l phases o f t h i s study. S p e c i a l thanks must be g i v e n t o Dr. Robert Schutz, my s u p e r v i s o r , f o r h i s l e a d e r s h i p i n a l l aspects o f t h i s t h e s i s and f o r h i s encouragement toward the depth o f t h i s study. I would a l s o l i k e t o thank my d e a r e s t f r i e n d Sung Won Yoon and my b i g b r o t h e r s i n Korea f o r t h e i r moral support and the time and energy they devoted t o p r e p a r i n g a l l game ta p e s . Furthermore, I was f o r t u n a t e t o have many s c h o o l mates and Dale Ohman o f f e r a s s i s t a n c e t o h e l p e d i t my w r i t i n g . F i n a l l y , I g r a t e f u l l y acknowledge and thank Doug Penner f o r f r e e l y d e v o t i n g so much o f h i s time t o develop the computer program which made t h i s study p o s s i b l e . Without everyones' h e l p t h i s study would have not been completed. 1 CHAPTER I I n t r o d u c t i o n Coaches encounter numerous o p p o r t u n i t i e s t o a s s e s s i n d i v i d u a l and team performances i n t h e i r d a i l y a c t i v i t i e s . The a b i l i t y t o a c c u r a t e l y e v a l u a t e these a t h l e t i c performances i s o f t e n a s i g n i f i c a n t f a c t o r i n d e t e r m i n i n g the e f f e c t i v e n e s s o f c o a c h i n g as w e l l as the success of c o a c h i n g programs. A t h l e t i c performance can be e v a l u a t e d i n e i t h e r a q u a l i t a t i v e or q u a n t i t a t i v e manner. H i g g i n s (1977) noted t h a t the method of assessment s e l e c t e d depends upon the n a t u r e of the q u e s t i o n s t o be asked, the purpose of the a n a l y s i s , and the type o f the i n f o r m a t i o n d e s i r e d . Coaches o f t e n attempt to p r o v i d e a t h l e t e s w i t h a continuous flow of feedback about t h e i r performance d u r i n g a c o m p e t i t i o n or a p r a c t i c e s e s s i o n . U n t i l r e c e n t l y , s u b j e c t i v e assessment of performance, mainly through v i s u a l o b s e r v a t i o n , has been the primary t o o l f o r the m a j o r i t y of s p o r t s i n the e s t i m a t i o n of a t h l e t i c performance i n o r d e r t o p r o v i d e t h i s i n f o r m a t i o n . The feedback g i v e n to the a t h l e t e s was o f t e n concerned w i t h the more g e n e r a l a s p e c t s o f performance and consequently d e s c r i p t i v e i n n a t u r e . As performance becomes more advanced and c o m p l i c a t e d , t h e r e e x i s t s e x t e n s i v e i n f o r m a t i o n i n any s p o r t event t h a t i s needed both d u r i n g and a f t e r a c o m p e t i t i o n . Given the f i n d i n g s t h a t i n f o r m a t i o n o b t a i n e d by the coach's s u b j e c t i v e assessment o f performance i s o f t e n i n a c c u r a t e and erroneous 2 (Franks & M i l l e r , 1986; M i l l e r , 1988), a method of i n c r e a s i n g the a c c u r a c y of the assessment would g r e a t l y h e l p the coaches i n t h e i r e f f o r t t o improve performance. One method of a c h i e v i n g t h i s i s t o s y s t e m a t i c a l l y r e c o r d and c o l l e c t o b j e c t i v e data which r e p r e s e n t the bes t approximate v a l u e s o f performance. The use of a r e l i a b l e r e c o r d i n g method can be an i n v a l u a b l e t o o l i n t h i s e f f o r t t o g a i n a complete and a c c u r a t e d e s c r i p t i o n o f performance, and thus a i d the coach i n the e v a l u a t i o n o f s t r e n g t h s and o f a team or an i n d i v i d u a l performance. Based upon an assumption t h a t an o b j e c t i v e a n a l y s i s o f performance should serve as the b a s i s f o r f u t u r e p l a n n i n g i n any c o a c h i n g process, the i s s u e o f q u a n t i t a t i v e a n a l y s i s has been w e l l documented i n s e v e r a l r e c e n t a r t i c l e s (Baacke, 1982; Ejem & Horak, 1980; L i r d l a , 1980; MacAdam, 1984). Recent developments i n the f i e l d of computer technology and the a v a i l a b i l i t y o f microcomputers have l e d t o a pronounced i n c r e a s e i n the a p p l i c a t i o n o f computer systems i n performance r e c o r d i n g and a n a l y s i s (Franks, 1988; Franks & Goodman, 1984, 1986b; Franks, Goodman & M i l l e r , 1983a; Franks, Wilson & Goodman, 1987; Hughes, 1988; Ladany & Machol, 1977; Purdy, 1974, 1977). In any team s p o r t , the a n a l y s i s and e v a l u a t i o n o f performance can have some problems. T h i s i s t r u e because the performance i s c h a r a c t e r i z e d by a g r e a t number and d i v e r s i t y o f p l a y i n g a c t i o n s , and the performance i t s e l f has interwoven 3 c o m p l e x i t i e s . T h e r e f o r e , the exact or e n t i r e measurement of a team's a c t u a l performance i n a c o m p e t i t i o n w i l l be v e r y d i f f i c u l t . However, i n v o l l e y b a l l team performance th e s e problems can be somewhat reduced because of the d i s c r e t e nature of the game. For example, 1. the c o u r t i s c l e a r l y d i v i d e d i n t o two d i s t i n c t areas by the net which does not a l l o w d i r e c t i n t e r a c t i o n of the teams; 2. the team i s a l l o w e d t o have o n l y t h r e e s e q u e n t i a l c o n t a c t s w i t h the b a l l b e f o r e sending i t t o the opponent; 3. each c o n t a c t w i t h the b a l l i s a b r i e f ; and 4. a f t e r a r a l l y i s ended, t h e r e i s enough time t o r e c o r d each c o n t a c t b e f o r e the next r a l l y s t a r t s a g a i n . In v o l l e y b a l l , t h e r e have been a number of attempts t o develop an o b j e c t i v e method i n which the r e s u l t of p l a y i n g a c t i o n s can be r e c o r d e d i n a q u a n t i f i e d form. The most commonly used method i s a manual r e c o r d i n g u s i n g a p a r t i c u l a r c h e c k l i s t d u r i n g a l i v e game or a v i d e o r e p l a y (Baacke, 1982; Byra & S c o t t , 1983; Ejem, 1980; L i r d l a , 1980; Sawula, 1977; V o j i k , 1980) . Penner (1985) developed a microcomputer program f o r the a n a l y s i s of v o l l e y b a l l game. However, alt h o u g h i t has some p r a c t i c a l uses i n a n a l y z i n g i n d i v i d u a l s k i l l performance, the manner i n which the data i s r e c o r d e d does not permit an a n a l y s i s of t r a n s i t i o n p a t t e r n s among the s e q u e n t i a l p l a y i n g a c t i o n s . The d e s i g n of a r e c o r d i n g method 4 must be c a r e f u l l y c o n s i d e r e d so t h a t the type o f data produced meets the nature of q u e s t i o n s t o be i n v e s t i g a t e d , and enables the i n v e s t i g a t o r t o answer those q u e s t i o n s . I t i s e v i d e n t from the r e l a t e d l i t e r a t u r e t h a t the p r e v i o u s approaches t o the a n a l y s i s o f team performance i n v o l l e y b a l l have some n o t i c e a b l e shortcomings i n terms of e f f i c i e n c y of data c o l l e c t i o n , e v a l u a t i o n o f s k i l l performance, and a n a l y s i s of s e q u e n t i a l s e r i e s o f performances. These l i m i t a t i o n s prompted the development of the c u r r e n t computerized r e c o r d i n g method. Based on the l a r g e amounts o f data o b t a i n e d by t h i s method, the c u r r e n t study demonstrates the u t i l i z a t i o n o f a p p r o p r i a t e s t a t i s t i c a l t e c h n i q u e s to i d e n t i f y the p a t t e r n s o f s u c c e s s f u l / u n s u c c e s s f u l p l a y i n g c h a r a c t e r i s t i c s . Once the nature and degree o f the r e l a t i o n s h i p s among the s e q u e n t i a l s k i l l performances has been tho r o u g h l y i n t e r p r e t e d , the r e s u l t s c o u l d form the b a s i s f o r c o n s t r u c t i n g a model f o r team performance i n v o l l e y b a l l . P r a g m a t i c a l l y , i f the p l a n n i n g of t r a i n i n g and game s t r a t e g i e s i s based on the d e c i s i o n s d e r i v e d from r e l e v a n t data, as opposed t o s u b j e c t i v e assessment, t h i s would l e a d t o more e f f e c t i v e and e f f i c i e n t t e c h n i c a l and t a c t i c a l c o aching t o f u l f i l l t he needs o f an i n d i v i d u a l a t h l e t e or teams o f a t h l e t e s . 5 Statement of the Problem The purpose of t h i s study i s t o develop and t e s t a computerized method t o analyze and e v a l u a t e team performance i n v o l l e y b a l l i n terms o f i n d i v i d u a l s k i l l performance as w e l l as s e q u e n t i a l s k i l l performances. Sub-problems The f i v e sub-problems of t h i s study are: a. To compare the p l a y i n g c h a r a c t e r i s t i c s o f the s e t and s p i k e between the a t t a c k p r o c e s s and c o u n t e r a t t a c k p r o c e s s ; b. To compare the s k i l l l e v e l s between winning and l o s i n g games, and between good and poor teams; c. To s e l e c t the b e s t p r e d i c t o r , or a set of p r e d i c t o r s , o f team success among the s e l e c t e d s k i l l components; d. To examine the dependency of the f i r s t - and second-order t r a n s i t i o n p r o b a b i l i t y s t r u c t u r e s among the s e q u e n t i a l s k i l l performances, and t o t e s t the e f f e c t s of the Game, Team and Process s t a t u s on these t r a n s i t i o n p a t t e r n s ; and e. To compare the degree of s e q u e n t i a l dependency among the p a t t e r n s o f o f f e n s i v e p l a y ( i . e . , types o f set or s p i k e ) . 6 D e l i m i t a t i o n s and L i m i t a t i o n s 1. The a n a l y s i s was based upon e i g h t s p e c i f i c teams, r e p r e s e n t a t i v e o f n a t i o n a l men's v o l l e y b a l l teams. Thus, the r e s u l t s may not be a p p l i c a b l e t o a lower l e v e l team ( i . e . , h i g h school) or women's v o l l e y b a l l . 2. The a n a l y s i s was concerned w i t h team performance only, i n d i v i d u a l s were not i d e n t i f i e d . 3. Only " a c t i o n s w i t h b a l l " were taken i n t o account i n the a n a l y s i s because i n v o l l e y b a l l these a c t i o n s have much more i n f l u e n c e s on the game than a c t i o n s "without b a l l " . 4. An experimental s c o r i n g system was used i n c o n j u n c t i o n w i t h the t r a d i t i o n a l s c o r i n g system i n the tournament. The f i r s t t h r e e games i n a match were p l a y e d under the t r a d i t i o n a l s c o r i n g system and the R a l l y - p o i n t system up t o 15 p o i n t s was a p p l i e d a f t e r the 3rd game. In the pre s e n t study, however, onl y those games p l a y e d under the t r a d i t i o n a l s c o r i n g system were used i n the a n a l y s i s . 7 CHAPTER II L i t e r a t u r e Review 2.1 Sport Analysis I t i s assumed t h a t the fundamental aim of any c o a c h i n g p r o c e s s i s t o improve the performance o f the a t h l e t e . More s p e c i f i c a l l y , coaches attempt t o g i v e i n f o r m a t i o n t o a t h l e t e s w i t h the e x p e c t a t i o n t h a t t h i s i n f o r m a t i o n w i l l r e s u l t i n a permanent improvement i n performance (Franks, S i n c l a i r , Thomson & Goodman, 1986). I f t h i s i s the case, the i n f o r m a t i o n g i v e n t o the a t h l e t e s must be both a c c u r a t e and d e t a i l e d . However, a number of recent s t u d i e s (Franks, E l l i o t & Johnson, 1985; Franks, Goodman & M i l l e r , 1983a; Franks & M i l l e r , 1986; M i l l e r , 1988) have shown t h a t the o b s e r v a t i o n a l s k i l l s o f coaches d u r i n g c o m p e t i t i v e a t h l e t i c events are o f t e n i n a c c u r a t e and erroneous. Most a t h l e t i c s k i l l s , e s p e c i a l l y at the e l i t e l e v e l o f competition, are performed at h i g h speed, not o n l y w i t h i n an environmental framework t h a t d i s t r a c t s o b s e r v e r s , but a l s o w i t h i n an interwoven complexity of the p l a y i n g a c t i o n s . As a r e s u l t , the s u b j e c t i v e assessment of performance may not always be an a c c u r a t e and complete d e s c r i p t i o n of what took p l a c e . Research on performance a n a l y s i s by Franks et a l . , (1983a) i d e n t i f i e d s e v e r a l e r r o r sources which may i n f l u e n c e or b i a s the accuracy of a coach's o b s e r v a t i o n s . Such f a c t o r s i n c l u d e the coaches' a t t e n t i o n b e i n g d i r e c t e d toward 8 h i g h l i g h t e d events, the l i m i t e d c a p a c i t y of human memory, and the emotional and p e r s o n a l b i a s e s which can s i g n i f i c a n t l y a f f e c t the s t o r a g e or nonstorage o f data i n the memory. MacDonald (1984) a l s o i d e n t i f i e d s e v e r a l p s y c h o l o g i c a l e r r o r s t h a t coaches can make when they observe and e v a l u a t e an a t h l e t e ' s performance. Such e r r o r s are "halo e f f e c t " , " l o g i c a l e r r o r " , " l e n i e n c y e r r o r " , and " c e n t r a l tendency e r r o r " . In a study t o t e s t the o b s e r v a t i o n a l accuracy o f n o v i c e coaches i n r e c a l l i n g c r i t i c a l events of a s o c c e r game, Franks and M i l l e r (1986) demonstrated the s u b j e c t s t o be h i g h l y i n a c c u r a t e i n t h e i r r e c a l l a b i l i t i e s . Three e x p e r i m e n t a l groups were d i s t i n g u i s h e d by the t i m i n g o f i n s t r u c t i o n s and the amount o f i n f o r m a t i o n i n a g i v e n i n s t r u c t i o n . The r e s u l t s showed t h a t the o v e r a l l p r o b a b i l i t y of c o r r e c t i o n a c r o s s t h r e e groups was approximately 0.42, wit h no s i g n i f i c a n t d i f f e r e n c e s among the e x p e r i m e n t a l groups. As a foll o w - u p t o t h i s study, M i l l e r (1988) r e p l i c a t e d the study with e x p e r i e n c e d coaches s e r v i n g as s u b j e c t s . In comparison with the p r e v i o u s study, M i l l e r c o n c l u d e d t h a t the e x p e r i e n c e d coaches were j u s t as much i n e r r o r as the n o v i c e coaches, though the e x p e r i e n c e d coaches were more a c c u r a t e i n r e c a l l i n g i n f o r m a t i o n r e l a t i v e t o t he s c o r i n g o f g o a l s . Researchers i n the s p o r t s c i e n c e f i e l d have endeavored t o d evelop a s y s t e m a t i c approach t o performance a n a l y s i s i n or d e r t o h e l p the coach t o e s t a b l i s h more a c c u r a t e and r e l i a b l e s p o r t - s p e c i f i c performance a n a l y s i s . A r n o l d (1983), 9 f o r e x a m p l e , s u g g e s t e d t h a t t h e p o t e n t i a l u s e o f t h e p r o p o s e d a p p r o a c h c a n be f u t h e r e n h a n c e d when t h e c o a c h c o n d u c t s h i s / h e r own a n a l y s i s t o a n s w e r o r t e s t h u n c h e s a n d o p i n i o n s b e c a u s e d a t a c a n b e c o l l e c t e d f o r p l a y e r s , l e v e l o f c o m p e t i t i o n , a n d w i t h i n h i s / h e r f r a m e w o r k o f i n t e r e s t s a n d c o n c e r n s . W i t h e x a m p l e s o f how game s t a t i s t i c s c a n i d e n t i f y w i n n i n g t r a i t s i n s e v e r a l s p o r t s , he p r o p o s e d a s y s t e m a t i c a p p r o a c h t o p e r f o r m a n c e a n a l y s i s , a n d s t a t e d , " B e g i n b y c l e a r l y d e f i n i n g t h e q u e s t i o n t o b e i n v e s t i g a t e d a n d i d e n t i f y i n g t h e s p e c i f i c d a t a n e e d e d t o a n s w e r i t . E s t a b l i s h c a t e g o r i e s f o r r e c o r d i n g t h e game s t a t s a n d t r y o u t t h e s y s t e m ... . R e v i s e t h e o b s e r v a t i o n p r o c e d u r e s , a s n e c e s s a r y . . . " (p. 49) . F r a n k s a n d Goodman (1984, 1986a) p r o p o s e d a s y s t e m a t i c , h i e r a r c h i c a l a p p r o a c h t o p e r f o r m a n c e a n a l y s i s . The m a j o r c o n c e r n o f t h e i r d i s c u s s i o n was a i m e d a t t h e e s t a b l i s h m e n t o f s o u n d b a s e f o r t h e a n a l y s i s a n d e v a l u a t i o n o f s p o r t s p e r f o r m a n c e . They d e v e l o p e d a g e n e r a l i z e d f r a m e w o r k f o r a t e a m a n d a n i n d i v i d u a l s p o r t i n w h i c h t h e k e y f a c t o r s o f p e r f o r m a n c e a r e h i e r a r c h i c a l l y p r i o r i z e d , w h i c h c o u l d s e r v e as a g u i d e f o r t h e c o a c h i n d e v e l o p i n g a s p o r t - s p e c i f i c s y s t e m . T hey s t a t e d t h a t a c o m p l e t e a n d a c c u r a t e d e s c r i p t i o n a n d t h e i d e n t i f i c a t i o n o f t h e k e y e l e m e n t s o f p e r f o r m a n c e s h o u l d be d e s i g n e d b e f o r e t r a i n i n g s e s s i o n s c a n b e i n i t i a t e d . T h ey a l s o r e commended e x t e n s i v e c o m m u n i c a t i o n s a t t h i s s t a g e b e t w e e n t h e t e c h n i c a l e x p e r t s o f t h e s p o r t a n d t h e s p o r t s c i e n t i s t i n 10 o r d e r t o e n s u r e t h a t t h e i n f o r m a t i o n c o l l e c t e d i s r e l e v a n t , n o t o n l y f o r t h e s t a t i s t i c a l p r o c e s s e s w h i c h may f o l l o w , b u t a l s o f o r t h e c o a c h i n t h e c o n t i n u a l m o n i t o r i n g a n d m o d i f i c a t i o n o f p e r f o r m a n c e . The n e x t s t e p o f t h e p r o p o s e d a p p r o a c h i s t o c a t e g o r i z e t h e p o s s i b l e o u t c o m e s o f p l a y i n g a c t i o n s o f t h e k e y f a c t o r s i n a q u a n t i t a t i v e manner a n d t o d e v e l o p a r e l i a b l e , e f f i c i e n t r e c o r d i n g m e t h o d t h r o u g h w h i c h d a t a c a n b e c o l l e c t e d . M o s t c o a c h e s h a v e u s e d a p a r t i c u l a r r e c o r d i n g m e t h o d i n o r d e r t o c o m p i l e some t y p e o f s t a t i s t i c s o r f r e q u e n c y c o u n t s d u r i n g s p o r t e v e n t s f o r l a t e r a n a l y s i s . A l t h o u g h P u r d y (1974) p o i n t e d o u t t h e p o t e n t i a l u s e s o f c o m p u t e r s y s t e m s i n p e r f o r m a n c e a n a l y s i s , h a n d n o t a t i o n s y s t e m s h a v e b e e n e x t e n s i v e l y u s e d a s a means o f o b j e c t i v e l y r e c o r d i n g d a t a d u r i n g s p o r t e v e n t s t o e n a b l e s t a t i s t i c a l a n a l y s e s o f p e r f o r m a n c e t o t a k e p l a c e . However, r e c e n t d e v e l o p m e n t s i n t h e f i e l d o f c o m p u t e r t e c h n o l o g y a n d t h e i n c r e a s i n g a v a i l a b i l i t y o f m i c r o c o m p u t e r s , i n a d d i t i o n t o d e c r e a s e s i n c o s t , h a v e a l l o w e d r e s e a r c h e r s t o u t i l i z e s u c h s y s t e m s t o i n c r e a s e t h e s p e e d , a c c u r a c y a n d e f f i c i e n c y o f t h e d a t a c o l l e c t i o n p r o c e d u r e . T h i s h a s l e d t o t h e s t o r a g e o f l a r g e a m o u n t s o f m a t c h r e l a t e d i n f o r m a t i o n a n d t h e b u i l d i n g o f a d a t a b a s e f o r a number o f s p o r t s . One o f t h e f i r s t c o m p u t e r i z e d a n a l y s i s s y s t e m s was d e v e l o p e d by F r a n k s , Goodman a n d M i l l e r ( 1 9 8 3 b ) . They c o n s t r u c t e d a k e y b o a r d on a m i n i -c o m p u t e r t o r e s e m b l e t h e l a y o u t o f a s o c c e r f i e l d a n d d e s i g n e d 11 a program which y i e l d e d frequency t a l l i e s o f v a r i o u s f e a t u r e s of p l a y i n c o l l e c t i n g data from the 1982 World Cup. The path of the b a l l was f o l l o w e d and a s p e c i f i c event was r e p r e s e n t e d by d e p r e s s i n g a s p e c i a l f u n c t i o n key on the key- board. A v i d e o was t i m e - l o c k e d i n t o the system so t h a t r e l e v a n t s e c t i o n s o f matches c o u l d be r e p l a y e d a l o n g s i d e the computer a n a l y s i s at a l a t e r date. Franks e t a l . (1983a) suggested t h a t t h i s system c o u l d be used f o r s e v e r a l purposes: a) immediate feedback; b) development o f a data base; c) e v a l u a t i o n p r o c e s s ; d) as a mechanism f o r s e l e c t i v e s e a r c h i n g through a v i d e o r e c o r d i n g o f the game. The a p p l i c a t i o n s o f such a computerized system t o v a r i o u s s p o r t s such as; Soccer, Squash, Tennis, F o o t b a l l , F i e l d hockey, B a s k e t b a l l , Fencing, W r e s t l i n g , B a s e b a l l and V o l l e y b a l l have been w e l l documented i n s e v e r a l r e c e n t a r t i c l e s (Franks, 1988; Franks & Goodman, 1986b; Franks, P a t e r s o n & Goodman, 1986; Franks, Wilson & Goodman, 1987; Hughes, 1988; Ladany & Machol, 1977; Purdy, 1974). Given t h a t computerized systems are a v a i l a b l e , one a p p l i c a t i o n o f such systems suggested by Purdy (1974) was t h a t the system can be u t i l i z e d t o c o n s t r u c t , based on a sound theory, and/or e v a l u a t e a mathematical model which r e f l e c t s c e r t a i n i n h e r e n t p r o b a b i l i s t i c t r e n d s or p a t t e r n s u n d e r l y i n g a s p e c i f i c s p o r t . T h i s p o i n t was a l s o emphasized by Franks and 12 Goodman (1986a) who commented t h a t "once the s p o r t s p e c i f i c d a ta base i s a v a i l a b l e , g a t h e r e d through the m o n i t o r i n g of performance, the g e n e r a t i o n of a mathematical model o f performance i s p o s s i b l e " (p. 10). Among these same l i n e s Schutz (1970a) had proposed the p o t e n t i a l a p p l i c a b i l i t y of s t o c h a s t i c models t o the study of s p o r t and p h y s i c a l a c t i v i t y . He p o i n t e d out t h a t the nature of s t o c h a s t i c p r o c e s s e s can make them a u s e f u l t o o l f o r the r e s e a r c h e r t o set up t h e o r i e s as mathematical models, t o t e s t these models and then t o adapt e i t h e r the theory, the model, or both. However, t o date very l i t t l e r e s e a r c h has a p p l i e d these concepts i n the f i e l d o f s p o r t s c i e n c e . In a more rec e n t a n a l y s i s of d i s c o u r s e on s p o r t and mathematics Schutz (1980) asked the q u e s t i o n "who s t u d i e s one o f the most c r u c i a l components o f s p o r t s p e r f o r m a n c e — d e c i s i o n making and s t r a t e g y ? " , and went on t o answer " u n f o r t u n a t e l y , at p r e s e n t no one i s doing i t i n a s y s t e m a t i c manner" (p. 3 7 ) . The major d i s c u s s i o n of t h i s study was d i r e c t e d towards the r o l e o f mathematical modeling i n a f i e l d o f study d e a l i n g w i t h the a n a l y s i s of s p o r t . The a p p l i c a t i o n s o f such te c h n i q u e s as p r o b a b i l i t y t h e o r y , Markov m o d e l l i n g , and computer s i m u l a t i o n t o the a n a l y s i s o f c o m p e t i t i v e s p o r t were a l s o d i s c u s s e d w i t h examples o f what mathematical a n a l y s e s have r e v e a l e d i n a number o f s p o r t s . Throughout examination o f many areas i n s p o r t and p h y s i c a l a c t i v i t y which r e q u i r e a mathematical s o l u t i o n , Schutz (1980) went on t o p o i n t out t h a t "... the 13 data are a v a i l a b l e , and the mathematical t o o l s are a v a i l a b l e . I f we are t o approach t h i s t a s k i n a s y s t e m a t i c manner, a l o g i c a l f i r s t s t e p i s t o d e f i n e t h i s area o f i n v e s t i g a t i o n and or g a n i z e i t i n t o some type o f taxonomy, or at l e a s t a s t r u c t u r a l framework" (p. 39). 2.2 Quantitative Analysis i n V o l l e y b a l l Most coaches have u t i l i z e d a method o f r e c o r d i n g t h e i r team performance i n order t o o b t a i n i n f o r m a t i o n about t h a t performance which they f e e l was important. Perhaps the most p o p u l a r method, and c e r t a i n l y the s i m p l e s t i s a c h e c k l i s t a n a l y s i s d u r i n g a l i v e game or a v i d e o r e p l a y . The d e s i g n or format o f a c h e c k l i s t can be v a r i e d a c c o r d i n g t o the q u e s t i o n s to be i n v e s t i g a t e d ( s p e c i f i c or g e n e r a l ) , and the purpose o f the a n a l y s i s ( i n d i v i d u a l or team performance). S e v e r a l s t u d i e s have been conducted i n the a n a l y s i s and e v a l u a t i o n of i n d i v i d u a l s and/or team performance i n v o l l e y b a l l (Baacke, 1982; Byra & S c o t t , 1983; Ejem, 1980; L i r d l a , 1980; Rose, 1983; Sawula, 1977; V o j i k , 1980). In these s t u d i e s the s i x s k i l l s * , o f serve, serve r e c e p t i o n , s e t , s p i k e , b l o c k , and d i g , were s e l e c t e d as key f a c t o r s o f performance and o b s e r v a t i o n s i n v o l v e d i n the c l a s s i f i c a t i o n and r e c o r d i n g o f these s e l e c t e d s k i l l s . They were f i r s t q u a n t i f i e d i n terms o f the q u a l i t y o f t h e i r e x e c u t i o n on a 3 , 4 , or 5-point n u m e r i c a l s c a l e , and t h i s was f o l l o w e d by a q u a l i t a t i v e i n t e r p r e t a t i o n o f the outcome of the performance. Frequency counts were then made o f 14 p a r t i c u l a r l e v e l s of performance w i t h i n each s k i l l and l a t e r compiled i n a s e r i e s o f summary t a b l e s . S t a t i s t i c a l t echniques o f e i t h e r d e s c r i p t i v e or i n f e r e n t i a l nature were then used t o an a l y z e the data f o r a number o f d i f f e r e n t purposes. D e s c r i p t i v e s t a t i s t i c s such as averages, s u c c e s s / e r r o r r a t e s and e f f i c i e n c y o f the performance gave an o v e r a l l i m p r e s s i o n o f the e f f e c t i v e n e s s o f a c e r t a i n p l a y i n g e n e r a l . T h i s i n f o r m a t i o n was p r i m a r i l y used i n the e v a l u a t i o n o f the performance and i n the p r e p a r a t i o n o f t r a i n i n g s e s s i o n s . I n f e r e n t i a l s t a t i s t i c s such as a n a l y s i s o f v a r i a n c e , r e g r e s s i o n or c o r r e l a t i o n i n e i t h e r a u n i v a r i a t e or a m u l t i v a r i a t e form have a l s o been used t o compare the p l a y i n g c h a r a c t e r i s t i c s between w i n n i n g / l o s i n g games or teams, t o p r e d i c t outcomes or group memberships, or t o i n v e s t i g a t e the r e l a t i o n s h i p between the s k i l l performance and team success (Cox, 1974; Ejem & Horak, 1980; N i s h i j i m a & Matsuura, 1988). A r e c e n t advance has been the use o f c o m p u t e r - a s s i s t e d r e c o r d i n g systems t o c o l l e c t l a r g e amounts of data f o r the e v a l u a t i o n o f i n d i v i d u a l and team performance i n many i n t e r n a t i o n a l v o l l e y b a l l tournaments. The s t a t i s t i c a l i n f o r m a t i o n about an i n d i v i d u a l and team performances was used mainly f o r o f f i c i a l r e c o r d s and d i s t r i b u t e d t o the world p r e s s and media. Penner (1985) developed a microcomputer program f o r use by an i n d i v i d u a l team. T h i s program all o w s an o p e r a t o r w i t h s u f f i c i e n t t r a i n i n g t o r e c o r d , p r e s s i n g t h r e e 15 keys per s k i l l , the a c t i o n s of both teams and then t o produce a v a r i e t y of d e s c r i p t i v e s t a t i s t i c s about the game. Regardless of whether a p a r t i c u l a r c h e c k l i s t or computer a s s i s t e d r e c o r d i n g method i s used, t h e r e are a number of shortcomings i n the c u r r e n t l y a v a i l a b l e systems. These are t h e i r p r a c t i c a l uses f o r the coach, the e v a l u a t i o n of team performance, and more i m p o r t a n t l y , the methodology of the data a n a l y s i s . F i r s t , the i n f o r m a t i o n o b t a i n e d by a c h e c k l i s t , a l t h o u g h easy to use, and i n e x p e n s i v e t o o b t a i n , may not be s u f f i c i e n t i n i t s e l f t o r e p r e s e n t a team's o v e r a l l performance u n l e s s a l a r g e number of observers are i n v o l v e d . I f a number of o b s e r v e r s are i n v o l v e d , t h e r e c o u l d be some v a r i a t i o n s among obs e r v e r s which cause the r e s u l t s t o be l e s s r e l i a b l e . Second, the game of v o l l e y b a l l c o n s i s t s of two main phases: o f f e n c e and defence, each h a v i n g t h r e e or f o u r s e q u e n t i a l s k i l l p l a y s ( B e r t u c c i , 1979; F r a s e r , 1988; Tennant, 1976). These s k i l l s i n each phase are supposed t o occur s e q u e n t i a l l y i n a h i e r a r c h i c a l order (see F i g u r e 1). W i t h i n each phase a t r a n s i t i o n occurs between the serve r e c e p t i o n (or dig) and s e t , and between the set and s p i k e . In p r e v i o u s s t u d i e s the performance of such s k i l l s as the s e t and s p i k e have been t r e a t e d and i n t e r p r e t e d i n the same manner, d i s r e g a r d i n g whether they occur i n an "Attack P r o c e s s " (AP) or i n a " C ounterattack P r o c e s s " (CP) (see F i g u r e 1 f o r d e f i n i t i o n s ) . The c o n c l u s i o n s based on data o b t a i n e d i n t h i s F i q u r e - 1 . A Flow Diagram of the Game of V o l l e y b a l l Team A Team B Serve (1 ->-Serve R e c e p t i o n (2)*" 1 Set (3) S p i k e (4 B l o c k (5)^ I -Dig (6) ^AD Serve 2) Serve R e c e p t i o n (3) Set ^AA) Spike 5) B l o c k (6) D i g A t t a c k P r o c e s s : S e q u e n t i a l s k i l l events from the s e r v e r e c e p t i o n (2) t o s e t (3) t o s p i k e (4). T h i s p r o c e s s i s i n i t i a t e d by the opponent's s e r v e and ends when a team r e t u r n s the b a l l t o the opponent w i t h a s p i k e . C o u n t e r a t t a c k P r o c e s s : S e q u e n t i a l s k i l l events from b l o c k (5) t o d i g (6) t o set ( 3 ) t o s p i k e (4). T h i s p r o c e s s i s i n i t i a t e d by t h e opponent's a t t a c k and ends when a team r e t u r n s the b a l l t o the opponent w i t h a c o u n t e r a t t a c k . Note: The s e t and s p i k e are i n v o l v e d i n both A t t a c k P r o c e s s and C o u n t e r a t t a c k P r o c e s s e s . However, they are s e p a r a t e l y r e c o r d e d and i n t e r p r e t e d a c c o r d i n g l y . 17 manner c o u l d m i s l e a d coaches i n t h e i r e v a l u a t i o n of the team's s t r e n g t h s or weaknesses, and u l t i m a t e l y i n the p r e p a r a t i o n of p r a c t i c e s e s s i o n s . For example, i f the e f f i c i e n c y o f the set or s p i k e was poor, what area s h o u l d the coach focus on i n the p r a c t i c e s e s s i o n s i n order t o i n c r e a s e the e f f i c i e n c y , i n i t i a l o f f e n s i v e p l a y s or t r a n s i t i o n p l a y s ? T h i s i s o f t e n an important coaching d e c i s i o n s i n c e an i n i t i a l o f f e n s i v e p l a y aims at g e t t i n g the r i g h t of serve back, whereas a t r a n s i t i o n p l a y , f o l l o w e d by the d i g , i s d i r e c t e d toward winning a p o i n t . T h i s concept was demonstrated i n a r e c e n t study by N i s h i j i m a , Ohsawa and Matwuura (1987) on the r e l a t i o n s h i p between team performance and s e l e c t e d s k i l l s i n v o l l e y b a l l . The s k i l l s were c l a s s i f i e d i n t o one of two c a t e g o r i e s , "Attack f o l l o w e d serve r e c e p t i o n " and "Attack f o l l o w e d r e c e p t i o n " ( d i g ) (p. 21). The s e t and s p i k e were i n v o l v e d i n both c a t e g o r i e s , but were t r e a t e d s e p a r a t e l y i n the a n a l y s e s and i n t e r p r e t a t i o n s which f o l l o w e d . A t h i r d shortcoming w i t h the methods used i n p a s t s t u d i e s i s t h a t the performance of a s k i l l was viewed and i n t e r p r e t e d as an independent event, without c o n s i d e r a t i o n of the q u a l i t y o f the p r e c e d i n g s k i l l performance i n the s e q u e n t i a l s e r i e s of e v e n t s . The a n a l y s i s o f the s k i l l performances was based on the data c o l l e c t e d on the performance at a p o i n t i n t ime. The r e s u l t s from t h i s type of independent s k i l l a n a l y s i s c o u l d a g a i n m i s l e a d the coach i n the e v a l u a t i o n of t h a t s k i l l . A complete understanding of a c e r t a i n r e l a t i o n s h i p or p l a y i n g 18 p a t t e r n t h a t e x i s t s amongst s k i l l s o c c u r r i n g i n a s e q u e n t i a l o r d e r might not be obtained. For example, i f the s p i k e e f f i c i e n c y o f a team i n a p a r t i c u l a r game was 80%, as compared t o 50% i n another game, one c o u l d not be sure from t h i s r e s u l t how t o account f o r the d i f f e r e n c e s between the two games. Was the d i f f e r e n c e due t o the i n c o n s i s t e n c y o f the s p i k e r ' s performances or the l e s s e r q u a l i t y o f the s e t t i n g ( i . e . , the s p i k e r s had poor s e t s f o r one game, and good s e t s f o r the ot h e r game). T h i s example c o u l d be e q u a l l y a p p l i e d t o the e v a l u a t i o n o f an i n d i v i d u a l ' s performance. There are many s i t u a t i o n s i n which a s e r i e s of r e l a t e d performances take p l a c e w i t h i n an o f f e n s i v e or d e f e n s i v e phase i n team s p o r t s . T h i s sequence of performances i s u s u a l l y s et up by the coach from the team t a c t i c p e r s p e c t i v e . The s u c c e s s f u l c o n n e c t i o n o f these performances o f t e n d i c t a t e s the success o f team p l a y and i n c r e a s e s the p r o b a b i l i t y o f a c h i e v i n g a g o a l or p o i n t i n an o f f e n s i v e phase. Coaches are q u i t e o f t e n c u r i o u s t o know what types o f passes or s e t s are more l i k e l y t o l e a d t o the success o f the g o a l or the spike, r a t h e r than the o v e r a l l percentage o f su c c e s s . The answer t o t h i s q u e s t i o n w i l l p r o v i d e the coach more d e t a i l e d and u s e f u l i n f o r m a t i o n about the performance than a f i g u r e on the o v e r a l l p e rcentage o f the success or s u c c e s s / e r r o r r a t e o f the s k i l l . Few s t u d i e s have attempted t o d e s c r i b e and i n t e r p r e t the degree of interdependency of the performance w i t h i n a phase of the s e q u e n t i a l s k i l l s , based on the d e s c r i p t i v e or 19 c o r r e l a t i o n a l d ata. In a study on the r e l a t i o n s h i p between serve r e c e p t i o n and s p i k i n g p r o f i c i e n c y w i t h the Canadian women's v o l l e y b a l l team, Sawula (1975) assumed t h a t "a team's o f f e n s i v e system i s b u i l t upon serve r e c e p t i o n because i t le a d s t o s e t and then t o s p i k e " (p 66). The major p o i n t made i n t h i s u n i t performance a n a l y s i s was t h a t when a bad r e c e p t i o n occurs, then the percentage o f e r r o r i n set i s g r e a t l y i n c r e a s e d and w i l l p robably r e s u l t i n a bad s p i k e . The same concept was pres e n t e d by McGown (1974) i n a t e c h n i c a l a r t i c l e on p r o b a b i l i t y and team o f f e n s e f o r the U.S.A. men's v o l l e y b a l l team. The o f f e n s i v e system was c o n s i d e r e d as a l i n k o f th r e e s k i l l s ; serve r e c e p t i o n , s e t , and s p i k e . He p o i n t e d out t h a t the percentage o f success i n those s k i l l s " d i c t a t e s what we can (and s h o u l d ) , and can't (and s h o u l d not) t r y to do on o f f e n s e " (p 11). What t h i s i n d i c a t e s i s t h a t i f a pass i s p e r f e c t , a s e t would be e a s i e r , thus a f a s t and m u l t i p l e o f f e n s e c o u l d be performed w i t h minimum e r r o r s . The u n d e r l y i n g concept i n these s t u d i e s was t h a t t h e r e e x i s t s a c e r t a i n r e l a t i o n s h i p i n the l i n k o f team o f f e n s e . However, no f u r t h e r a n a l y s i s was c a r r i e d out t o support t h e s e assumptions. T h i s p o i n t was s i m i l a r l y demonstrated i n a rec e n t study on the a n a l y s i s o f c r o s s e s i n s o c c e r by Franks (1988). He p o i n t e d out t h a t the o v e r a l l c r o s s - g o a l r a t i o was only 27:1. However, t h i s r a t i o d r a m a t i c a l l y i n c r e a s e s a c c o r d i n g t o the q u a l i t y o f c r o s s . In "cr o s s e s t h a t were c o n t a c t e d by an 20 a t t a c k e r " the g o a l r a t i o was only 8:1 and of these the " c r o s s e s t h a t l e a d to s t r i k e s " g o a l r a t i o was 5:1. He went on t o s t a t e t h a t "... i f you can have an a t t a c k e r c o n t a c t the c r o s s , and t h i s c o n t a c t leads t o a s t r i k e on g o a l , your p r o b a b i l i t y of s c o r i n g i s t wice what i t would have been g i v e n another type of shot. A l s o , t h e r e s h o u l d be c l o s e s c r u t i n y p a i d t o the q u a l i t y of c r o s s e s ... too many poor q u a l i t y c r o s s e s are b e i n g d e l i v e r e d " (p 39). 2.3 Analysis of Sequential Events i n Sport Any team s p o r t c o n s i s t s of a s e r i e s of dependent and independent d i s c r e t e events, each w i t h a q u a n t i f i a b l e outcome. The r e s u l t of p l a y i n g a c t i o n i s o f t e n c l a s s i f i e d a c c o r d i n g t o i t s outcome (success or e r r o r ) , i t s c o n d i t i o n ( l o c a t i o n , d i r e c t i o n or p l a c e ) , or a combination of the two. Frequency counts or the p r o p o r t i o n of the outcome w i t h i n r e s p e c t i v e c a t e g o r i e s are summarized i n v a r i o u s ways to d e s c r i b e the c h a r a c t e r i s t i c s of team and/or i n d i v i d u a l performance. The s t a t i s t i c a l t e c h n i q u e s most f r e q u e n t l y used have been c o r r e l a t i o n , r e g r e s s i o n or a n a l y s i s o f v a r i a n c e . C o r r e l a t i o n c o e f f i c i e n t s can be o b t a i n e d by a v e r a g i n g out the d i s t r i b u t i o n o f the outcome w i t h i n c a t e g o r i e s and i s u s u a l l y used to d e s c r i b e the degree of r e l a t i o n s h i p between performances. A l t h o u g h t h i s may p r o v i d e coaches w i t h a g e n e r a l u n d e r s t a n d i n g o f the r e l a t i o n s h i p between performances, i t p r e c l u d e s c e r t a i n p r o b a b i l i s t i c p a t t e r n s of performance i n each c a t e g o r y which 21 c o u l d p r o v i d e more v a l u a b l e i n f o r m a t i o n f o r the coach. A n a l y s i s o f v a r i a n c e techniques p r o v i d e t e s t s f o r the e f f e c t s o f v a r i o u s f a c t o r s on a dependent v a r i a b l e . However, they may not be a p p r o p r i a t e t o analyze s p o r t - r e l a t e d data, where the o b s e r v a t i o n s are not from p o p u l a t i o n s t h a t are normally d i s t r i b u t e d w i t h constant v a r i a n c e . In r e v i e w i n g r e l a t e d l i t e r a t u r e t h e r e are two a v a i l a b l e methods which c o u l d be u t i l i z e d t o i n v e s t i g a t e the r e l a t i o n s h i p , or p a t t e r n o f performance, i n the s e q u e n t i a l events i n s p o r t . These are s t o c h a s t i c p r o c e s s e s and l o g -l i n e a r c o n t i n g e n c y t a b l e a n a l y s i s . 2.3.1 S t o c h a s t i c Processes The a p p l i c a t i o n s o f s t o c h a s t i c p r o c e s s e s t o the study o f sp o r t and p h y s i c a l a c t i v i t y has w e l l been documented i n a paper by Schutz (1970a). He p o i n t e d out t h a t "they possess a number o f q u a l i t i e s , such as be i n g s u i t a b l e f o r dependent o b s e r v a t i o n s and not r e q u i r i n g assumptions o f n o r m a l i t y or h o m o s c e d a s t i c i t y , which make them e s p e c i a l l y s u i t a b l e i n the study o f s p o r t and p h y s i c a l a c t i v i t y " (p. 212). S t o c h a s t i c p r o c e s s e s are u s u a l l y d e s c r i b e d i n terms o f a set o f d i s c r e t e s t a t e s and a s e t of one-step t r a n s i t i o n p r o b a b i l i t i e s . Among the p r o p e r t i e s o f s t o c h a s t i c p r o c e s s e s , the p r o p e r t y of sequence, i n v o l v i n g f i r s t - o r d e r or second-order Markov p r o c e s s e s , may be most a p p r o p r i a t e t o the a n a l y s i s o f s e q u e n t i a l events i n s p o r t . Any g i v e n s e r i e s o f events y i e l d s 22 a s e r i e s of outcomes c a l l e d " s t a t e s " , t o which p r o b a b i l i t i e s can be a t t a c h e d . The p r o b a b i l i t y o f moving from one s t a t e to another i s c a l l e d t r a n s i t i o n p r o b a b i l i t y . When data are o r g a n i z e d as contingency t a b l e s w i t h the s t a r t i n g s t a t e (response at time t) i n the rows, and the ending s t a t e (response at time t+1) i n the columns, the t r a n s i t i o n m a t r i x c o n t a i n i n g the p r o b a b i l i t i e s , which events i n any g i v e n s t a t e at time t w i l l be i n some p a r t i c u l a r s t a t e at time t+1, can be e s t i m a t e d by forming the p r o p o r t i o n s w i t h i n rows (see Table 2-1). With data from at l e a s t t h r e e time p o i n t s , t h e r e are two s e t s o f f i r s t - o r d e r Markov p r o c e s s t r a n s i t i o n p r o b a b i l i t i e s : those from time 1 t o time 2 and from time 2 t o time 3, and one second-order t r a n s i t i o n p r o b a b i l i t y : t h a t from time 1 t o time 3. Thus, examining the c h a r a c t e r i s t i c s o f these p r o b a b i l i t i e s , one can e i t h e r i d e n t i f y antecedents o f a p a r t i c u l a r s t a t e , p r e d i c t the outcome of some event i n the f u t u r e or compare a change between two s e t s o f t r a n s i t i o n p r o b a b i l i t y over time p e r i o d . Kenyon and Schutz (1970) made use o f such procedures as a r e s e a r c h t o o l t o i n v e s t i g a t e the p a t t e r n s o f involvement i n g o l f and h a n d b a l l . They examined the s t o c h a s t i c p r o p e r t i e s of data c o l l e c t e d on 132 g o l f e r s and 27 h a n d b a l l e r s over a season of p l a y . The model u t i l i z e d was a d i s c r e t e s p a c e - d i s c r e t e time p r o c e s s w i t h the f o u r s t a t e s d e f i n i n g the frequency o f p l a y . The t r a n s i t i o n data m a t r i c e s were t e s t e d f o r independence between the outcomes of two events by c h i - s q u a r e 23 s t a t i s t i c s . A f t e r f i n d i n g the presence of dependence, f u r t h e r i n v e s t i g a t i o n s were c a r r i e d out to examine the nature of t h i s dependence by employing a f i r s t - o r d e r or second-order Markov p r o c e s s t o answer the q u e s t i o n of what would be the e f f e c t of success (or f a i l u r e ) at time t on the degree of involvement at time t+1. A f u r t h e r a n a l y s i s was c a r r i e d out t o determine whether t h e two s e t s of t r a n s i t i o n p r o b a b i l i t i e s are constant from one p o i n t i n time t o the next (time s t a t i o n a r i t y h y p o t h e s i s ) . T able 2-1 T r a n s i t i o n M a t r i x T r a n s i t i o n a l P r o b a b i l i t y : the degree o f s e q u e n t i a l dependency among the p l a y i n g a c t i o n s . S k i l l at time t+1 or t+2 S k i l l at time t S c a l e 4 3 2 1 ID 3 P 0 P P P P Where i j p i j s c a l e 4,3,2, and 1 i n s t a t e t , s c a l e 4,3,2,1, and 0 i n s t a t e t+1 or t+2, and the p r o b a b i l i t y of b e i n g i n s t a t e j at s k i l l t+1 or s k i l l t+2, g i v e n t h a t the p r o c e s s was i n s t a t e i at s k i l l t . 24 Trueman (1977) a l s o used the Markov p r o c e s s i n a n a l y z i n g the game o f b a s e b a l l . He developed a mathematical model of the o f f e n s i v e a s p e c t s of b a s e b a l l based upon p r o b a b i l i t y t h e o r y , i n o r d e r t o e v a l u a t e the e f f e c t i v e n e s s of d i f f e r e n t l i n e u p s and b a t t i n g o r d e r s . Through the use of a computer program the p r o b a b i l i t y d i s t r i b u t i o n s o f the number o f b a t t e r s f o r every i n n i n g and r e s p e c t i v e l i n e u p s were c a l c u l a t e d , and these r e s u l t s were used t o e v a l u a t e a v a r i e t y of d i f f e r e n t s t r a t e g i e s which attempted t o i n c r e a s e the expected success p r o b a b i l i t i e s . S t o c h a s t i c p r o c e s s e s have been a p p l i e d i n a number of s t u d i e s t o i n v e s t i g a t e a wide v a r i e t y of phenomena i n s p o r t and p h y s i c a l a c t i v i t y : s c o r i n g systems ( M i l e s , 1984; P f e i f e r & Deutsch, 1981; P o l l a r d , 1983; Schutz, 1970b; Schutz & Kinsey, 1977), d e c i s i o n s and team s t r a t e g y (Morrison, 1976; H e f f l e y , 1977), motor b e h a v i o r (Kenyon & Schutz, 1970; Tonge, 1976; Schutz, 1972); and a n a l y z i n g performance (Ladany and Machol, 1977). Schutz (1980) i n h i s study on s p o r t and mathematics p r o v i d e d an e x t e n s i v e review of the a p p l i c a t i o n s of p r o b a b i l i t y t h e o r y and computer s i m u l a t i o n s t o v a r i o u s r e l a t e d areas which r e q u i r e a mathematical s o l u t i o n . In p a r t i c u l a r , p r a c t i c a l a p p l i c a t i o n o f mathematical methods t o a number of c o m p e t i t i v e s p o r t s , known as mathematical a n a l y s i s of s p o r t , has been w e l l documented i n two p u b l i c a t i o n s : Optimal  S t r a t e g i e s i n Sports (Ladany & Machol, 1977) and Management 25 S c i e n c e i n Sports (Machol, Ladany, & Morrison, 1976) . 2.3.2 Log-linear Analysis U n t i l r e c e n t l y Chi-square t e s t f o r independence was l i m i t e d t o analyze two-dimensional t a b l e s s i n c e i t s a p p l i c a t i o n t o t a b l e s o f more than two v a r i a b l e s u s u a l l y d i d not r e s u l t i n a s y s t e m a t i c e v a l u a t i o n of the r e l a t i o n s h i p among the v a r i a b l e s . However, r e s e a r c h e r s o f t e n possess i n f o r m a t i o n s u f f i c i e n t t o s t r u c t u r e contingency t a b l e s of more than two dimensions. F u r t h e r , they d e s i r e t o s u b j e c t these m u l t i p l e dimensions t o a comprehensive, simultaneous a n a l y s i s . Recent t h e o r e t i c a l developments and the appearance of computer programs have l e d the emergence of a number of procedures t h a t can examine m u l t i d i m e n s i o n a l c o n t i n g e n c y t a b l e s , p e r m i t t i n g the examination of v a r i o u s types of h i g h e r -o r d e r i n t e r a c t i o n s among v a r i a b l e s . T h i s s t a t i s t i c a l a n a l y s i s i s r e f e r r e d t o as l o g - l i n e a r contingency t a b l e a n a l y s i s , and i s a g e n e r a l procedure t h a t a l l o w s f o r model f i t t i n g , h y p o t h e s i s t e s t i n g , and parameter e s t i m a t i o n f o r any model t h a t has c a t e g o r i c a l v a r i a b l e s as i t s major components ( A g r e s t i , 1984; F e i n b e r g , 1980; Goodman, 1978; Kennedy, 1983; M a r a s c u i l o & L e v i n , 1983). The s t a t i s t i c s used f o r the t e s t o f a h y p o t h e s i s t h a t a p a r t i c u l a r model f i t s the observed data can be based on e i t h e r Pearson c h i - s q u a r e or maximum l i k e l i h o o d c h i - s q u a r e s t a t i s t i c s . The advantage of the l a t t e r one i s t h a t i t can be 26 s u b d i v i d e d i n t o i n t e r p r e t a b l e p a r t s t h a t add up to the t o t a l , s i m i l a r t o a decomposition o f the t o t a l sum of squares i n ANOVA. Sin c e the parameters i n l o g - l i n e a r model are d i r e c t l y analogous t o i t s c o r r e s p o n d i n g members i n co n v e n t i o n a l , m u l t i f a c t o r ANOVA, e f f e c t parameters i n l o g - l i n e a r models may be l e g i t i m a t e l y viewed and subsequently i n t e r p r e t e d i n a manner c o n s i s t e n t with c o n v e n t i o n a l ANOVA procedures (Kennedy, 1983). However, one fundamental d i f f e r e n c e between ANOVA models and l o g - l i n e a r models i s t h a t ANOVA models are p r e d i c a t e d on e x p l a n a t i o n s based on a p a r t i t i o n i n g o f v a r i a n c e , whereas l o g - l i n e a r models are based on the p r o b a b i l i t i e s a s s o c i a t e d w i t h the v a r i o u s c e l l s i n the con t i n g e n c y t a b l e . The b a s i c g o a l i n a l o g - l i n e a r model approach i s t o s p e c i f y a model t h a t p r e d i c t s c e l l f r e q u e n c i e s , p r o p o r t i o n s , or p r o b a b i l i t i e s (Burnett, 1983). Knoke and Burke (1980) p o i n t e d out t h a t " d u r i n g the past decade a r e v o l u t i o n i n contingency t a b l e a n a l y s i s has swept through the s o c i a l s c i e n c e s , c a s t i n g a s i d e most of the o l d e r forms f o r de t e r m i n i n g r e l a t i o n s h i p s among v a r i a b l e s measured at d i s c r e t e l e v e l s " (p. 7 ) . Recent s t u d i e s have p r o v i d e d f o r the a p p l i c a t i o n o f l o g - l i n e a r procedures i n the examination o f v a r i o u s s o c i a l r e l a t i o n s h i p s i n b e h a v i o r a l s c i e n c e (Baker, 1981; B u r n e t t , 1983; Knoke & Burke, 1980; M a r a s c u i l o & Busk, 1987) . The examples p r o v i d e d i n these s t u d i e s i l l u s t r a t e the g e n e r a l procedure o f a l o g - l i n e a r model f o r h y p o t h e s i s t e s t i n g and model b u i l d i n g , i n c l u d i n g d e t a i l e d g u i d e l i n e s f o r 27 p e r f o r m i n g an a n a l y s i s on frequency data f o r two, t h r e e and fo u r d i mensional t a b l e s . A l l i s o n and L i k e r (1982) have a l s o shown the use of such procedures f o r a n a l y z i n g s e q u e n t i a l c a t e g o r i c a l d ata. With data c o l l e c t e d on the b e h a v i o r o f a m a r r i e d couple at a sequence o f n p o i n t s i n time, they t e s t e d whether the responses o f husband's b e h a v i o r at time t+k are a f f e c t e d by t h a t o f w i f e ' s b e h a v i o r at time t . Often s i t u a t i o n s a r i s e i n which one wishes t o d i s t i n g u i s h between e x p l a n a t o r y (independent) and response (dependent) v a r i a b l e s i n h i g h e r - o r d e r dimension t a b l e s . Such a d i s t i n c t i o n u s u a l l y l e a d s the r e s e a r c h e r i n t o the realm o f l o g i t - l i n e a r a n a l y s i s . L o g i t a n a l y s i s i s a s p e c i a l case o f l o g - l i n e a r a n a l y s i s i n which the purpose o f the models i s t o i d e n t i f y a f a c t o r or f a c t o r s (independent v a r i a b l e s ) t h a t are r e s p o n s i b l e f o r the d i s t r i b u t i o n o f responses i n the dependent v a r i a b l e ( s ) . Baker (1981) p r o v i d e d a d e t a i l e d comparison of l o g - l i n e a r and l o g i t - l i n e a r approach w i t h r e s p e c t i v e computations and i n t e r p r e t a t i o n s . M a r a s c u i l o and Busk (1987) have a l s o proposed a comparable procedure t o the l o g i t model. When one or more v a r i a b l e s are t r e a t e d as dependent v a r i a b l e s i n a l o g - l i n e a r model, t h i s model can be d i s p l a y e d as a c o n v e n t i o n a l ANOVA or MANOVA t a b l e . U s i n g a n u m e r i c a l example o f a f o u r - d i m e n s i o n a l c o n t i n g e n c y t a b l e , they showed a t r a n s f o r m a t i o n procedure t o decompose the c h i - s q u a r e t a b l e i n a l o g - l i n e a r model and c o n s t r u c t a MANOVA-like t a b l e i n which the main e f f e c t s and 28 the i n t e r a c t i o n o f two independent v a r i a b l e s can be a s s e s s e d f o r both dependent v a r i a b l e s . They suggested t h a t t o d i s p l a y l o g - l i n e a r models i n the form o f a ANOVA or MANOVA t a b l e p r o v i d e s f o r easy i n t e r p r e t a t i o n and consequently i s p r e f e r r e d by many r e s e a r c h e r s . 29 CHAPTER III Method and Procedure 3.1 Subject of Observation The 3rd " F e d e r a t i o n of I n t e r n a t i o n a l V o l l e y b a l l " (FIVB) Cup f o r men, h e l d i n Seoul, Korea from November 6 through 11, 1987, was chosen f o r a n a l y s i s . A l l 162 games were ta p e d w i t h a v i d e o camera i n a p p r o p r i a t e f i l m i n g c o n d i t i o n s by an expert working f o r the Sport Science I n s t i t u t e i n Seoul, Korea. Ta b l e 3-1 Number o f Games Per Team P l a y e d i n the P r e l i m i n a r y Round Team Winning L o s i n g T o t a l Top 4 U.S.S.R. 7 2 9 U.S.A. 7 2 9 H o l l a n d 6 3 9 B u l g a r i a 4 5 9 Bottom 4 Korea 4 5 9 Canada 4 5 9 France 3 6 9 Japan 1 8 9 T o t a l 36 36 72 There were e i g h t n a t i o n a l teams ( B u l g a r i a , Canada, France, H o l l a n d , Japan, Korea, U.S.A., U.S.S.R.) p a r t i c i p a t i n g i n the tournament. These teams were grouped i n t o two c a t e g o r i e s (top 4 teams and bottom 4 teams) based on a team s t a n d i n g a f t e r the p r e l i m i n a r y round. A sample o f 72 games which took p l a c e i n 30 the p r e l i m i n a r y round was a l s o grouped i n t o two c a t e g o r i e s : winning and l o s i n g games. Table 3-1 p r e s e n t s teams i n a group and the number of winning and l o s i n g games per team used i n the p r e s e n t study. 3.2 S k i l l Components of Observation Over the l a s t 20 years, the a n a l y s i s of the game of v o l l e y b a l l has been based on the assumption t h a t i t c o n s i s t s of t h r e e d i s t i n c t c a t e g o r i e s : o f f e n s i v e s k i l l s (serve and s p i k e ) , t r a n s i t i o n s k i l l s (pass and s e t ) , and d e f e n s i v e s k i l l s (block and dig) ( B e r t u c c i , 1979; N i c h o l l s , 1973; Scates, 1976; Tennant, 1976). In the p r e s e n t study, these s i x s k i l l s were s e l e c t e d as key elements which r e p r e s e n t team performance i n v o l l e y b a l l . Such s k i l l s as set and s p i k e were f u r t h e r s u b c a t e g o r i z e d i n o r d e r t o o b t a i n more s p e c i f i c i n f o r m a t i o n r e g a r d i n g the c h a r a c t e r i s t i c s of performance. T h i r t e e n d i f f e r e n t t y p e s of s e t s were, f o r example, grouped i n t o t h r e e c a t e g o r i e s (high-s e t , medium-set, q u i c k - s e t ) (see Appendix A f o r types o f the s e t ) . Because each s e t type i s a s s o c i a t e d w i t h a s p e c i f i c s p i k e type, s p i k e was a l s o s u b c a t e g o r i z e d i n the same manner as the s e t . The i n f o r m a t i o n r e g a r d i n g the types o f serve ( s p i n and f l o a t ) and the number of b l o c k e r was a v a i l a b l e through the computer output program, but they were not i n c l u d e d i n the a n a l y s i s . 31 3.3 Observation C r i t e r i a For the e v a l u a t i o n of i n d i v i d u a l p l a y i n g a c t i o n s a 5-p o i n t n u m e r i c a l r a t i n g s c a l e was developed t o q u a n t i f y the e f f e c t i v e n e s s o f each performance, w i t h 0 r e p r e s e n t i n g an e r r o r and 4 r e p r e s e n t i n g a p e r f e c t e x e c u t i o n . The f o l l o w i n g s u b j e c t i v e e s t i m a t i o n s of p l a y i n g a c t i o n s were d e f i n e d as o b j e c t i v e l y as p o s s i b l e f o r the c r i t e r i a of o b s e r v a t i o n of each s k i l l performance (see Appendix B f o r the f u l l d e s c r i p t i o n s of each s k i l l performance). S c a l e 0: An e r r o r r e s u l t i n g i n a l o s t p o i n t or s i d e - o u t . S c a l e 1: A poor e x e c u t i o n , but does not l o s e a p o i n t or s i d e -out d i r e c t l y from i t . T h i s e x e c u t i o n p r o v i d e s a bad or good s i t u a t i o n f o r a team or f o r i t s opponent, r e s p e c t i v e l y . S c a l e 2: An average e x e c u t i o n . N e i t h e r team has a good o p p o r t u n i t y d i r e c t l y from i t i n i t s a t t a c k or c o u n t e r a t t a c k p r o c e s s . S c a l e 3: A good e x e c u t i o n , but does not g a i n a p o i n t or s i d e -out d i r e c t l y from i t . T h i s e x e c u t i o n p r e s e r v e s the advantage o f p l a y or gains a f r e e - b a l l from the opponent. S c a l e 4: An e x c e l l e n t e x e c u t i o n . T h i s e x e c u t i o n p r o v i d e s the b e s t p o s s i b l e s i t u a t i o n f o r the team i n the cases f o r serve r e c e p t i o n , d i g and s e t . In the cases of serve, s p i k e and b l o c k , i t g a i n s a p o i n t or s i d e - o u t . 3.4 V a l i d i t y of Observation C r i t e r i a An e d i t e d game tape which c o n t a i n s 89 p l a y i n g a c t i o n s was p r e s e n t e d t o t h r e e e x p e r t s i n the v o l l e y b a l l f i e l d , a l ong w i t h a b r i e f d e s c r i p t i o n o f the 5-point r a t i n g s c a l e f o r each o f the s i x s e l e c t e d s k i l l s . The tape c o n s i s t e d of 19 s e c t i o n s , each having a s e r i e s of t h r e e t o f i v e p l a y i n g 32 a c t i o n s . Each s e c t i o n s t a r t s w i t h i n s t r u c t i o n s e x p l a i n i n g the content and t a s k . The coaches were asked t o a s s e s s the performance and w r i t e the score on a p r o v i d e d r e c o r d i n g sheet ( r e f e r t o Appendix C f o r d e t a i l s ) . The purpose o f t h i s procedure was t o o b t a i n feedback as to whether the c r i t e r i a f o r each s k i l l performance was r e a s o n a b l y d e f i n e d i n terms of p r a c t i c a l a p p l i c a b i l i t y . More s p e c i f i c a l l y , i t was aimed t o determine whether e x p e r i e n c e d coaches have commonly agreeable o p i n i o n s when e v a l u a t i n g the s k i l l e d performance based on a 5-point r a t i n g s c a l e , and t o what e x t e n t t h e i r r e s u l t s were i n agreement w i t h t h a t of the c r i t e r i o n . The v a l i d i t y o f the system was e s t a b l i s h e d by c a l c u l a t i n g the p ercentage of agreement between the r e s u l t o f each o f the t h r e e coaches and t h a t of the r e s e a r c h e r , which s e r v e d as a c r i t e r i o n . As seen i n Table 3-2, o v e r a l l agreement between the c r i t e r i o n and the responses by the coaches was about 80 p e r c e n t , w i t h l i t t l e v a r i a t i o n among the coaches. The l a r g e s t d i s c r e p a n c y was shown i n the s e t (70%) , f o l l o w e d by the s p i k e (75%). T h i s c o u l d be due t o the f a c t t h a t both the set and s p i k e i n c l u d e a d i v e r s i t y o f d i f f e r e n t p l a y i n g a c t i o n s (13 t y p e s ) . However, when c o n s i d e r i n g the f a c t t h a t the coaches were g i v e n only a b r i e f d e s c r i p t i o n o f the c r i t e r i a f o r each s k i l l , i t can be concluded t h a t the c r i t e r i a were adequately d e f i n e d w i t h an a c c e p t a b l e degree o f p r a c t i c a l a p p l i c a b i l i t y . 33 T a b l e 3-2 Percentage o f Agreement Between the C r i t e r i a and the Coaches  i n the C l a s s i f i c a t i o n of the S k i l l s S k i l l s Coach A Coach B Coach C Average Serve 82 82 82 82 ^ S.R. 73 82 82 79 Set 70 75 65 70 Spike 75 75 75 75 Block 85 92 77 85 D i g 80 100 80 87 O v e r a l l Agreement 78 84 77 80 Table 3-3 i l l u s t r a t e s an example o f the c r o s s t a b u l a t e d r e s u l t s between the c r i t e r i a and coach C f o r the s p i k e . The f r e q u e n c i e s i n the main d i a g o n a l o f the t a b l e i n d i c a t e t h a t coach C and the c r i t e r i a are i n agreement, whereas f r e q u e n c i e s i n the o f f - d i a g o n a l are i n disagreement. O v e r a l l , t h e r e were 21, 16, and 22 cases f o r coach A, B and C, r e s p e c t i v e l y , which r e s u l t e d i n disagreement i n the c l a s s i f i c a t i o n of the s k i l l p erformances. However, v i r t u a l l y a l l d i s c r e p a n c i e s between the c r i t e r i a and the coaches were w i t h i n e i t h e r one p o i n t above or below the c r i t e r i o n , with o n l y f i v e o c c a s i o n s (2%) of the t o t a l cases b e i n g two or more p o i n t s away from the c r i t e r i o n . 34 Table 3-3 Comparison Between the C r i t e r i o n and Coach C i n Spike C r i t e r i o n / Coach C S c a l e : 4 3 2 1 0 T o t a l 4: 8 0 0 l a 0 9 3: 0 0 1 0 0 1 2: 0 2 6 0 0 8 1: 0 0 0 1 0 1 0: 0 0 0 2 3 5 T o t a l 8 2 7 4 3 24 18 b/24 = .75 c a: Frequency count t h a t was 3 p o i n t s away from the c r i t e r i o n . b: Sum of main d i a g o n a l . c: P ercent o f Agreement (75%). 3.5 Intra-Observer R e l i a b i l i t y R e l i a b i l i t y o f r e c o r d i n g procedures on the s i x s e l e c t e d s k i l l components was e s t a b l i s h e d i n the f o l l o w i n g manner. 1. E i g h t games, one game f o r each team, were s e l e c t e d f o r the o b s e r v a t i o n s . 2. D u r i n g a r e p l a y of the games, the s i x s k i l l components were q u a n t i f i e d based on the c r i t e r i a and r e c o r d e d onto the keyboard. 3. D e s c r i p t i v e s t a t i s t i c s o f the s k i l l performances such as mean and frequency counts were produced. 4. A few days l a t e r , the same procedure was r e p e a t e d and the r e s u l t s (mean performance) o b t a i n e d from the two o b s e r v a t i o n s were compared i n order t o determine the degree of the i n t r a - o b s e r v e r r e l i a b i l i t y f o r each s k i l l component expressed by a Pearson c o r r e l a t i o n c o e f f i c i e n t . 35 As seen i n Table 3-4, the r e s u l t i n g c o e f f i c i e n t s f o r the s i x s k i l l s were above .90 i n a l l cases, i n d i c a t i n g h i g h c o n s i s t e n c y i n the r e c o r d i n g procedure. The w e l l - t r a i n e d o bserver can t h e r e f o r e be expected t o produce r e l i a b l e s c o r i n g . Table 3-4 R e l i a b i l i t y C o e f f i c i e n t s f o r the S e l e c t e d S k i l l s S k i l l Obs. 1 Obs. 2 r12 Serve 1.65 a 1.66 .91 Serve r e c e p t i o n 3.10 3.09 .95 Set 2.47 2.49 . 97 Spike 2.74 2.73 .98 Block 1.36 1.39 . 97 Dig 2.14 2.19 .94 a: A mean v a l u e of a s k i l l . o f a s k i l l performance averaged acr o s s s c a l e s 3.6 Computer Program The computer program used f o r analyses was w r i t t e n f o r an ATARI 520 ST and i s compatible with the r e s t of the ATARI ST l i n e . The program c o n s i s t s o f two p a r t s : input and output. The i n p u t program i s used f o r data r e c o r d i n g and the output program produces a v a r i e t y o f game r e l a t e d d e s c r i p t i v e s t a t i s t i c s as w e l l as a t r a n s i t i o n p r o b a b i l i t y matrix between two s e l e c t e d s k i l l s . 3.6.1 Input Program A flow diagram o f the sequence of the game of v o l l e y b a l l i s g i v e n i n F i g u r e 1. Each event i s supposed t o occur s e q u e n t i a l l y i n a h i e r a r c h i c a l o r d e r , s t a r t i n g w i t h a s e r v e . The i n p u t program i s developed based on t h i s flow diagram. F i g u r e - 1 . A Flow Diagram o f the Game o f V o l l e y b a l l Team A Team B Serve (1 ->-Serve Reception (2)*" I Set (3) Spike (4 -Dig (6) ^ 1 ) Serve 2) Serve Reception<-^Ak) Spike (6) D i g A t t a c k P r o c e s s (AP): S e q u e n t i a l s k i l l events from the se r v e r e c e p t i o n (2) t o s e t (3) t o s p i k e ( 4 ) . T h i s p r o c e s s i s i n i t i a t e d by the opponent's s e r v e and ends when a team r e t u r n s the b a l l t o t h e opponent w i t h a s p i k e . C o u n t e r a t t a c k Process (CP): S e q u e n t i a l s k i l l events from b l o c k (5) t o d i g (6) t o set ( 3 ) t o s p i k e (4). T h i s p r o c e s s i s i n i t i a t e d by the opponent's a t t a c k and ends when a team r e t u r n s the b a l l t o t h e opponent w i t h a c o u n t e r a t t a c k . Note: The s e t and s p i k e a r e i n v o l v e d i n bot h A t t a c k P r o c e s s and C o u n t e r a t t a c k P r o c e s s e s . However, they are s e p a r a t e l y r e c o r d e d and i n t e r p r e t e d a c c o r d i n g l y . 37 While o b s e r v i n g the videotape the performance o f a s k i l l was g i v e n a n u m e r i c a l value r e p r e s e n t i n g i t s e f f e c t i v e n e s s d e f i n e d by the c r i t e r i a o f o b s e r v a t i o n , which was d i r e c t l y recorded onto a microcomputer keyboard. T h i s was done f o r each p l a y i n g a c t i o n of both teams. For each time a team c o n t a c t s w i t h the b a l l , an o p e r a t o r had to press a maximum o f two keys. T h i s was deemed t o be an acceptable r a t e of data i n p u t f o r the games r e p l a y e d on a video machine at normal speed and perhaps f o r a l i v e game. The "acceptable r a t e " means t h a t one with adequate knowledge of v o l l e y b a l l and moderate t y p i n g s k i l l can be expected t o accomplish a r e l i a b l e data i n p u t . Keyboard layout. The arrangement of the keyboard was designed by i n t e r p r e t i n g the keys as s c a l e s of performance and types of s k i l l (see Appendix D f o r the keyboard l a y o u t ) . Screen display. For each contact d u r i n g a r a l l y , the computer scre e n d i s p l a y s the next p o s s i b l e events, f o l l o w i n g a s e q u e n t i a l o r d e r (e.g., a spike a f t e r a s e t ) , as w e l l as those p o s s i b l e events, which do not f o l l o w a s e q u e n t i a l order ( i . e . , a s p i k e a f t e r a pass, or a set a f t e r a b l o c k ) . Once a key i s pressed, the s c r e e n shows what has been entered, namely types of s k i l l , s c a l e of performance, and p o s s e s s i o n o f the b a l l . T h i s i n f o r m a t i o n i s l a t e r s t o r e d i n a computer generated data f i l e and used t o produce d e s i r e d s t a t i s t i c a l outputs through the output program (see Appendix E f o r an example of the screen d i s p l a y and data f i l e ) . 38 3 6.2 Output Program The s t a t i s t i c s menu i n t h e o u t p u t p r o g r a m c o n s i s t o f "modes" t h a t d e t e r m i n e w h i c h m a t c h , game, team, a n d s k i l l (s) i s t o b e e v a l u a t e d . Once a d e s i r e d mode o r a c o m b i n a t i o n o f modes h a s b e e n s e l e c t e d , i t p r o d u c e s two t y p e s o f i n f o r m a t i o n : one f o r an i n d i v i d u a l s k i l l a n d t h e o t h e r f o r s e q u e n t i a l s k i l l s . Output f o r i n d i v i d u a l s k i l l . T a b l e 3-5 shows an e x a m p l e o f t h e d e s c r i p t i v e s t a t i s t i c a l o u t p u t f o r s e t t i n g p e r f o r m a n c e f o r t h e C a n a d i a n t e a m i n a m a t c h a g a i n s t K o r e a . The u p p e r p a r t o f t h e t a b l e d i s p l a y s t h e f r e q u e n c y c o u n t s a n d row p r o b a b i l i t i e s f o r t h e s u b c a t e g o r i e s o f t h e s e t i n e a c h s c a l e , w h e r e a s t h e l o w e r p a r t g i v e s a summary, a l o n g w i t h a s s o c i a t e d d e s c r i p t i v e s t a t i s t i c s f o r o v e r a l l a n d s u b s k i l l p e r f o r m a n c e s i n t h e s e t . The o u t p u t p r o g r a m p r o v i d e s f i v e d i f f e r e n t m e a s u r e s o f t h e p e r f o r m a n c e o f a s k i l l ( t h e s e t i n t h i s e x a m p l e ) s u c h a s mean p e r f o r m a n c e (MP), a v e r a g e p e r f o r m a n c e ( A P % ) , i n d i v i d u a l s k i l l e f f i c i e n c y ( I S E % ) , s u c c e s s r a t e ( S R % ) , a n d e r r o r r a t e ( E R % ) . E a c h o f w h i c h c o n t a i n s p a r t i c u l a r i n f o r m a t i o n p r o v i d i n g t h e c o a c h w i t h a d i f f e r e n t v i e w i n e v a l u a t i n g t h e p e r f o r m a n c e o f t h a t s k i l l ( r e f e r t o T a b l e 3-7 f o r d e f i n i t i o n s a n d e q u a t i o n s ) . 39 Table 3-5 An Example of S t a t i s t i c a l Output f o r S e t t i n g Performance Canada: 18:00, Canada 06/11. 1 vs. Korea Korean cup, 2 (11-Seoul 15, 5-•15, 15-13) S c a l e : 4 3 2 1 0 Mean T.Fre High P 10 .12 10 .12 37 .45 26 .31 0 .0 2.05 83 1.0 Set type Medium P 12 .29 16 .39 11 .27 2 .05 0 .0 2.93 41 1.0 Quick P 12 .32 14 .38 4 . 11 6 .16 1 .03 2.81 37 1. 0 Save 0 0 0 5 0 1.00 5 T o t a l : 34 40 52 39 1 2.40 166 S t a t s : F r e . MP AP% SR% ER% ISE% O v e r a l l 166 2.40 60.0 20.48 0.60 20.18 High 83 2.05 51.25 12.05 0.0 2.41 Medium 41 2.93 73.23 29.72 0.0 46.34 Quick 37 2.81 70.25 32.43 2.70 40.54 Save 5 - -T e c h n i c a l F a u l t s i n s c a l e 0:1. Over/Free b a l l i n s c a l e 1:0. *: Row p r o b a b i l i t i e s Output f o r sequential s k i l l s . When i n f o r m a t i o n c o n c e r n i n g the r e l a t i o n s h i p between two s k i l l s o c c u r r i n g i n a s e q u e n t i a l order i s d e s i r e d , the output program produces a t r a n s i t i o n matrix d i s p l a y i n g frequency counts and row p r o b a b i l i t i e s of each s c a l e f o r the s e l e c t e d two s k i l l s on a 40 two-dimensional t a b l e . Table 3-6 i l l u s t r a t e s a t r a n s i t i o n m a t r i x between the set and s p i k e f o r the Canadian team, along with d e s c r i p t i v e summary s t a t i s t i c s of the two s k i l l s . T able 3-6 An Example of T r a n s i t i o n M a t r i x Between Set and Spike Canada: Canada 1 v s . Korea 2 (11-15, 5-15, 15-13) 18:00, 06/11. Korean cup, Seoul SPIKE S c a l e : 4 3 2 1 0 MP T.Fre 4 : 24 2 3 1 4 3.21 34 SET a P b . .71 .06 .09 .03 .12 1. 0 ( o v e r a l l ) 3 : 20 2 16 1 1 2.98 40 P : .50 .05 .40 .03 .03 1.0 2 : 30 2 10 3 7 2.87 52 P : .58 .04 .19 .06 .13 1.0 1 : 2 0 6 22 7 1.14 37 P : .05 .00 .16 .59 .19 1.0 T o t a l : 76 6 35 27 19 2 .57 163 S t a t s : F r e . MP AP% SR% ER% ISE% DSE% SET 163 2 .44 61.0 20. 9 21.8 SPIKE 163 2 .57 64.25 46. 6 11.7 28.5 105.5 a: Types of s e t are not i d e n t i f i e d i n t h i s t a b l e , b: Row p r o b a b i l i t y . The t r a n s i t i o n matrix and the summary s t a t i s t i c s i n the t a b l e are produced based on the frequency o f the s k i l l s t h a t 41 f o l l o w e d a s e q u e n t i a l order, as d e f i n e d i n the flow diagram. That i s , i f an event v i o l a t e s the s e q u e n t i a l order, a frequency of t h i s event i s excluded from the t r a n s i t i o n p r o b a b i l i t y c a l c u l a t i o n s . For example, as can be seen i n Table 3-6, the t o t a l frequency of the set i s 163, as opposed to t h a t of 166 i n Table 3-5. The d i f f e r e n c e i n the t o t a l frequency between the two t a b l e s i n d i c a t e s t h a t t h e r e were 3 occasions of the set which were not connected t o the spike i n t h i s match. From t h i s output, the coach can o b t a i n a v a r i e t y of d e s c r i p t i v e i n f o r m a t i o n about the r e l a t i o n s h i p between the s k i l l s and a d i s t r i b u t i o n of the p l a y i n g p a t t e r n s . For example, of the t o t a l s e t s (163) t h a t were connected to the s p i k e (see Table 3-6), 34 s e t s (20.9%) r e s u l t e d i n Scale 4, r e p r e s e n t i n g p e r f e c t e x e c u t i o n s . The mean performance (MP) of the s p i k e with these s e t s was 3.21 and 24 (71%) out of 34 p e r f e c t s e t s r e s u l t e d i n winning a r a l l y i n the s p i k e . When these r e s u l t s are compared to the performance of the spike with lower s c a l e s o f the set, one can n o t i c e a s t r o n g dependence between the performance of the two s k i l l s i n t h i s match, i n d i c a t i n g t h a t the h i g h e r s c a l e i n the set, the b e t t e r performance i n the spike, or v i c e v e r s a . Dependent s k i l l e f f i c i e n c y (DSE), along with other measures, i n the summary t a b l e p r o v i d e s a means of comparing performances of the two s k i l l s which may be u s e f u l f o r the coach i n p r a c t i c e p l a n n i n g (see Table 3-7 f o r equation and d e f i n i t i o n ) . For example, the 42 v a l u e o f DSE% (105.5) of the s p i k e i n d i c a t e d that the o v e r a l l performance of the spi k e was s u p e r i o r , given the q u a l i t y of the set i n t h i s match ( i f DSE i s 100%, i t means an equal q u a l i t y i n both a c t i o n s ) . T able 3-7 O p e r a t i o n a l D e f i n i t i o n s and Equations 1. Mean Performance (MP): SUM (s^ x n-;) (e.g.,) 4 n 4 + 3 n 3 + 2n 2 + ln1 + 0n 0 N T o t a l frequency Where s^ = Scale o f the performance, 0 to 4, nj = Frequency w i t h i n a s c a l e , and N = T o t a l frequency o f the s k i l l . (Range: minimum v a l u e 0 t o maximum 4) 2. Success Rate(SR%) - the p r o p o r t i o n o f the number of s c a l e 4 i n a s k i l l : Frequency i n s c a l e 4 x !oo = SR% T o t a l frequency (Range: 0 t o 100) 3. E r r o r Rate (ER%) - the p r o p o r t i o n o f the number o f s c a l e 0 i n a s k i l l . Frequency i n s c a l e 0 x ioo = ER% T o t a l frequency (Range: 0 t o 100) 4. Average Performance (AP%) - a MP i s expressed as a percentage of maximum performance 4: MP/4 x 100 = AP% (Range: 0 t o 100) cont'd 43 5. Independent S k i l l E f f i c i e n c y (ISE%) - e f f e c t i v e n e s s o f a s k i l l performance. This i s c a l c u l a t e d by f o l l o w i n g formulas; (a) (s4n x 2 + s3n x 1) - ( s i n x 1 + sOn x 2) x 1 0 0 N x 2 Where s = s c a l e , n = frequency i n corresponding s c a l e ' and N = t o t a l frequency. (b) ISE% i s a d i r e c t l i n e a r f u n c t i o n of MP: (MP/2 - 1) x 100 = ISE% (Range: -100 t o 100, 0% being a MP of 2.0) 6. Dependent S k i l l E f f i c i e n c y (DSE%) - the degree of r e l a t i v e success i n a s k i l l t h a t i s c a l c u l a t e d while c o n s i d e r i n g the q u a l i t y o f the p r e c e d i n g s k i l l performance. Thus, DSE i s only c a l c u l a t e d from a t r a n s i t i o n matrix f o r a s k i l l at time t+1, or t+2, gi v e n the performance of a s k i l l at time t . The formula f o r t h i s c a l c u l a t i o n i s : SUM S-5 n-s / N x 100 = DSE% SUM S i n i / N Where Sj = s c a l e 0,1,2,3 and 4 i n a s k i l l at t+1 or t+2, S i = s c a l e 1,2,3 and 4 i n a s k i l l at t , n = frequency i n a corresponding s c a l e , and N = t o t a l frequency. (Range: 0 t o 400) 3.7 S t a t i s t i c a l Analysis S t a t i s t i c a l a n a l y s i s o f the data was completed i n two p a r t s : a n a l y s i s o f i n d i v i d u a l s k i l l and a n a l y s i s o f s e q u e n t i a l s k i l l s . 44 3.7.1 A n a l y s i s o f I n d i v i d u a l S k i l l The sample games were c l a s s i f i e d i n t o one of the two grouping f a c t o r s , each having two l e v e l s : Team Status (top 4 or bottom 4 teams) and Game Status (winning or l o s i n g games). The mean performances (MP) of each of the e i g h t s k i l l s were ser v e d as dependent v a r i a b l e s i n subsequent i n f e r e n t i a l s t a t i s t i c a l a n a l y s e s . In a d d i t i o n , the d e s c r i p t i v e i n f o r m a t i o n r e g a r d i n g the p r o p o r t i o n s o f each performance s c a l e i n c l u d i n g success and e r r o r r a t e were used t o d e s c r i b e and e x p l a i n g e n e r a l c h a r a c t e r i s t i c s o f s k i l l performance i n men's v o l l e y b a l l at the i n t e r n a t i o n a l l e v e l of c o m p e t i t i o n . The d i f f e r e n c e between the mean performance of the s k i l l s (set and s p i k e ) , o c c u r r i n g both i n the attack p r o c e s s (AP) and i n the c o u n t e r a t t a c k process (CP), was analyzed u s i n g a m u l t i v a r i a t e a n a l y s i s o f v a r i a n c e mixed model (MMM) d e s i g n (Schutz & G e s s a r o l i , 1987). A s i g n i f i c a n t r e s u l t was found and t h e r e f o r e such s k i l l s as the set and spike had to be t r e a t e d s e p a r a t e l y i n the subsequent analyses, a c c o r d i n g t o the r e s p e c t i v e p r o c e s s i n which they took p l a c e . A f a c t o r i a l MANOVA f o r randomized groups was conducted u s i n g BMDP4V s t a t i s t i c a l software i n order to compare the p l a y i n g c h a r a c t e r i s t i c s between the games and between the teams on each s k i l l performance. As a follow-up procedure t o MANOVA, a stepwise d i s c r i m i n a n t f u n c t i o n a n a l y s i s was used t o determine which s k i l l , or a s e t of s k i l l performances, c o n t r i b u t e d s i g n i f i c a n t l y t o team success, viewed as win or 45 l o s s . In a d d i t i o n , the s t r e n g t h o f the p r e d i c t i o n was d e s c r i b e d i n terms of a h i t r a t e formed from c r o s s t a b u l a t i o n s of a c t u a l and expected c l a s s i f i c a t i o n i n t o winning or l o s i n g group. 3.7.2 A n a l y s i s o f S e q u e n t i a l S k i l l s F i r s t and second order t r a n s i t i o n m a t r i c e s generated from the computer output program were an a l y z e d u s i n g Log l i n e a r procedures (BMDP4F) to study the nature and degree of the t r a n s i t i o n p a t t e r n s among the s e q u e n t i a l p l a y i n g a c t i o n s . The presence o f the interdependency between two s e q u e n t i a l s k i l l s was f i r s t examined i n the p r e l i m i n a r y a n a l y s i s . Then, f u r t h e r a n a l y s i s was conducted t o i n v e s t i g a t e whether the p a t t e r n of the t r a n s i t i o n p l a y between the two s e q u e n t i a l s k i l l s are a f f e c t e d by the Team, Game or Process S t a t u s , or combination among them. In a d d i t i o n , as a f o l l o w up t o the t r a n s i t i o n between the s e t and spike, a comparison o f the t r a n s i t i o n p a t t e r n s among the o f f e n s i v e p l a y s ( i . e . , high, medium and quick) was undertaken. The r e s u l t s o f each a n a l y s i s were d i s p l a y e d i n an ANOVA-like t a b l e , along w i t h corresponding i n t e r p r e t a t i o n s of these r e s u l t s , a procedure suggested by M a r a s c u i l o and Busk (1987). 46 CHAPTER IV Results and Discussion 4.1 ANALYSIS OF INDIVIDUAL SKILL 4.1.1 MANOVA Mixed Model Design The primary concern o f t h i s a n a l y s i s was t o examine whether or not such s k i l l s as the s e t and spike t h a t took p l a c e i n both the a t t a c k p r o c e s s (AP) and c o u n t e r a t t a c k process (CP) c o u l d be t r e a t e d and i n t e r p r e t e d i n the same manner, d i s r e g a r d i n g the Process i n which they took p l a c e . In order to t e s t t h i s , a 2 (Team) by 2 (Game) by 2 (Process) MANOVA, with repeated measures on the l a s t f a c t o r , was conducted on the two dependent v a r i a b l e s : the mean performance (MP) of the set and the s p i k e . D e s c r i p t i v e s t a t i s t i c s f o r the set and spike are pr e s e n t e d i n t a b l e 4-1. Table 4-1 Means and Standard D e v i a t i o n s f o r Set and Spike Process Team AP CP Game n Set Spike Set Spike Top 4 Win 24 2 .80 ( .29) * 2 .83 ( .30) 2. 19( .22) 2. 62 ( .35) Loss 12 2 .65 ( .27) 2 .59( .16) 1. 95 ( .20) 2. 25 ( .45) Bottom 4 Win 12 2 .86( .31) 2 .86( .29) 1. 96( .23) 2. 35 ( .54) Loss 24 2 .72 ( .24) 2 .75 ( .21) 1. 98 ( .19) 2. 16( .42) *: Standard d e v i a t i o n i n parentheses 4 7 As can be seen i n Table 4-2, r e s u l t s showed no s i g n i f i c a n t m u l t i v a r i a t e F r a t i o f o r the Team Status main e f f e c t (p_ > . l l ) , i n d i c a t i n g no d i f f e r e n c e i n the performance of the set and s p i k e between the top 4 (2.43, 2.62) and bottom 4 teams (2.37, 2.50) when averaged over the other two f a c t o r s . Therefore, u n i v a r i a t e ANOVAs f o r the dependent v a r i a b l e s were not examined. However, a s i g n i f i c a n t m u l t i v a r i a t e F r a t i o was o b t a i n e d f o r the Game Status main e f f e c t (p_ <.001). Examination of the follow-up u n i v a r i a t e ANOVAs r e v e a l e d t h a t both the set and s p i k e v a r i a b l e s c o n t r i b u t e d t o the s i g n i f i c a n t o v e r a l l t e s t . That i s , the mean performance of the set and s p i k e f o r the wining games (2.46, 2.68) was g r e a t e r than t h a t f o r the l o s i n g games (2.33, 2.44) when averaged over the Team and Process f a c t o r s . In a d d i t i o n , the non- s i g n i f i c a n t m u l t i v a r i a t e F r a t i o f o r the Game by Team i n t e r a c t i o n (p >.28) i n d i c a t e d t h a t the d i f f e r e n c e between the winning and l o s i n g games, averaged over the Process f a c t o r , was constant over the l e v e l o f Team S t a t u s . These r e s u l t s suggest t h a t when averaged over the Game and Process f a c t o r s , the top 4 teams were not d i s t i n g u i s h a b l e from the bottom 4 teams i n terms of the s e t and s p i k e performance. However, t h i s was not t r u e f o r the Game S t a t u s . Although the magnitude of the d i f f e r e n c e i n the s e t and s p i k e between the winning and l o s i n g games seemed t o be s m a l l , t h i s d i f f e r e n c e would appear to be a c o n t r i b u t o r y f a c t o r t o a game won or l o s t at the i n t e r n a t i o n a l l e v e l o f men's c o m p e t i t i o n s . 4 8 Table 4-2 R e s u l t s of MANOVA and U n i v a r i a t e Follow-ups * E f f e c t M u l t i v a r i a t e Follow-up u n i v a r i a t e r e s u l t s Set Spike df(2,67) d f ( l , 6 8 ) d f ( l , 6 8 ) F p F p F Game(G) 9 .3 .0003 7.9 .0064 16.3 <.0001 Team(T) 2 .2 .1197 u n i v a r i a t e s not examined G x T 1 .3 .2855 u n i v a r i a t e s not examined Process(P) 236 .7 <.0001 479.6 <.0001 51.2 <.0001 P x T 4 .9 .0101 5.6 .0205 7.9 .0064 P x G 1 .7 .1930 u n i v a r i a t e s not examined P x G x T 1 . 9 .1596 u n i v a r i a t e s not examined *: Alpha l e v e l s o f 0.05 and 0.025 were used f o r the m u l t i v a r i a t e and u n i v a r i a t e t e s t s , r e s p e c t i v e l y . Examination o f the within-group e f f e c t s showed no s i g n i f i c a n t m u l t i v a r i a t e F r a t i o s (p >.15) f o r the Process by Game by Team, and Process by Game i n t e r a c t i o n s (see t a b l e 4-2). That i s , d i f f e r e n c e s i n the performance of the set and sp i k e between the AP and CP were the same f o r the Team-Game combination, and f o r the l e v e l s o f Game Status when averaged over the Team Status f a c t o r . However, a s i g n i f i c a n t m u l t i v a r i a t e F r a t i o was o b t a i n e d f o r the Process by Team i n t e r a c t i o n (p =.0101). T h i s r e s u l t i n d i c a t e d t h a t the magnitude o f d i f f e r e n c e i n e i t h e r the s e t or spi k e , or the combination o f both between the AP and CP, were not the same f o r the top 4 and bottom 4 teams when averaged over the Game S t a t u s . Follow-up ANOVAs showed a s i g n i f i c a n t F r a t i o f o r 49 b o t h the set (p =.0205) and s p i k e (p=.0064). The mean v a l u e f o r the set and s p i k e i n the AP, which i s the process of g e t t i n g the r i g h t t o serve back, was v i r t u a l l y i d e n t i c a l between the top 4 teams (2.75, 2.75) and the bottom 4 teams (2.76, 2.79) (see t a b l e 4-3). However, these v a l u e s i n the CP were g r e a t e r f o r the top 4 teams (2.11, 2.50) than the bottom 4 teams (1.97, 2.22). That i s , the top 4 teams d i d not perform any b e t t e r on the set and s p i k e i n the AP, but outperformed the bottom 4 teams on those two s k i l l s i n the CP, which i s the primary process of s c o r i n g a p o i n t . Table 4-3 Means and Standard D e v i a t i o n s , Averaged over the Game F a c t o r Team Process n Top 4 B o t t . 4 Marginal M AP Set 36 2.75 (.29) 2.76 (.27) 2.76 (.27) Spike 36 2.75 (.28) 2.79 (.24) 2.77 (.26) CP Set 36 2.11 (.24) 1.97 (.20) 2.04 (.28) Spike 36 2.50 (.42) 2.22 (.46) 2.36 (.46) R e s u l t s f o r the Process main e f f e c t showed a h i g h l y s i g n i f i c a n t m u l t i v a r i a t e F r a t i o (p<.0001) and follow-up ANOVAs r e v e a l e d t h a t both the s e t (F=479.6, p<.0001) and spike (F=51.2, p<.0001) were, with more weight on the set, r e s p o n s i b l e f o r the s i g n i f i c a n t P r o c e s s main e f f e c t . In f a c t , 50 the mean value f o r the s e t (2.76) and spike (2.77) i n the AP i s c o n s i d e r a b l y g r e a t e r than t h a t f o r the set (2.04) and spi k e (2.36) i n the CP. That i s , the performance of the set' and spik e i n the AP was s u p e r i o r t o t h a t i n the CP, thus sugges t i n g t h a t the s e t and spi k e i n the AP should not be analyzed and e v a l u a t e d i n the same manner as those i n the CP. The mean performance of the two s k i l l s was broken down i n t o i t s components ( i . e . , p r o p o r t i o n o f each s c a l e ) i n order t o compare the performance p a t t e r n o f the set and s p i k e between the AP and CP. As can be seen i n Table 4-4, the d i f f e r e n c e s were n o t i c e a b l y apparent when comparing a d i s t r i b u t i o n of the p r o p o r t i o n between the AP and CP f o r the two s k i l l s . For example, wi t h r e s p e c t t o the set, the p r o p o r t i o n of p e r f e c t e x e c u t i o n i n the AP (29.8%) was almost t h r e e times g r e a t e r than t h a t i n the CP (9.7%). T a k i n g S c a l e s 3 and 4 together, 56.4% of the t o t a l s e t s i n the AP, as opposed t o 18.6% i n the CP, were not only a c c u r a t e l y d e l i v e r e d to the s p i k e r , but a l s o gave u n c e r t a i n t y t o the opponent's b l o c k e r s as t o the i n t e n d e d d i r e c t i o n or p l a c e of the s e t . Furthermore, 79.9% of the t o t a l s e t s (sum of the s c a l e 1 and 2) i n the CP, compared t o 42.4% i n the AP, were e i t h e r i n a c c u r a t e or p r e d i c t a b l e f o r the opponent's b l o c k e r s . T h i s meant t h a t the o p p o s i t i o n c o u l d e a s i l y f o l l o w and form a s o l i d b l o c k a g a i n s t the s p i k e r , thus p l a c i n g g r e a t e r d i f f i c u l t y i n g a i n i n g a p o i n t . The e r r o r r a t e ( s c a l e 0) was i n t e r e s t i n g l y almost i d e n t i c a l i n both AP (1.1%) and CP (1.4%), s u g g e s t i n g 51 v e r y few u n f o r c e d s e t t i n g e r r o r s being made at the i n t e r n a t i o n a l l e v e l of c o m p e t i t i o n . O v e r a l l , these d i f f e r e n c e s i n the p r o p o r t i o n of each s c a l e between the AP and CP r e s u l t e d i n the h i g h l y s i g n i f i c a n t d i f f e r e n c e i n the mean performance. Table 4-4. Observed Frequency and P r o p o r t i o n f o r Set and Spike Process Scale S k i l l s4 s3 s2 s i sO T o t a l Set AP 675 603 809 152 24 2263 p* 29.8 26.6 35.7 6.7 1.1 100.0 CP 119 109 708 269 17 1222 p 9.7 8.9 57.9 22.0 1.4 100.0 Spike AP 1180 217 359 160 315 2231 p 52.9 9.7 16.1 7.2 14.1 100.0 CP 471 99 219 206 203 1198 p 39.3 8.3 18.3 17.2 16.9 100.0 *: P r o p o r t i o n of each s c a l e (%) S i m i l a r , but l e s s d i s t i n c t i v e r e s u l t s were shown i n the comparison of the s p i k e between the AP and . CP. The main d i f f e r e n c e s are e v i d e n t i n the p r o p o r t i o n of S c a l e 1 and 4. The success r a t e (52.9%) i n the AP seemed to be c o n s i d e r a b l y g r e a t e r than t h a t (39.3%) i n the CP, whereas the p r o p o r t i o n of the s c a l e 1 i n the AP (7.2%) was s m a l l e r than t h a t i n the CP (17.2%), i n d i c a t i n g more s p i k e s i n the CP r e s u l t e d i n a 52 f r e e b a l l f o r the o p p o s i t i o n . However, the e r r o r r a t e i n the AP (14.1%) was approximately the same as t h a t i n the CP (16.9%). This c o u l d be due t o the f a c t t h a t the s p i k e i s a s k i l l which has d i r e c t team i n t e r a c t i o n s with the opponent's b l o c k at the net and thus r e s u l t i n g i n f o r c e d or u n f o r c e d e r r o r s i n the performance. In summary, i t was ev i d e n t from these r e s u l t s t h a t the performance of the set and spi k e should not be ana l y z e d and e v a l u a t e d without the d i s t i n c t i o n o f the Process i n which they took p l a c e . That i s , although the s k i l l o f the set and spi k e i t s e l f does not v a r y whether i t i s performed i n the a t t a c k process (AP) or c o u n t e r a t t a c k process (CP), the performance of these s k i l l s are v e r y much a f f e c t e d by the Process i n which they take p l a c e , as r e v e a l e d by the s i g n i f i c a n t Process main e f f e c t . In a d d i t i o n , the top 4 teams d i d not d i f f e r at a l l from the bottom 4 teams on the performance of the set and s p i k e when averaged over the Process f a c t o r . However, the performance d i f f e r e n c e between the top 4 and bottom 4 teams on the two s k i l l s was s u b s t a n t i a l when compared i n the context of the AP and CP, as r e v e a l e d i n the Process by Team i n t e r a c t i o n . Taken together, the r e s u l t s suggest t h a t i g n o r i n g the Process f a c t o r i n the performance a n a l y s i s o f the set and s p i k e c o u l d c o n c e a l an important f a c e t r e l a t e d t o team succ e s s . U l t i m a t e l y , t h i s c o u l d mislead the coach i n e v a l u a t i o n and d e c i s i o n making r e g a r d i n g the p l a n n i n g o f t r a i n i n g s e s s i o n s . 53 4.1.2 MANOVA f o r Randomized Groups Design As a r e s u l t o f the p r e v i o u s f i n d i n g s , the set and spi k e i n the AP and CP were t r e a t e d and i n t e r p r e t e d independently i n t h i s a n a l y s i s a c c o r d i n g t o the Process i n which they took p l a c e . In order t o compare p l a y i n g c h a r a c t e r i s t i c s o f the e i g h t s k i l l components s e r v i n g as dependent v a r i a b l e s , a 2 (Team) by 2 (Game) f a c t o r i a l MANOVA was performed u s i n g the BMDP4V program. D e s c r i p t i v e s t a t i s t i c s f o r the e i g h t s k i l l components, marginals only, are p r e s e n t e d i n Table 4-5. Table 4-5 D e s c r i p t i v e S t a t i s t i c s f o r the E i g h t S k i l l s Team Game S k i l l * Top 4 Bott . 4 Win Loss SE 1.79(.21) 1.76 ( .21) 1.77 ( • 19) 1.78 ( .23) SR 2.93 (.25) 2.94 ( .27) 2.93 ( .29) 2.95 ( .24) SAP 2.75 (.29) 2.76( .27) 2.82 ( .29) 2. 69 ( .25) SKAP 2.75 (.28) 2.79 ( .24) 2.84 ( .30) 2.70 ( .21) BLO 1.50(.20) 1.37 ( .19) 1.53 ( .20) 1.34 ( .17) DIG 2.14 (.27) 1.96( .22) 2.07 ( .29) 2.03 ( .24) SCP 2.11 (.24) 1.97 ( .20) 2.11 ( .25) 1.97 ( .19) SKCP 2.50 (.42) 2.22 ( .46) 2.53 ( .43) 2.19 ( .43) *: SE=Serve, SR=Serve Reception, SAP=Set i n the AP, SKAP=Spike i n the AP, BLO=Block, SCP=Set i n the CP, SKCP=Spike i n the CP. As can be seen i n Table 4-6, no s i g n i f i c a n t (p >.21) m u l t i v a r i a t e F r a t i o was obt a i n e d f o r the Team and Game 54 i n t e r a c t i o n , i n d i c a t i n g t h a t the d i f f e r e n c e i n the performance of each or combination of the e i g h t s k i l l s between the winning and l o s i n g games was constant a c r o s s the l e v e l o f the Team St a t u s . U n i v a r i a t e ANOVAs f o r the i n t e r a c t i o n were, t h e r e f o r e , not examined. As would be expected, there were h i g h l y s i g n i f i c a n t m u l t i v a r i a t e F r a t i o s f o r both the Team and Game main e f f e c t s (p_=.0037, p_=<.0001). The magnitude o f the d i f f e r e n c e i n each s k i l l performance (see Table 4-5) was smal l f o r some s k i l l s , but f a i r l y s u b s t a n t i a l f o r the o t h e r s . Thus, i n order t o f i n d out which of dependent v a r i a b l e ( s ) were r e s p o n s i b l e f o r the o v e r a l l s i g n i f i c a n c e s , u n i v a r i a t e ANOVAs were examined as fol l o w - u p s . Since u n i v a r i a t e F's r e p r e s e n t the a b i l i t y o f each dependent v a r i a b l e by i t s e l f to c o n t r i b u t e to the main e f f e c t , they n e i t h e r take i n t o account i n t e r c o r r e l a t i o n s among the dependent v a r i a b l e s nor compensate f o r i n c r e a s e d Type I e r r o r s w i t h m u l t i p l e t e s t i n g s (Tabachnick & F i d e l l , 1983). Therefore, i n an attempt t o c o n t r o l an i n f l a t i o n o f Type I e r r o r r a t e , 0.01 alpha l e v e l was used f o r a l l u n i v a r i a t e t e s t s . Examination o f the follow-up u n i v a r i a t e ANOVAs f o r the Team main e f f e c t r e v e a l e d t h a t f o u r of the e i g h t v a r i a b l e s , b l o c k (BLO), d i g (DIG), set i n the CP (SCP), and spi k e i n the CP (SKCP) y i e l d e d s i g n i f i c a n t F r a t i o s (p_ £.007) . When c o n s i d e r i n g the c h a r a c t e r i s t i c s o f the v a r i a b l e s t h a t were 55 Table 4-6 R e s u l t s of MANOVA and U n i v a r i a t e ANOVA Follow-ups * E f f e c t s M u l t i v a r i a t e F P df(8,61) Team(T) 3.27 .0037 Game(G) 6.46 <.0001 T x G 1.40 .2128 U n i v a r i a t e ANOVA Follow-ups Team Game V a r i a b l e F(df=l,68) p F ( d f = l , 68) P SE .49 .4863 .04 .8475 SR .03 .8651 .11 .7442 SAP .07 .7908 3. 61 .0617 SKAP .48 .4928 5.36 .0236 BLO 8.89 .0040 19.36 <.0001 DIG 9.45 .0030 .41 .5263 SCP 7.76 .0069 8.43 .0050 SKCP 7.74 .0070 11.74 . 0010 *: .05 alpha l e v e l was used f o r the m u l t i v a r i a t e F's. s i g n i f i c a n t , i t can be noted t h a t those are the ones which take p l a c e i n the c o u n t e r a t t a c k process (CP) i n v o l l e y b a l l c o m p e t i t i o n . That i s , the teams were not s i g n i f i c a n t l y d i f f e r e n t (p>.45) on the performance o f s k i l l s o c c u r r i n g i n the AP, serve (SE), serve r e c e p t i o n (SR), set (SAP), and spi k e (SKAP), which i s the pro c e s s of r e g a i n i n g the serve back from the o p p o s i t i o n . However, the top 4 teams outperformed the bottom 4 teams on a l l the s k i l l s which took p l a c e i n the CP, which i s the process of s c o r i n g a p o i n t . 56 The same c h a r a c t e r i s t i c p a t t e r n was found i n the examination of u n i v a r i a t e ANOVAs f o r the Game main e f f e c t . R e s u l t s showed t h a t those s k i l l s o c c u r r i n g i n the CP were s i g n i f i c a n t (p_ <.005) and thus c o n t r i b u t i n g t o the o v e r a l l s i g n i f i c a n t t e s t , except f o r the DIG v a r i a b l e b e i n g n o n s i g n i f i c a n t (p_=.5263) . With r e s p e c t t o the performance o f the set and s p i k e , these r e s u l t s r e a f f i r m the f i n d i n g s o b t a i n e d i n the p r e v i o u s a n a l y s i s . The p r e v i o u s a n a l y s i s showed no s i g n i f i c a n t d i f f e r e n c e i n the set and spike between the Team Status when they were analyzed without d i s t i n c t i o n o f the process i n which they took p l a c e . However, the r e s u l t s i n t h i s a n a l y s i s r e v e a l e d t h a t the top 4 teams outperformed the bottom 4 teams on the SCP and SKCP, but there were no s u b s t a n t i a l d i f f e r e n c e s on the SAP and SKAP between them. In a d d i t i o n , the s i g n i f i c a n t Game main e f f e c t o b tained i n the p r e v i o u s a n a l y s i s was mainly due to the e f f e c t of the performance on the SCP and SKCP, as shown no s i g n i f i c a n t u n i v a r i a t e F r a t i o f o r the SAP and SKAP i n t h i s a n a l y s i s . T h i s r e s u l t i s b a s i c a l l y i n agreement wi t h the f i n d i n g of N i s h i j i m a e t a l . (1987). They found t h a t the s k i l l o f the SKCP, termed as "a t t a c k f o l l o w e d r e c e p t i o n " , was a b e t t e r p r e d i c t o r o f the success of the game (winning) than the SKAP, termed as " a t t a c k f o l l o w e d serve r e c e p t i o n " i n the a n a l y s i s of an i n t e r c o l l e g i a t e championship. However, the performance of the set i n t h e i r a n a l y s i s was t r e a t e d without the d i s t i n c t i o n of the p r o c e s s . 57 Comparisons of the r e s u l t s w i t h f i n d i n g s i n r e l a t e d s t u d i e s showed t h a t the s k i l l performances were found to be g e n e r a l l y higher than those r e p o r t e d i n s t u d i e s of s t a t i s t i c a l a n a l y s i s of u n i v e r s i t y or c l u b team l e v e l of c ompetitions (Cox, 1974; Ejem S.Horak, 1980; Rose, 1983). T h i s was e s p e c i a l l y t r u e i n the performance of " w i t h i n team-oriented" s k i l l s such as the serve r e c e p t i o n , d i g , and set b e i n g s u p e r i o r to that of u n i v e r s i t y l e v e l o f c o m p e t i t i o n . However, t h e r e was l i t t l e d i f f e r e n c e i n "between team-oriented" s k i l l s such as the spike and b l o c k . T h i s c o u l d be due to the f a c t t h a t the s k i l l of the spike and b l o c k i s e v a l u a t e d by i t s r e l a t i v e e f f e c t i v e n e s s r e s u l t e d from a d i r e c t team i n t e r a c t i o n w i t h the o p p o s i t i o n at the net, r a t h e r than performance i t s e l f . Examination o f the s k i l l performances between the AP and CP r e v e a l e d t h a t t h e r e was a g r e a t d i f f e r e n c e between the two processes i n terms of the mean performance of the s k i l l s . T h i s d i f f e r e n c e s t a r t e d from the serve r e c e p t i o n i n the AP and the d i g i n the CP. As d e f i n e d i n the o b s e r v a t i o n c r i t e r i a , the performance o f the serve r e c e p t i o n (SR) and d i g was e v a l u a t e d based on the same c r i t e r i a s i n c e those are the s k i l l s p l a y e d w i t h forearms. As would be expected, the mean performance of the SR (2.94) and d i g (2.05) was s u b s t a n t i a l l y d i f f e r e n t . T h i s i s t r u e because the SR was proceeded by the serve, whereas the d i g was f o l l o w e d by the opponent's s p i k e which i s much f a s t e r and more powerful than the s e r v e . When 58 c o n s i d e r i n g t h a t the set i s supposed t o take p l a c e a f t e r these two s k i l l s , i t seems t o be obvious t h a t a great d i f f e r e n c e between the performance of the SR and d i g c o u l d s i g n i f i c a n t l y i n f l u e n c e the performance of the s e t . T h i s was evidenced i n the o v e r a l l mean v a l u e (2.76, 2.04 f o r the SAP and SCP, r e s p e c t i v e l y ) . The same holds t r u e f o r the performance of the sp i k e t h a t o c c u r r e d f o l l o w e d by the s e t (2.77, 2.36 f o r the SKAP and SKCP, r e s p e c t i v e l y ) . From these r e s u l t s , i t can be suspected t h a t t h e r e i s a c e r t a i n p a t t e r n o f r e l a t i o n s h i p i n the l i n k o f these s e q u e n t i a l s k i l l s . The i n v e s t i g a t i o n o f the r e l a t i o n s h i p between the s e q u e n t i a l s k i l l s was d e a l t w i t h i n the a n a l y s i s of s e q u e n t i a l s k i l l s . In summary, the r e s u l t s o f t h i s a n a l y s i s suggest t h a t the p l a y i n g c h a r a c t e r i s t i c s between the t o p 4 and bottom 4 teams, and between the winning and l o s i n g games are e s s e n t i a l l y s i m i l a r on the performance of the serve, serve r e c e p t i o n , set and spike i n the a t t a c k process (AP). What seemed t o account f o r the team success was mainly the q u a l i t y o f the performance on such s k i l l s as the s e t , s p i k e and b l o c k t a k i n g p l a c e i n the co u n t e r a t t a c k process (CP). C o n s i d e r i n g the f a c t t h a t these s k i l l s are performed t o g a i n a p o i n t , a b e t t e r performance on these s k i l l s w i l l l e a d a team t o win a game i n a match. Therefore, g i v e n the f i n d i n g s t h a t t h e r e i s no s i g n i f i c a n t d i f f e r e n c e between the teams and games i n the performance of the i n i t i a l o f f e n s i v e p l a y , a s u c c e s s f u l team has the a b i l i t y t o b e t t e r recover from the opponent's i n i t i a l a t t a c k , 59 r e o r g a n i z e a team pla y , and g i v e a s u c c e s s f u l c o u n t e r a t t a c k back t o the opponent's c o u r t . P r a g m a t i c a l l y , t h i s r e s u l t suggests t h a t more emphasis on the CP d u r i n g p r a c t i c e s e s s i o n s c o u l d l e a d t o more e f f e c t i v e c o aching and perhaps winning a game. The performance o f each o f the e i g h t s k i l l s was f u r t h e r examined i n terms of the p l a y i n g p a t t e r n s o f the s k i l l s . The mean performance of each o f the e i g h t s k i l l s was decomposed i n t o i t s components ( i . e . , p r o p o r t i o n of each s c a l e ) i n order t o compare the performance p a t t e r n o f each s k i l l between the Top-Bottom teams and Winning-Losing games. D e t a i l e d r e s u l t s o f these comparisons are p r e s e n t e d i n Appendix F. In g e n e r a l , the d i f f e r e n t i a t i o n between the Team and Game Status was due t o a g r e a t e r p r o p o r t i o n o f s u c c e s s f u l performance (Scale 4) on the four s k i l l s , block, d i g , s e t and spi k e o c c u r r i n g i n the CP, demonstrated by the top 4 teams and i n winning games. However, the e r r o r r a t e (Scale 0) of each s k i l l performance between the Team and Game St a t u s was s i m i l a r , except f o r the performance o f the b l o c k . 4.1.3 D i s c r i m i n a n t F u n c t i o n A n a l y s i s D i s c r i m i n a n t f u n c t i o n a n a l y s i s was conducted u s i n g BMDP7M s t a t i s t i c a l program i n order t o s e l e c t the best p r e d i c t o r or a se t o f p r e d i c t o r s of team success among the e i g h t s k i l l components. With a stepwise procedure i t was p o s s i b l e t o i d e n t i f y the r e l a t i v e importance o f s e l e c t e d v a r i a b l e s i n 60 d i s c r i m i n a t i n g between the winning and l o s i n g games. The measure of team success (dependent v a r i a b l e ) was game outcome, scored as a "win" or " l o s e " . The reasons f o r u s i n g the game outcome are: a) as mentioned, the e i g h t teams i n t h i s tournament were grouped i n t o one o f the two po o l s and pla y e d a round r o b i n w i t h i n the r e s p e c t i v e p o o l i n the p r e l i m i n a r y round. Since a l l teams d i d not p l a y one another, i t may not be ap p r o p r i a t e t o determine the team success based on the team sta n d i n g a f t e r the p r e l i m i n a r y round; b) the Team Status i s determined by the number of matches won, which i s a f u n c t i o n of games won. In a d d i t i o n , a winning game i s determined by the number of p o i n t s i n t h a t game. Since the s c o r i n g system i n v o l l e y b a l l does not c a r r y o b t a i n e d p o i n t s i n one game over the next game, winning a match does not n e c e s s a r i l y mean t h a t a team obtained more p o i n t s than the o p p o s i t i o n i n that match; and c) the r e s u l t s o f p r e v i o u s a n a l y s i s showed almost i d e n t i c a l i n f o r m a t i o n as t o the v a r i a b l e s r e s p o n s i b l e f o r the s i g n i f i c a n t Team and Game main e f f e c t s . Therefore, i d e n t i f y i n g a s e t of p r e d i c t o r s of team success by a means of winning and l o s i n g games can be c o n s i d e r e d t o be r e p r e s e n t a t i v e o f team succ e s s . I n s p e c t i o n o f the F v a l u e s at Step 0 i n Table 4-7 i n d i c a t e s t hat the performance of the b l o c k (BLO) (19.185) was the best v a r i a b l e t o d i s c r i m i n a t e between winning and l o s i n g , and, thus entered f i r s t i n t o the d i s c r i m i n a n t f u n c t i o n . Because of the presence o f i n t e r c o r r e l a t i o n s among the 61 v a r i a b l e s , once the BLO v a r i a b l e entered i n t o the equation, Table 4-7 R e s u l t s o f D i s c r i m i n a n t F u n c t i o n A n a l y s i s V a r i a b l e s F-To-Enter i n Each Step S t a n d a r d i z e d C o e f f i c i e n t s 0 1 (E<.001)* 2 (p_<.001) 3 <P_<.01) BLO 19.185 Entered .973 SKCP 11.460 14.976 Entered .406 SKAP 5.246 8.566 7.320 Entered .313 DIG .352 .002 1.495 .844 SR .110 . 018 .559 .747 SAP 3.667 3.424 2.195 .314 SE .038 .072 .028 .292 SCP 7.543 4 .520 .174 .222 *: S i g n i f i c a n c e l e v e l at each step. the F v a l u e s o f the remaining v a r i a b l e s were a d j u s t e d a c c o r d i n g t o the degree of the c o r r e l a t i o n with the BLO v a r i a b l e . That i s , i f a v a r i a b l e i s p o s i t i v e l y c o r r e l a t e d t o the v a r i a b l e t h a t i s a l r e a d y i n the equation, the F va l u e of t h a t v a r i a b l e w i l l decrease or v i s e v e r s a due to the e f f e c t of the c o r r e l a t i o n . The F v a l u e s f o r the SKCP and SKAP v a r i a b l e s ( i . e . , s p i k e i n the CP and AP) at Step 1, f o r example, now i n c r e a s e d t o 14.976 and 8.566, r e s p e c t i v e l y , due to i t s ne g a t i v e c o r r e l a t i o n w i t h the BLO v a r i a b l e (-.209, -.218, r e s p e c t i v e l y ) (see Table 4-8) . As can be seen i n Table 4-7, the stepwise d i s c r i m i n a n t a n a l y s i s i d e n t i f i e d t h r e e s k i l l s as most s i g n i f i c a n t 62 c o n t r i b u t o r s t o d i s c r i m i n a t i n g between the winning and l o s i n g . These are the BLO (.973), SKCP (.406), and SKAP (. 313) i n order of r e l a t i v e importance, as i n d i c a t e d the magnitude of the s t a n d a r d i z e d c o e f f i c i e n t s or e q u i v a l e n t l y F-To -Enter v a l u e s f o r the th r e e v a r i a b l e s • Table 4-8 W i t h i n C o r r e l a t i o n M atrix SE SR SAP SKAP BLO DIG SCP SE 1.000 SR -.251 1.000 SAP -.044 .512 1.000 SKAP -.146 .077 .341 1 .000 BLO .025 -.110 -.043 - .218 1.000 DIG .042 .107 -.081 - .119 .123 1.000 SCP .085 .255 .318 - .052 .077 .557 1.000 SKCP -.120 .259 .061 .026 -.209 .306 .415 The adequacy of the d i s c r i m i n a n t f u n c t i o n t o c o r r e c t l y c l a s s i f y the sample games i n t o the winning or l o s i n g group was es t i m a t e d by percent c o r r e c t c l a s s i f i c a t i o n (see Table 4-9). Of the a c t u a l winning games, 75% (27 games) were c o r r e c t l y c l a s s i f i e d , and f o r the a c t u a l l o s i n g games, 80.6% (29 games) were c o r r e c t l y c l a s s i f i e d . O v e r a l l , w i t h knowledge of the performance on the block and s p i k e i n both the CP and AP, 77.8% o f the t o t a l sample games were c o r r e c t l y c l a s s i f i e d as the winning or l o s i n g game, which i s s i g n i f i c a n t l y (X2 (1) =22.44, p_<.001) b e t t e r than chance c l a s s i f i c a t i o n (50%). Table 4-9 C l a s s i f i c a t i o n R e s u l t s w i t h D i s c r i m i n a n t Function P r e d i c t e d Group A c t u a l Group a Win Loss T o t a l Win 27 75.0% 9 36 Loss 7 29 80.6% 36 T o t a l 36 36 77.8% b a: Expected percent c o r r e c t c l a s s i f i c a t i o n by chance = 50%. b: P r e d i c t e d percent c o r r e c t c l a s s i f i c a t i o n The c h a r a c t e r i s t i c s o f the v a r i a b l e s s e l e c t e d i n t h i s a n a l y s i s are noteworthy. I n t e r e s t i n g l y , those v a r i a b l e s are the ones which have d i r e c t team i n t e r a c t i o n s at the net. That i s , the main purpose of the bl o c k (BLO) i s to stop the opponent's spike at the net, whereas t h a t of the s p i k e ( e i t h e r SKAP or SKCP) i s p u t t i n g the b a l l on the opponent's c o u r t by a v o i d i n g the b l o c k . Therefore, as i n d i c a t e d i n the n e g a t i v e c o r r e l a t i o n between the s k i l l s , b e t t e r performance of the b l o c k f o r a team would suggest l e s s e f f e c t i v e n e s s i n the s p i k e performance f o r the o p p o s i t i o n . In a d d i t i o n , these s e l e c t e d s k i l l s are the ones i n which t h e i r p e r f e c t execution i n the performance terminate a r a l l y , r e s u l t i n g i n e i t h e r s c o r i n g a p o i n t or r e g a i n i n g a serve back from the o p p o s i t i o n . Therefore, b e t t e r performance on these s k i l l s i s d i r e c t l y 64 r e l a t e d t o game success, s i n c e a game win i s determined by the number of winning p o i n t s . The r e s u l t s of t h i s a n a l y s i s are i n agreement w i t h the f i n d i n g s of p r e v i o u s s t u d i e s . Cox (1974), u s i n g d i s c r i m i n a n t f u n c t i o n a n a l y s i s , s e l e c t e d the s p i k e as the best p r e d i c t o r of team success among the s i x s e l e c t e d s k i l l i n the N.C.A.A. men's championship. However, i n the absence of the s k i l l of the b l o c k i n h i s a n a l y s i s , the d i g was s e l e c t e d as a second important v a r i a b l e to d i s c r i m i n a t e between winning and l o s i n g games. Another study by Ejem and Horak (1980) was attempted to s e l e c t the best p r e d i c t o r of a team standing based on the performance of the spike, block, serve, and serve r e c e p t i o n . They a l s o s e l e c t e d , u s i n g m u l t i p l e r e g r e s s i o n procedure, the s p i k e as the best p r e d i c t o r , f o l l o w e d by the serve r e c e p t i o n , of the team standing i n the Czechoslovak Club Team Championship. More r e c e n t l y , N i s h i j i m a et a l . (1987) a l s o found t h a t the spike was the best predictc-r, f o l l o w e d by the set and d i g , of the success of the game at I n t e r c o l l e g i a t e men's championship. From these r e s u l t s , i t i s evident t h a t the s k i l l o f spike i s o b v i o u s l y the best p r e d i c t o r of the success of the game (winning or l o s i n g ) or of the team s t a n d i n g . However, the s e l e c t i o n of next p r e d i c t o r ( s ) was not c o n s i s t e n t among the s t u d i e s . T h i s c o u l d be due to d i f f e r e n t c h a r a c t e r i s t i c s of the sample games used i n the a n a l y s i s . In summary, the r e s u l t o f the d i s c r i m i n a n t a n a l y s i s i d e n t i f i e d the performance of the b l o c k , spike i n the CP and 65 s p i k e i n the AP as the best p r e d i c t o r v a r i a b l e s i n d i s c r i m i n a t i n g between the winning and l o s i n g . Given the f a c t t h a t the teams are v e r y c l o s e t o each other i n terms o f the l e v e l o f performance at the i n t e r n a t i o n a l l e v e l o f men's competition, the r e s u l t s of the d i s c r i m i n a n t f u n c t i o n a n a l y s i s suggest t h a t the performance of "between team-oriented" s k i l l s (spike & block) which have a d i r e c t team i n t e r a c t i o n at the net i s the best p r e d i c t o r s o f team success, whereas the performance of " w i t h i n team-oriented" s k i l l s ( i . e , pass and set) i s i n d i c a t o r s of the l e v e l o f the p l a y i n g a b i l i t y o f the team, somewhat independent of the opponent's a b i l i t y . 4.2 ANALYSIS OF SEQUENTIAL SKILLS In the p r e v i o u s s e c t i o n , the a n a l y s i s of the t r a n s i t i o n p a t t e r n between s e q u e n t i a l s k i l l s was l i m i t e d due t o the c h a r a c t e r i s t i c s o f the data c o l l e c t e d as i t was based only on i n d i v i d u a l s k i l l performance. However, p r e v i o u s r e s u l t s suggested t h a t c e r t a i n trends i n s e q u e n t i a l s k i l l performances may e x i s t , thus the purpose of t h i s a n a l y s i s i s to i n v e s t i g a t e the r e l a t i o n s h i p between s e q u e n t i a l s k i l l performances. That i s , t o t e s t whether a performance at time t+1 or t+2 i s dependent upon a performance at time t . I n v e s t i g a t i o n i s a l s o d i r e c t e d toward the q u e s t i o n of t o what extent the p a t t e r n of t h i s r e l a t i o n s h i p i s a f f e c t e d by the Game, Team or Process s t a t u s , or i n t e r a c t i o n among them. In order t o answer these 66 q u e s t i o n s , the f i r s t - o r d e r and second-order t r a n s i t i o n m a t r i c e s produced through the computer output program were s e p a r a t e l y analyzed u s i n g BMDP s t a t i s t i c a l software. In a d d i t i o n , as a follow-up a n a l y s i s t o the f i r s t - o r d e r t r a n s i t i o n from the set to sp i k e , the comparison of the t r a n s i t i o n p a t t e r n among the o f f e n s i v e p l a y s ( i . e . , high, medium and quick) was a l s o undertaken. 4.2.1 F i r s t - O r d e r T r a n s i t i o n from the Reception t o Set Thi s a n a l y s i s was conducted u s i n g l o g - l i n e a r procedures i n BMDP program (Dixon, 1981) t o determine whether the d i s t r i b u t i o n of the s e t t i n g performance i s dependent upon the outcome of the r e c e p t i o n . The r e s u l t s of the p r e l i m i n a r y a n a l y s i s are presented i n Table 4-10, which d i s p l a y s p a r t i t i o n e d L i k e l i h o o d - r a t i o Chi-square s t a t i s t i c s (L^) f o r each term with the corresp o n d i n g degrees of freedom. U n l i k e a c o n v e n t i o n a l ANOVA, the degrees of freedom i n t h i s t a b l e r e p r e s e n t the number o f c e l l s f o r the corresponding term, and thus the t o t a l of 159 degrees o f freedom i n d i c a t e s t h a t the f u l l t a b l e i n t h i s a n a l y s i s c o n s i s t s o f 160 c e l l s . The magnitude o f 1?- s t a t i s t i c s i s used t o judge the r e l a t i v e importance o f a s p e c i f i c term t o account f o r the d i s t r i b u t i o n o f observed c e l l f r e q u e n c i e s or e q u i v a l e n t c e l l p r o b a b i l i t i e s . I n s p e c t i o n of the 5 f i r s t - o r d e r terms i n Table 4-10 r e v e a l e d t h a t the t e s t s f o r homogeneity of row p r o b a b i l i t i e s were h i g h l y s i g n i f i c a n t (p_<.01) f o r a l l f i v e terms. That i s , 67 the p r o p o r t i o n of the outcomes are not e q u a l l y d i s t r i b u t e d a c r o s s the l e v e l s of the f a c t o r . For example, the p r o p o r t i o n s o f each s c a l e of the Reception were 13%, 30.8%, 21.5%, and 34.7% f o r Scale 1, 2, 3, and 4, r e s p e c t i v e l y . For the second-order or h i g h e r - o r d e r terms, two types of L2 s t a t i s t i c s are g i v e n f o r each term: one under the l a b e l of " P a r t i a l A s s o c i a t i o n " and the other under the l a b e l of "Marginal A s s o c i a t i o n " . Since the f i r s t - o r d e r terms are not independent o f one another, the p a r t i a l !?• s t a t i s t i c s are c a l c u l a t e d a f t e r subsequent adjustment f o r the p o t e n t i a l i n f l u e n c e of the remaining v a r i a b l e s . T h i s i s s i m i l a r t o the c a l c u l a t i o n of the sum of squares i n the unbalanced ANOVA d e s i g n . On the ot h e r hand, the marginal s t a t i s t i c s are c a l c u l a t e d by c o l l a p s i n g or summing over the remaining v a r i a b l e s without any adjustment. The p a r t i a l s t a t i s t i c s can, t h e r e f o r e , be c o n s i d e r e d t o be more c o n s e r v a t i v e , but a l s o , more a p p r o p r i a t e t o measure pure e f f e c t s of s p e c i f i c i n t e r a c t i o n terms. For example, the p a r t i a l L2 v a l u e f o r the second-order Reception(R) by Set(S) term, a t e s t of independence f o r the r e c e p t i o n t o the set, was 1299.20 as opposed to 1693.20 f o r the marginal L2 s t a t i s t i c s . In r e l a t i o n t o the a n a l y s i s of the t r a n s i t i o n p a t t e r n , the p r e l i m i n a r y a n a l y s i s suggests t h a t because the d i s t r i b u t i o n s of the main marginals are unequal i n the l e v e l s 68 Table 4-10 Decomposition of iX f o r T r a n s i t i o n from Reception to Set P a r t i a l A s s o c i a t i o n M arginal A s s o c i a t i o n ( c o n d i t i o n a l t e s t ) ( u n c o n d i t i o n a l t e s t ) E f f e c t d f L2 P L2 P Set (S) 4 1865.51 <.0001 Reception(R) 3 411.53 <.0001 Game(G) 1 6.63 .01 Team(T) 1 18.15 <.0001 Process(P) 1 325.04 <.0001 SR 12 1299.20 <.0001 1693.20 <.0001 SG 4 30.26 <.0001 27.55 <.0001 ST 4 2.25 . 6907 4.61 .3299 SP 4 99.00 <.0001 493.88 <.0001 RG 3 6.67 .0832 4.00 .2615 RT 3 3.81 .2822 3.03 .3874 RP 3 273.69 <.0001 672.13 <.0001 GT 1 414.91 <.0001 415.80 <.0001 GP 1 6. 62 .0101 4.99 .0255 TP 1 1.38 .2394 -.05 1.0000 SRG 12 5.30 . 9470 4.27 . 9780 SRT 12 7.47 .8250 9.27 . 6800 SRP 12 23.83 .0215 23. 99 .0204 SGT 4 10.63 .0310 9.44 . 0511 SGP 4 4.11 .3914 .83 . 9338 STP 4 9.64 .0470 18.03 .0012 RGT 3 3.01 .3899 3.55 .3147 RGP 3 5.45 .1415 2.15 .5422 RTP 3 5.87 .1181 14.62 .0022 GTP 1 .93 .3350 .02 . 9005 SRGT 12 12.89 .3773 13.87 .3093 SRGP 12 4.00 .9835 5.13 .9537 SRTP 12 7.20 .8441 9.12 . 6927 SGTP 4 4.82 .3065 6.01 .1981 RGTP 3 2.53 .4695 3. 64 .3032 SRGTP 12 5.34 .9458 T o t a l 159 Note: Reception r e f e r s t o both serve r e c e p t i o n and d i g , but they are d i s t i n g u i s h e d by the Process f a c t o r 69 of the c l a s s i f i c a t i o n s t a t u s such as the Game, Team and Process, t h i s i n i t i a l d i f f e r e n c e c o u l d have u n d e s i r e d e f f e c t s upon the t r a n s i t i o n p r o b a b i l i t y matrix f o r a s p e c i f i c i n t e r a c t i o n term. This may d i s t o r t the p i c t u r e of the t r a n s i t i o n p a t t e r n . Consequently, t h i s i r r e l e v a n t e f f e c t must be c o n t r o l l e d by f i x i n g the main marginal i n the l e v e l of the f a c t o r s i n order to i n v e s t i g a t e pure e f f e c t s . Since the question i n t h i s a n a l y s i s i s not concerned with b u i l d i n g a parsimonious l o g - l i n e a r model to estimate the c e l l p r o b a b i l i t y or frequency, i t i s not of i n t e r e s t t o examine a l l of these terms. As a r e s u l t , the Table 4-10 i s transformed to an ANOVA-like t a b l e , which d i s p l a y s only those terms a s s o c i a t e d with t e s t i n g f o r the e f f e c t of the v a r i a b l e s on the d i s t r i b u t i o n of the s e t t i n g performance. The i n t e r p r e t a t i o n s of the t a b l e i s analogous t o th a t o f a c o n v e n t i o n a l ANOVA (see Table 4-11). The set v a r i a b l e i n the t a b l e i s t r e a t e d as a dependent v a r i a b l e and the remaining f a c t o r s are t r e a t e d as independent v a r i a b l e s . There was a h i g h l y s i g n i f i c a n t (p_<.001) Reception e f f e c t , i n d i c a t i n g t h a t the d i s t r i b u t i o n o f the s e t t i n g performance was dependent upon the outcome of the r e c e p t i o n (see Table 4-11). The va l u e of the L 2 s t a t i s t i c (1299.20) i s ve r y l a r g e compared t o the others, which suggests a str o n g dependency i n the t r a n s i t i o n p a t t e r n from the r e c e p t i o n t o the s e t . 70 Table 4-11 Decomposition o f iZ- f o r the T r a n s i t i o n from Reception t o Set  wi t h Set being t r e a t e d as the Dependent Measure V a r i a b l e s P a r t i a l Tests Independent Dependent d f L 2 p Game(G) Team(T) Process (P) Reception(R) Set (S) 12 1299.20 <.001 G x R S 12 5.30 .947 T x R S 12 7.47 .825 P x R S 12 23.83 .022 G x T x R S 12 12.89 .377 G x P x R S 12 4.00 .984 T x P x R S 12 7.20 .844 G x T x P x R S 12 5.34 .946 Although the nature o f t h i s dependency has yet to be c l o s e l y examined, t h i s r e s u l t i m p l i e s t h a t f a i r l y a ccurate p r e d i c t i o n s f o r the d i s t r i b u t i o n o f the s e t t i n g performance can be obt a i n e d u s i n g i n f o r m a t i o n r e g a r d i n g the outcomes of the r e c e p t i o n . Given the s i g n i f i c a n t dependency i n the t r a n s i t i o n p l a y from the r e c e p t i o n t o the s e t , the a n a l y s i s i s c o n t i n u e d t o i n v e s t i g a t e whether the p a t t e r n o f t h i s r e l a t i o n s h i p i s a f f e c t e d by the Game, Team, Process sta t u s or combination o f them. Examination o f the r e s u l t s showed t h a t the p a t t e r n o f t h i s dependency does not v a r y a c c o r d i n g to the Game or Team s t a t u s , as i n d i c a t e d from the n o n s i g n i f i c a n t Game by R e c e p t i o n 71 (p_=.947) and Team by Reception (p_=.825) i n t e r a c t i o n e f f e c t s . In a d d i t i o n , a n o n s i g n i f i c a n t Game by Team by Reception i n t e r a c t i o n e f f e c t (p_=.377) f u r t h e r suggests t h a t the p a t t e r n of t r a n s i t i o n p l a y from the r e c e p t i o n t o set i s very s t a b l e and c o n s i s t e n t r e g a r d l e s s o f the teams and winning or l o s i n g games. The t e s t o f whether the p a t t e r n o f t r a n s i t i o n p l a y i n the at t a c k process (AP) i s the same as t h a t i n the c o u n t e r a t t a c k p rocess was found t o be s i g n i f i c a n t , as r e v e a l e d i n the Process by Reception i n t e r a c t i o n e f f e c t (p_=.022). When comparing the magnitude of L 2 (23.83) t o t h a t o f L 2 of 1299.20 f o r the Reception by Set, i t seems t h a t the Process s t a t u s does not add meaningful i n f o r m a t i o n t o the e x i s t i n g t r a n s i t i o n p a t t e r n . However, t h i s r e s u l t demonstrates c e r t a i n c h a r a c t e r i s t i c s o f the s k i l l s i n v o l v e d i n the AP and CP. The Process by Reception i n t e r a c t i o n e f f e c t examines whether the t r a n s i t i o n p l a y between the serve r e c e p t i o n (SR) and set i n the AP have the same p a t t e r n as t h a t between the d i g and set i n the CP. As mentioned i n the a n a l y s i s o f the i n d i v i d u a l s k i l l s e c t i o n , the performance of the serve r e c e p t i o n and d i g i s e v a l u a t e d based on the same o b s e r v a t i o n c r i t e r i a due t o the same purpose, d e l i v e r i n g the b a l l t o a s e t t e r . Moreover, these two s k i l l s are the s t a r t i n g s k i l l s f o r a s e q u e n t i a l p l a y i n the AP and CP, r e s p e c t i v e l y . Therefore, t h i s s i g n i f i c a n t r e s u l t suggests t h a t t h e r e are c e r t a i n d i s t i n c t i v e components i n the performance o f the s e t i n the AP th a t are d i f f e r e n t 72 from those i n the CP. Consequently, a c l o s e examination and comparison of the p a t t e r n of the t r a n s i t i o n p l a y between the AP and CP could p r o v i d e the coach wi t h u s e f u l i n f o r m a t i o n r e g a r d i n g the e f f e c t i v e n e s s of the p r a c t i c e p l a n n i n g a c c o r d i n g t o the needs of h i s / h e r s e t t e r . Table 4-12 d i s p l a y s the t r a n s i t i o n p a t t e r n between the SR and set i n the AP, and between the d i g and set i n the CP. The d i s c u s s i o n s are d i r e c t e d toward e x p l a n a t i o n of the nature and degree of the t r a n s i t i o n p a t t e r n between the two s k i l l s . A l s o , the uses and a p p l i c a t i o n s of t h i s i n f o r m a t i o n to the p r a c t i c a l coaching s i t u a t i o n are i n c l u d e d from the coach's p o i n t of view. Table 4-12 T r a n s i t i o n P a t t e r n from the Reception t o the Set Reception (Process) Set Mean Mar g i n a l S c a l e : s4 s3 s2 s i sO P e r f . Frequency s4 44.3 30.5 22.1 2.4 0.8 3.15 1046 SR s3 29.4 34.5 33.3 2.4 0.3 2.90 574 (AP) s2 9.4 17.3 65.6 6.8 0.9 2.28 456 s i 0.0 3.9 47.0 43. 6 5.5 1.49 181 T o t a l 29.9 26.7 35.7 6.6 1.1 2257 s4 37.3 27.5 30.7 3.9 0.7 2.97 153 DIG S 3 23.4 21.0 50.9 3.6 1.2 2.62 167 (CP) s2 3.6 4.3 79.3 11.7 1.2 1.98 608 s i 0.4 2.6 30.8 63.5 2.6 1.35 266 T o t a l 10.0 9.2 58.3 21.1 1.4 1194 73 The f o l l o w i n g d i s c u s s i o n s are d e r i v e d from Table 4-12. (a) With r e s p e c t t o the n o t i o n o f sequence i n the game of v o l l e y b a l l , 99.7% of the t o t a l s e t s (2263) i n the AP and 97.7% of t h a t (1222) i n the CP were connected from the SR or Dig, r e s p e c t i v e l y . T h i s suggests t h a t , o v e r a l l , about 99% of the s e t s were s e q u e n t i a l l y connected from the p r e c e d i n g s k i l l , e i t h e r serve r e c e p t i o n or d i g . T h i s supports the b a s i c assumption of the sequence of the s k i l l performances a p p l i e d i n d e s i g n i n g the computer input program. (b) Upon i n s p e c t i o n of Table 4-12, i t i s apparent that a d i s c e r n a b l e p a t t e r n of dependency e x i s t s w i t h i n each t r a n s i t i o n matrix. For both AP and CP, the average s e t t i n g performance ( i . e . , mean p e r f . ) f o r a g i v e n s c a l e of the r e c e p t i o n i n c r e a s e s as a f u n c t i o n o f the q u a l i t y of the r e c e p t i o n . T h i s can be f u r t h e r evidenced by the d i s t r i b u t i o n o f g r e a t e r p r o p o r t i o n s along the main d i a g o n a l (e.g., g r e a t e r p r o p o r t i o n s under Scale 3 and 4 of the s e t are a s s o c i a t e d w i t h Scale 3 and 4 of the r e c e p t i o n ) . Assuming t h a t the s e t t e r at h i g h l e v e l s o f c o m p e t i t i o n would be able t o set up a m u l t i p l e o f f e n s e with Scale 3 and 4 of the r e c e p t i o n , t h i s p a t t e r n suggests t h a t the q u a l i t y o f the r e c e p t i o n i s d i r e c t l y r e l a t e d t o the q u a l i t y o f the s e t produced. On the other hand, the s e t t i n g performance w i t h S c a l e 1 and 2 of the r e c e p t i o n was very l i m i t e d and r e s u l t e d i n a poor set performance. T h i s was e s p e c i a l l y t r u e f o r the s e t t i n g 74 performance i n the CP. (c) Although both AP and CP m a t r i c e s show a s i m i l a r t r a n s i t i o n p a t t e r n , t h e r e are some d i f f e r e n c e s i n terms of the degree of t h e i r row p r o p o r t i o n s . A comparison of the two matrices i n d i c a t e s t h a t the set i n the AP outperformed the set i n the CP f o r a g i v e n q u a l i t y of the r e c e p t i o n . For example, when the b a l l was a c c u r a t e l y d e l i v e r e d t o the t a r g e t area (Scale 4), 44.3% of the s e t s i n the AP, as opposed t o 37.3% i n the CP, were performed i n such a way t h a t the s e t t e r deceived, along with accuracy, the opponent's b l o c k e r ( s ) i n terms of h i s intended set d i r e c t i o n and p l a c e . Thus, the s p i k e r c o u l d have the best chance at s u c c e s s f u l l y s p i k i n g the b a l l . T h i s d i f f e r e n c e i n the s e t t i n g performance between the AP and CP seems to be a l s o c o n s i s t e n t f o r lower Sc a l e s of the r e c e p t i o n . (d) O v e r a l l , r e g a r d l e s s of the q u a l i t y of r e c e p t i o n , a r e l a t i v e l y l a r g e p r o p o r t i o n o f s e t s i n Scale 2 i n d i c a t e d t h a t a c o n s i d e r a b l e number o f s e t s were performed i n such a way t h a t they were e i t h e r p r e d i c t a b l e f o r the opponent's b l o c k e r ( s ) or were executed w i t h a f a i r l y high t r a j e c t o r y . T h i s allowed the b l o c k e r s to f o l l o w the set and form a s o l i d b l o c k against the s p i k e r who was g i v e n the s e t . T h i s occurs p a r t i c u l a r l y when a s e t t e r i s p o s i t i o n e d i n f r o n t row w i t h two o t h e r s p i k e r s , making i t e a s i e r f o r the b l o c k e r s t o f o l l o w the s e t , thus i n c r e a s i n g d i f f i c u l t y f o r the s p i k e r i n a c h i e v i n g a s u c c e s s f u l s p i k e . A good s t r a t e g y t o put more p r e s s u r e on the b l o c k e r s would be t o make use o f a back row attack, e s p e c i a l l y 75 when the b a l l i s not a c c u r a t e l y d e l i v e r e d t o the t a r g e t area. (e) S u b s t a n t i a l d i f f e r e n c e s i n the marginal f r e q u e n c i e s between the serve r e c e p t i o n (SR) and the d i g p r o v i d e the coach w i t h i n f o r m a t i o n r e g a r d i n g the t r a i n i n g focus f o r the s e t t e r . For example, 71.8% of the t o t a l SRs are a c c u r a t e l y d e l i v e r e d (Scale 4), or c l o s e t o the t a r g e t area (Scale .3) , as opposed t o 26.8% of the t o t a l d i g s (sum of S c a l e 3 and 4). Therefore, the focus of t r a i n i n g s h o u l d be d i r e c t e d more toward p r a c t i c i n g d e c e p t i v e s e t t i n g techniques and d i s t r i b u t i o n s t r a t e g i e s needed i n m u l t i p l e o f f e n s i v e p l a y i n the AP. A l s o , p r a c t i c i n g the set i n the CP should focus on improving a g i l i t y and f a s t r e a c t i o n s t o d e a l w i t h the u n c e r t a i n t y of the b a l l and a n t i c i p a t i n g the path o f the b a l l from a r e c o g n i t i o n of the r e c e i v e r ' s form. 4.2.2 F i r s t - O r d e r T r a n s i t i o n from the Set t o Spike The same procedure of the p r e l i m i n a r y a n a l y s i s was f o l l o w e d t o o b t a i n p a r t i t i o n e d s t a t i s t i c s f o r the t r a n s i t i o n matrix from the set t o s p i k e . The output of the p r e l i m i n a r y a n a l y s i s was again transformed t o a ANOVA-like t a b l e , which d i s p l a y s the v a l u e s f o r the a p p r o p r i a t e terms (see Appendix G f o r the output o f BMDP4F program). In the t a b l e , the spike was t r e a t e d as a dependent v a r i a b l e and the remaining v a r i a b l e s are t r e a t e d as independent v a r i a b l e s . 76 Table 4-13 Decomposition of L2- f o r the T r a n s i t i o n from Set to Spike with  Spike being t r e a t e d as the Dependent Measure V a r i a b l e s P a r t i a l T e s t s Independent Dependent df L 2 p Game(G) Team(T) Process(P) Set (S) Spike(K) 12 917.51 <.001 G x S K 12 12.90 .376 T x S K 12 11.86 .457 P x S K 12 20.27 .062 G x T x S K 12 16.22 .181 G x P x S K 12 13.96 .304 T x P x S K 12 12.01 .445 G x T x P x S K 12 16.01 .191 The h i g h l y s i g n i f i c a n t Set e f f e c t (p<.001) i n d i c a t e s t h a t the d i s t r i b u t i o n o f the s p i k i n g performance was dependent upon the given outcome of the set (see Table 4-13). In a d d i t i o n , n o n s i g n i f i c a n t r e s u l t s f o r any of the h i g h e r - o r d e r i n t e r a c t i o n s i n d i c a t e t h a t the t r a n s i t i o n p a t t e r n from the set t o spike i s very s t a b l e and not a f f e c t e d by the Game, Team, Process or combinations of these s t a t u s . These r e s u l t s suggest t h a t the s p i k e r s ' a b i l i t y t o d e a l with a c e r t a i n q u a l i t y o f the s e t i s c o n s i s t e n t and does not f l u c t u a t e very much among the teams and games. In the f i n d i n g s o b t a i n e d from the i n d i v i d u a l s k i l l 77 a n a l y s i s , t h e r e were marked d i f f e r e n c e s i n the performance of the set as w e l l as the s p i k e between the Game, Team and Process S t a t u s . I n t e r e s t i n g l y , when l o o k i n g at the c h a r a c t e r i s t i c s of the t r a n s i t i o n per se, a t r a n s i t i o n p a t t e r n seems t o e x i s t , which i s common r e g a r d l e s s of the c l a s s i f i c a t i o n s t a t u s . The c o n s i s t e n t c h a r a c t e r i s t i c s i n the p a t t e r n of the t r a n s i t i o n p l a y seem t o be p e c u l i a r to the c o m p e t i t i v e nature of the c o m p e t i t i o n which i s f i r m l y e s t a b l i s h e d at the i n t e r n a t i o n a l l e v e l of men's v o l l e y b a l l . Table 4-14 T r a n s i t i o n P a t t e r n from the Set to the Spike Set Spike Mean Ma r g i n a l S c a l e : s4 s3 s2 s i sO P e r f . Frequency s4 74.8 8.9 8.1 1.5 6.7 3.44 795 S3 54.1 9.4 22.4 2.8 11.3 2.92 711 s2 40.9 10.4 21.3 6.8 20.6 2.44 1484 s i 8.5 5.8 9.0 55.9 20.8 1.25 399 T o t a l 47.8 9.3 17.0 10.5 15.4 3389 The f o l l o w i n g d i s c u s s i o n s are d e r i v e d from Table 4-14. (a) The t o t a l frequency o f 3389 i n Table 4-14 suggests t h a t 98.8% of the e n t i r e s p i k e s (3429) i n the sample games were s e q u e n t i a l l y preceded by the s e t . T h i s r e s u l t again supports the concept of a sequence o f the s k i l l s i n the game of v o l l e y b a l l . 78 (b) The presence of a s t r o n g dependency between two s k i l l performances appears i n Sc a l e 4 and 1, even though a gross p a t t e r n i s shown i n Scale 2 and 3. In Scale 4 of the s e t , 74.8% of the sp i k e s r e s u l t e d i n success, whereas with S c a l e 1 o f the set, 76.7% of the s p i k e s r e s u l t e d i n e i t h e r a s p i k i n g e r r o r or a f r e e b a l l f o r the o p p o s i t i o n . From t h i s r e s u l t one c o u l d be f a i r l y c o n f i d e n t t o p r e d i c t that the s p i k e r s would accomplish a hi g h success r a t e i n h i s s p i k i n g when p r o v i d e d w i t h an accurate s e t, along w i t h one-man or l e s s i n the opponent's b l o c k . When an i n a c c u r a t e set (Scale 1) was giv e n t o the s p i k e r s , they performed c o r r e s p o n d i n g l y . Since S c a l e 1 and 4 of the set i s at e i t h e r extreme f o r the s p i k e r i n terms of i t s q u a l i t y , i n d i v i d u a l d i f f e r e n c e s i n terms of s p i k i n g a b i l i t y may not make a s u b s t a n t i a l d i f f e r e n c e i n the degree of t h i s p r e d i c t i o n . (c) With Scale 2 and 3 o f the s e t , the p r o p o r t i o n s o f success r a t e (Scale 4) i n s p i k i n g performance are r e l a t i v e l y h i g h ( i . e . , 40.9% and 54.1%, r e s p e c t i v e l y ) . T h i s p o s i t i v e departure from the dependency can be e x p l a i n e d by the f a c t t h a t the sp i k e i s a s k i l l t h a t i s supposed t o terminate a r a l l y i n fav o r o f the s p i k i n g team i n an i n t e r a c t i o n with the opponent's b l o c k at the net. Therefore, as long as an a c c e p t a b l e q u a l i t y of set was performed f o r the s p i k e r s , they can take advantage of the predominant c h a r a c t e r of the s p i k e over the d e f e n s i v e nature of the b l o c k . As a r e s u l t , the success i n s p i k i n g as seen i n Scale 2 and 3 i s probably 7 9 dependent upon the s p i k e r ' s a b i l i t i e s t o d e a l w i t h v a r i a t i o n s i n the given set and a v o i d a s o l i d two-man block of t h e i r opponent. 4.2.3 Transition Pattern among the Offensive Plays As a follow-up a n a l y s i s t o the s i g n i f i c a n t dependency between the set and s p i k e , an attempt was made to compare the t r a n s i t i o n p a t t e r n among the o f f e n s i v e p l a y s . The t r a n s i t i o n m a t r i x f o r the set t o the spike was subd i v i d e d i n t o the th r e e c a t e g o r i e s ; h i g h - s e t , medium-set and q u i c k - s e t . These submatrices are p r e s e n t e d i n Table 4-15. Since t h e r e were no s i g n i f i c a n t Game, Team and Process s t a t u s e f f e c t s on the p a t t e r n of the t r a n s i t i o n p l a y from the set to s p i k e , i t was assumed t h a t they would not have e f f e c t s on the t r a n s i t i o n p a t t e r n of the types o f s e t s e i t h e r . Therefore, a t e s t of whether there are d i f f e r e n c e s among t h r e e o f f e n s i v e p l a y s i n terms of the t r a n s i t i o n p a t t e r n was conducted. The r e s u l t showed that there were s i g n i f i c a n t ( L 2 (24) =64.92, p_<.001) d i f f e r e n c e s among t h r e e o f f e n s i v e p l a y s i n terms o f t h e i r t r a n s i t i o n p a t t e r n . T h i s suggests t h a t the d i s t r i b u t i o n s o f the s p i k i n g performance among the high, medium and qu i c k p l a y s are d i f f e r e n t from one another. The f o l l o w i n g d i s c u s s i o n s are d e r i v e d from Table 4-15. (a) Looking at the t o t a l f r e q u e n c i e s f o r the t h r e e types o f s e t s showed t h a t 46.1%, 27.5% and 23.6% of the t o t a l s e t s 8 0 were d i s t r i b u t e d to high, medium and quick sets, r e s p e c t i v e l y . The remaining 2.8% of the s e t s were under a "Save" category when the type of set was not i d e n t i f i a b l e . Of the t o t a l h i g h s e t s , 84.1% were e i t h e r S cale 1 or 2. The r e l a t i v e l y l a r g e p r o p o r t i o n s of the h i g h s e t , wit h most o f them being of a poor q u a l i t y d e l i v e r y , suggest t h a t i n order t o be s u c c e s s f u l a team should be able t o develop s t r o n g power h i t t e r s who are mainly r e s p o n s i b l e f o r h i g h s e t s and are able t o handle u n d e s i r a b l e s e t s i n f a v o r of the s p i k i n g team. Table 4-15 T r a n s i t i o n M a t r i c e s f o r the Three O f f e n s i v e Plays \ Type of Set Spike Mean Ma r g i n a l S c a l e : s4 s3 s2 s i sO P e r f . Frequency s4 62.2 13.3 14.8 2.2 7.4 3.21 135 High s3 57 .5 8.8 16.8 3.5 13.3 2.94 113 set s2 43.1 9.7 20.9 6.6 19.8 2.50 1077 s i 10.0 6.3 12.6 48.5 22.6 1.33 239 T o t a l 40.7 9.4 18.8 12.4 18.7 1564 s4 74.2 9.5 8.2 1.1 7.1 3.43 368 Med. s3 60.6 7.0 19.9 2.4 10.1 3.06 287 set s2 43.7 9.8 20. 9 5.1 20.5 2.51 254 s i 9.1 4.5 0.0 63.6 22.7 1.14 22 T o t a l 60.2 8.7 15.0 4.1 12.0 931 s4 81.4 6.2 4.8 1.7 5.9 3.56 290 Quick s3 46.9 11.9 26.7 2.9 11.6 2.80 311 set s2 20.9 17.0 24.8 11.1 26.1 1.95 153 s i 6.7 8.9 6.7 53.3 24.4 1.20 45 T o t a l 52.2 10.6 17.3 6.9 13.0 799 81 (b) In g e n e r a l , the p a t t e r n o f dependency i n each of the t h r e e o f f e n s i v e t r a n s i t i o n m a t r i c e s i s s i m i l a r t o t h a t of the t r a n s i t i o n matrix between the s e t and spike shown i n Table 4-14. This i s e s p e c i a l l y t r u e f o r the s p i k i n g performance w i t h S c a l e 1 and 4 of the set, though t h e r e are some v a r i a t i o n s i n the degree of p r o p o r t i o n s among the three m a t r i c e s . As p r e v i o u s l y mentioned, the p o s i t i v e departure from the dependency i n the th r e e o f f e n s i v e s p i k i n g performances wi t h S c a l e 2 and 3 of the set again demonstrates the nature o f t a s k s i n v o l v e d i n the s k i l l of the s p i k e . (c) In comparing the t h r e e t r a n s i t i o n matrices, s p i k i n g the q u i c k - s e t showed the h i g h e s t success r a t e . With S c a l e 4 o f the set, 81.4% o f the q u i c k - s e t s p i k i n g r e s u l t e d i n winning a r a l l y , as opposed t o 74.2% and 62.2% of the medium-set and h i g h - s e t s p i k i n g , r e s p e c t i v e l y . When lower Scales o f the set were d e l i v e r e d t o the s p i k e r , the success r a t e f o r the q u i c k -s e t s p i k i n g decreased much more d r a m a t i c a l l y than t h a t f o r the medium-set and h i g h - s e t s p i k i n g . A s i m i l a r p a t t e r n can a l s o be seen i n the average s p i k i n g performance f o r a g i v e n s c a l e o f the set (see Mean p e r f . ) . These d i f f e r e n c e s can be e x p l a i n e d by the f a c t t h a t the qu i c k p l a y i s based upon ac c u r a t e and p r e c i s e t i m i n g i n the se t e x e c u t i o n . I f the set i s executed i n a c c u r a t e l y w i t h i n c o r r e c t t i m i n g i n r e l a t i o n t o a s p i k e r ' s jump, the s p i k e r w i l l not have time t o a d j u s t . On the other hand, the medium-82 set and hi g h - s e t t r a v e l f o r a r e l a t i v e l y longer p e r i o d o f time a f t e r the set has been executed. The s p i k e r c o u l d use advanced s p i k i n g techniques to a d j u s t f o r the i n a c c u r a c y and i n c o r r e c t t i m i n g , and i s thus l e s s dependent upon the giv e n outcomes of the s e t . As a r e s u l t , the s u c c e s s f u l s p i k i n g performance i n the quick p l a y tended t o be more dependent upon good q u a l i t y of the s e t t i n g performance than t h a t i n the medium and hig h ones, as shown i n the d i s t r i b u t i o n s o f the p r o p o r t i o n s i n Table 4-15. 4.2.4 Second-Order T r a n s i t i o n from Reception t o Spike A major i n t e r e s t i n t h i s a n a l y s i s i s t o i n v e s t i g a t e whether the d i s t r i b u t i o n of the s p i k i n g performance can a l s o be a c c u r a t e l y p r e d i c t e d from the knowledge of the outcomes of the r e c e p t i o n without c o n s i d e r i n g the s e t t i n g performance. In order t o t e s t t h i s , the same procedure o f the p r e l i m i n a r y a n a l y s i s was again f o l l o w e d . Since the L 2 s t a t i s t i c s f o r the t e s t o f independence between the r e c e p t i o n and spi k e was found t o be s i g n i f i c a n t , the subsequent a n a l y s i s was undertaken t o i n v e s t i g a t e whether t h i s t r a n s i t i o n p a t t e r n v a r i e s s i g n i f i c a n t l y a c c o r d i n g t o the l e v e l s o f c l a s s i f i c a t i o n f a c t o r s such as the Game, Team, and Process (see Table 4-16) . The a p p r o p r i a t e terms f o r t e s t i n g t h i s q u e s t i o n from the output o f the p r e l i m i n a r y a n a l y s i s was transformed t o a ANOVA-l i k e t a b l e (see Appendix H f o r the output from BMDP). 83 Table 4-16 Decomposition of f o r the 2nd-order T r a n s i t i o n from Reception to Spike with Spike b e i n g t r e a t e d as the Dependent  Measure V a r i a b l e s P a r t i a l T e s t s Independent Dependent df 1/ p Game(G) Team(T) Process(P) Reception(R) Spike(K) 12 297.11 <.001 G x R K 12 7.55 .819 T x R K 12 18.31 . 107 P x R K 12 15.22 .230 G x T x R K 12 14.48 .271 G x P x R K 12 8.90 .712 T x P x R K 12 6.70 .877 G x T x P x R K 12 11.55 .483 The s i g n i f i c a n t R eception e f f e c t (p_<.001) i n d i c a t e d t h a t the d i s t r i b u t i o n of the s p i k i n g performance i s dependent upon the outcomes of the r e c e p t i o n . That i s , one c o u l d p r e d i c t the s p i k i n g performance with some degree of accuracy from the outcomes of the r e c e p t i o n without c o n s i d e r i n g the s e t t i n g performance. The f a c t t h a t the v a l u e (297.11) f o r t h i s second-order t r a n s i t i o n i s much s m a l l e r than t h a t (917.51) f o r the f i r s t - o r d e r t r a n s i t i o n from the set to s p i k e i n d i c a t e d t h a t the d i s t r i b u t i o n s o f the s p i k i n g performance became l e s s dependent upon the r e c e p t i o n than the s e t . As a r e s u l t , one cannot be as c o n f i d e n t i n p r e d i c t i n g the performance of the s p i k e from such i n f o r m a t i o n as i s p o s s i b l e with knowledge of 84 the performance of the s e t . T h i s comparison c l e a r l y i n d i c a t e s the importance o f the r o l e o f the s e t t i n g i n the game of v o l l e y b a l l . F u r t h e r examinations o f the h i g h e r - o r d e r i n t e r a c t i o n terms showed t h a t the c l a s s i f i c a t i o n s t a t u s does not have a s i g n i f i c a n t e f f e c t upon the p a t t e r n o f the t r a n s i t i o n matrix between the r e c e p t i o n and s p i k e . T h i s r e s u l t again suggests t h a t t h e r e e x i s t s c e r t a i n c h a r a c t e r i s t i c s of p l a y i n g p a t t e r n e s t a b l i s h e d at the i n t e r n a t i o n a l l e v e l of men's co m p e t i t i o n . Table 4-17 T r a n s i t i o n P a t t e r n from the Reception t o the Spike Reception Spike Mean Marginal S c a l e : s4 s3 s2 s i sO P e r f . Frequency s4 58.1 9.3 15.3 4.8 12.4 2.96 1189 s3 52.4 9.5 18.1 6.4 13.6 2.81 735 s2 44.7 9.7 19.5 8.9 17.1 2.56 1044 s i 22.1 7.9 12.9 37.9 19.2 1.76 443 T o t a l 48.1 9.3 16.9 10.7 15.0 3411 The f o l l o w i n g d i s c u s s i o n s are d e r i v e d from Table 4-17. (a) In gene r a l , the p a t t e r n o f the d i s t r i b u t i o n i n Table 4-17 shows that the s p i k i n g performance was much l e s s dependent upon the q u a l i t y o f the r e c e p t i o n than i t was i n the f i r s t - o r d e r t r a n s i t i o n between the s e t and s p i k e (see Table 4-85 14). This i s apparent when comparing the d i s t r i b u t i o n s of s p i k i n g success r a t e between the f i r s t - and second-order t r a n s i t i o n p a t t e r n s , t h e r e are much s m a l l e r d i f f e r e n c e s i n p r o p o r t i o n s among Sc a l e s o f the r e c e p t i o n than those o f the s e t . For example, 58.1% o f S c a l e 4 of the r e c e p t i o n , as opposed t o 74.8% of the se t , were a s s o c i a t e d with s u c c e s s f u l s p i k i n g . In other words, the s p i k i n g performance i s l e s s dependent upon the g i v e n outcomes of the r e c e p t i o n than those o f the s e t . (b) When a s e q u e n t i a l p l a y i s i n i t i a t e d by a p e r f e c t pass (Scale 4), 58.1% of the s p i k e s r e s u l t e d i n success. Although i t does not n e c e s s a r i l y mean t h a t a p e r f e c t pass a u t o m a t i c a l l y ensures a s u c c e s s f u l s p i k e , i t i m p l i e s t h a t a good pass t o a s e t t e r i s more l i k e l y t o be t r a n s l a t e d i n t o a s u c c e s s f u l s p i k e . The r e l a t i v e l y l a r g e p r o p o r t i o n of the spike success r a t e (22.1%) with Scale 1 of the r e c e p t i o n , as compared t o 8.5% with Scale 1 of the set (see Table 4-14), g i v e an impression t h a t the s e t t i n g performance had negative i n f l u e n c e s on the success r a t e o f the s p i k e . However, as can be seen i n Table 4-12 ( t r a n s i t i o n from the r e c e p t i o n t o set) a l a r g e p r o p o r t i o n of the S c a l e 1 r e c e p t i o n s r e s u l t e d i n an acc e p t a b l e set q u a l i t y f o r the s p i k e r due t o the e f f o r t s of the s e t t e r . Therefore, the success r a t e o f the s p i k e w i t h S c a l e 1 of the r e c e p t i o n r e f l e c t s an i n d i r e c t i n f l u e n c e of the s e t t i n g , r a t h e r than a d i r e c t r e l a t i o n s h i p between the r e c e p t i o n and s p i k e . 86 (c) A comparison of the p r o p o r t i o n s of the s p i k i n g performance with Scale 2 and 3 between the f i r s t - and second-o r d e r t r a n s i t i o n matrices showed almost i d e n t i c a l d i s t r i b u t i o n s . T h i s c o n s i s t e n t p a t t e r n of s p i k i n g performance confirms the p r e v i o u s d i s c u s s i o n s i n which the success o f the s p i k e i s more l i k e l y dependent upon the s p i k e r ' s a b i l i t y when the s p i k e r was given Scale 2 or 3 o f the s e t . From t h i s p o i n t o f view, one i n d i c a t o r of an e x c e l l e n t s e t t e r can be c o n s i d e r e d by the p r o p o r t i o n of the p e r f e c t passes (Scale 4) he i s able to convert i n t o an i d e a l s p i k i n g s i t u a t i o n w i t h h i s d e c e p t i v e s e t t i n g techniques and/or d i s t r i b u t i o n a l s t r a t e g i e s . Another c h a r a c t e r i s t i c of an e x c e l l e n t s e t t e r can then be thought of as the a b i l i t y t o convert a poor pass (Scale 1) from a r e c e i v e r i n t o an a c c e p t a b l e s e t f o r the s p i k e r . T h i s comparison would be more r e a l i s t i c t o e v a l u a t e the performance o f the s e t t e r i f an i n d i v i d u a l team-oriented a n a l y s i s i s to be c a r r i e d out. In summary, the r e s u l t s showed t h a t a c o n s i s t e n t t r a n s i t i o n p a t t e r n e x i s t s between the s k i l l s which take p l a c e s e q u e n t i a l l y i n the game of v o l l e y b a l l . The a n a l y s i s o f the f i r s t - o r d e r t r a n s i t i o n from the r e c e p t i o n t o set r e v e a l e d t h a t t h e d i s t r i b u t i o n of the s e t t i n g performance was s i g n i f i c a n t l y dependent upon the given outcomes o f the r e c e p t i o n . F u r t h e r examination of t h i s t r a n s i t i o n p a t t e r n suggested that the s e t t i n g performance w i t h a g i v e n q u a l i t y of the serve r e c e p t i o n was s u p e r i o r t o t h a t w i t h the outcomes of the d i g . 87 The d i f f e r e n c e i n the t r a n s i t i o n p a t t e r n between the AP and CP p r o v i d e s p r a c t i c a l i n f o r m a t i o n f o r the coach r e g a r d i n g the focus of the t r a i n i n g a c c o r d i n g to the needs of h i s / h e r s e t t e r . The presence of dependency i n the t r a n s i t i o n p a t t e r n from the set t o spike a l s o suggested t h a t g r e a t e r success r a t e i n the s p i k i n g performance was r e l a t e d d i r e c t l y t o h i g h q u a l i t y of the set p r o v i d e d . However, the success of the s p i k i n g with S c a l e 2 and 3 of the set seemed to be r a t h e r dependent upon the s p i k e r ' s a b i l i t y t o d e a l with the opponent's b l o c k or v a r i a t i o n s i n a given s e t . Furthermore, the p a t t e r n of t h i s t r a n s i t i o n p l a y between the s e t and s p i k e was s t a b l e r e g a r d l e s s of the Game, Team or Process Status. T h i s r e s u l t demonstrated the c o m p e t i t i v e nature and c h a r a c t e r i s t i c s of p l a y i n g p a t t e r n e s t a b l i s h e d at the i n t e r n a t i o n a l l e v e l o f men's com p e t i t i o n . Comparisons of the t r a n s i t i o n p a t t e r n among the o f f e n s i v e p l a y s showed t h a t the s p i k i n g performance wit h the q u i c k - s e t tended t o be more dependent upon the q u a l i t y of the set than t h a t w i t h the medium and h i g h - s e t s p i k i n g . The a n a l y s i s o f the second-order t r a n s i t i o n from the r e c e p t i o n to s p i k e showed a s i m i l a r p a t t e r n , but weaker dependency emerged, w i t h t h a t from the set to s p i k e i n terms o f d i s t r i b u t i o n of the s p i k i n g performance. The comparison of the d i s t r i b u t i o n of the p r o p o r t i o n s between the f i r s t - o r d e r and second-order t r a n s i t i o n m a t r i c e s w i t h r e s p e c t t o the 8 8 s p i k i n g performance r e v e a l e d t h a t a good pass t o a s e t t e r w i l l more l i k e l y l e a d t o a s u c c e s s f u l s p i k e . These s t a t i s t i c a l r e s u l t s a l s o r e i n f o r c e d the importance of the r o l e of the s e t t i n g i n the game of v o l l e y b a l l . 89 CHAPTER V Summary and Co n c l u s i o n s The purpose of t h i s study was to analyze and e v a l u a t e team performance i n v o l l e y b a l l i n terms of i n d i v i d u a l s k i l l performance as w e l l as s e q u e n t i a l s k i l l performances. In order to q u a n t i f y the performance of the s e l e c t e d s k i l l components, a 5-point s c a l e o b s e r v a t i o n c r i t e r i a was developed f o r each of s i x s k i l l components. A computer program was developed based on the concept of a sequence of the s k i l l s i n the game of v o l l e y b a l l . The computer program was used to r e c o r d a c t i o n s of the s k i l l s (input) and produce d e s c r i p t i v e s t a t i s t i c s f o r an i n d i v i d u a l s k i l l and t r a n s i t i o n m a t r i c e s f o r s e q u e n t i a l s k i l l s (output). R e l i a b i l i t y of the q u a n t i f i c a t i o n o f a s k i l l performance i n the r e c o r d i n g process was computed by a Pearson c o r r e l a t i o n c o e f f i c i e n t u s i n g an i n t r a o b s e r v e r t e s t - r e t e s t procedure. V a l i d i t y of the o b s e r v a t i o n c r i t e r i a f o r each s k i l l was e s t a b l i s h e d by a p r o p o r t i o n of agreement between the c r i t e r i o n and the feedback from v o l l e y b a l l e x p e r t s . Seventy-two sample games from the F.I.V.B Cup i n t e r n a t i o n a l men's v o l l e y b a l l c o m petition were v i d e o taped, computer recorded, and s t a t i s t i c a l l y analyzed. Games were grouped i n t o two c a t e g o r i e s according t o the team s t a n d i n g and game s t a t u s : Top 4-Bottom 4 teams and Winning-Losing games. The p l a y i n g c h a r a c t e r i s t i c s of the i n d i v i d u a l s k i l l 90 performance were i n v e s t i g a t e d u s i n g m u l t i v a r i a t e analyses of v a r i a n c e (MANOVA), and as a f o l l o w up t o MANOVA, d i s c r i m i n a n t f u n c t i o n a n a l y s i s was a p p l i e d t o s e l e c t the best p r e d i c t o r ( s ) o f team success among the e i g h t s k i l l components. The nature and degree of the mathematical r e l a t i o n s h i p s ( f i r s t - and second-order t r a n s i t i o n p a t t e r n s ) among the s e q u e n t i a l p l a y i n g a c t i o n s were examined u s i n g l o g - l i n e a r procedures. The f o l l o w i n g c o n c l u s i o n s have been drawn from the r e s u l t s a t t a i n e d i n these a n a l y s e s . With r e s p e c t to the computer program: 1) A developed computer r e c o r d i n g system i n c r e a s e d the e f f i c i e n c y and accuracy i n c o l l e c t i n g the data. Games c o u l d be a c c u r a t e l y and r e l i a b l y recorded. 2) An output program produced a v a r i e t y of d e s c r i p t i v e summary s t a t i s t i c s as w e l l as t r a n s i t i o n p r o b a b i l i t i e s among the s e q u e n t i a l events. • More than 95% of s k i l l performances took p l a c e i n a s e q u e n t i a l order. T h i s was deemed t o be u s e f u l f o r the coach i n e v a l u a t i n g team performance. 91 With r e s p e c t to i n d i v i d u a l s k i l l a n a l y ses: 1) U n i v a r i a t e ANOVAs f o l l o w i n g by a s i g n i f i c a n t MANOVA with repeated measures on the Process f a c t o r r e v e a l e d s i g n i f i c a n t d i f f e r e n c e s i n the performance o f both the set and spike between the AP and CP. These r e s u l t s suggested t h a t the s e t and spike i n the AP sh o u l d not be t r e a t e d i n the same manner as those i n the CP i n the e v a l u a t i o n process.. 2) F a c t o r i a l MANOVA f o r randomized groups design showed s i g n i f i c a n t Team and Game Status e f f e c t s . The fol l o w - u p u n i v a r i a t e ANOVAs r e v e a l e d t h a t the d i f f e r e n c e s were due to b e t t e r performances on those s k i l l s which took p l a c e i n the CP; block, d i g , s et and spike, demonstrated by the top 4 teams and i n the winning games. 3) D i s c r i m i n a n t f u n c t i o n a n a l y s i s showed that the b l o c k and the spike i n both the AP and CP among the e i g h t s k i l l components were the ( r e l a t i v e l y ) most important s k i l l s d etermining team succ e s s . With knowledge o f the performance o f these s k i l l s , 7 7.8% o f the t o t a l sample games were c o r r e c t l y c l a s s i f i e d as winning or l o s i n g games. 92 t h respect to s e q u e n t i a l s k i l l a n a l y s e s : 1) A n a l y s i s of the f i r s t - o r d e r t r a n s i t i o n between the r e c e p t i o n and s e t showed t h a t the performance of the set was s i g n i f i c a n t l y dependent upon the given outcome o f the r e c e p t i o n . A comparison of the t r a n s i t i o n p a t t e r n s between the serve r e c e p t i o n and set, and the d i g and set r e v e a l e d t h a t a g r e a t e r p r o p o r t i o n (44.3%) of the p e r f e c t execution i n the set was accomplished from the serve r e c e p t i o n than from the d i g (37.3%). 2) The analyses of the f i r s t - and second-order t r a n s i t i o n between the s e t and s p i k e , and the r e c e p t i o n and s p i k e showed that success i n the s p i k i n g performance was s i g n i f i c a n t l y dependent upon the g i v e n outcomes of both the set and the r e c e p t i o n . However, the degree of the dependence was much weaker i n the second-order t r a n s i t i o n (58.1%) than i n the f i r s t - o r d e r t r a n s i t i o n (74.8%) between the s e t and s p i k e . These r e s u l t s suggested the importance of the r o l e of the s e t t i n g i n the game of the v o l l e y b a l l . 3) Comparison of the t r a n s i t i o n p a t t e r n s among the t h r e e o f f e n s i v e p l a y s r e v e a l e d t h a t success i n the s p i k i n g performance w i t h the q u i c k - s e t was more dependent upon the q u a l i t y of the set than t h a t with the medium-set and h i g h - s e t (81.4%, 74.2%, and 62.2%, r e s p e c t i v e l y ) . 93 4) The p a t t e r n s of the f i r s t - and second-order t r a n s i t i o n s were s t a b l e and c o n s i s t e n t r e g a r d l e s s of the Team, Game and Process S t a t u s . These r e s u l t s suggested t h a t the c o n s i s t e n t p a t t e r n of the t r a n s i t i o n p l a y s seemed to be f i r m l y e s t a b l i s h e d at the c o m p e t i t i v e i n t e r n a t i o n a l l e v e l of men's v o l l e y b a l l . Recommendations 1) I t i s recommended t h a t f u r t h e r expansion of the computer program be needed when one d e s i r e s t o o b t a i n i n f o r m a t i o n about the performance of an i n d i v i d u a l p l a y e r . 2) I t i s a l s o recommended that coaches use the proposed analyses and e v a l u a t i o n of team performance as a t o o l f o r a thorough understanding of the c h a r a c t e r i s t i c s of the s k i l l performances and the nature and degree o f the t r a n s i t i o n p a t t e r n s among the s e q u e n t i a l events i n v o l l e y b a l l . 3) A f i n a l recommendation i s t h a t the concept of s e q u e n t i a l performance a n a l y s i s as proposed i n t h i s study w i l l serve as an example and a stimulus f o r s p o r t s c i e n t i s t s i n c o n s t r u c t i n g a p r o b a b i l i s t i c model o f team performance f o r t h e i r s p o r t i n g areas. 94 References A g r e s t i , A. (1984). 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I n t e r n a t i o n a l J o u r n a l of Man-Machine Studies, 8, 125-147. 9 9 Trueman, R.E. (1977). A n a l y s i s of b a s e b a l l as Markov p r o c e s s . In S.P. Ladany and R.E. Machol (Eds.). Optimal S t r a t e g i e s  i n S p o r t s . Amsterdam, North H o l l a n d . 68-76. V o j i k , J . (1980). S e v e r a l remarks to a system of accumulating data i n v o l l e y b a l l . V o l l e y b a l l T e c h n i c a l J o u r n a l . V(3), 35-41. 1 0 0 Appendix A Types of Set In c o m p e t i t i v e v o l l e y b a l l b a l l such as u n i v e r s i t y or n a t i o n a l l e v e l the s e t s performed by the s e t t e r can be c l a s s i f i e d i n t o a p p r o x i m a t e l y 13 k i n d s . These a r e : Qu i c k - s e t : A (51), B (61), C (31); Medium-set: D (53 or X - s e t ) , E (33), F (63 or back X - s e t ) , G (13 or S h o o t - s e t ) , H (73 or back S h o o t - s e t ) ; High-set : I (high l e f t ) , J (high middle), K (high r i g h t ) , L ( l e f t backrow) , M ( r i g h t backrow). NOTES: 1 The l e n g t h o f the net i s d i v i d e d i n t o 7 areas, 0 b e i n g l e f t s i d e and 7 b e i n g r i g h t s i d e . The ar e a 5 i n d i c a t e s the s e t t e r ' s p o s i t i o n a l o n g t h e net. Thus, 53 s e t means the s e t which i s up 3 f e e t h i g h above the net on the area 5 a l o n g the net, o f t e n c a l l e d as X-se t . Each s e t can be s l i g h t l y v a r i e d i n terms o f h e i g h t and d i s t a n c e a c c o r d i n g t o a team's i n d i v i d u a l c h a r a c t e r i s t i c s . 101 Appendix B Observation C r i t e r i a A d e t a i l e d d e s c r i p t i o n of the s c a l e f o r each i n d i v i d u a l s k i l l now f o l l o w s : S E R V E Serve i s the f i r s t s k i l l i n i t i a t i n g the game. As modern v o l l e y b a l l has developed more dynamic and powerful o f f e n s i v e p l a y , the serve has been used as a f i r s t weapon i n order t o reduce the o p t i o n s of the opponent's m u l t i p l e a t t a c k . Since the s c a l e of the serve r e c e p t i o n (S.R) was d e f i n e d by how w e l l the serve was passed, the s c a l e of the e f f e c t of the serve can be e a s i l y o b tained by r e v e r s i n g the s c a l e of the S.R.. A s c a l e of serve i s given a u t o m a t i c a l l y through the i n p u t program i n the f o l l o w i n g manner. Scale 4 (Point) The serve gained a p o i n t . T h i s i s e q u i v a l e n t t o the s c a l e 0 i n S.R. ( e i t h e r an e r r o r or t e c h n i c a l f a u l t by the r e c e i v e r , or the b a l l h i t the f l o o r d i r e c t l y ) . * I f a p o i n t i s s c o r e d because of a red c a r d or a t e c h n i c a l f a u l t u n r e l a t e d t o the serve, n o t h i n g i s recorded f o r the r a l l y ( i n t h i s case, p r e s s (+) key f o r a p o i n t or (-) key f o r a s i d e - o u t ) . S c a l e 3 (Good) The served b a l l was up somewhere on the middle or back of the c o u r t or i n a c c u r a t e l y passed (more than 3m away from the t a r g e t area e i t h e r along the net or o f f the net) so t h a t the opponent's s e t t e r c o u l d not use a m u l t i p l e a t t a c k (I.e., connected to a h i g h s e t ) . T h i s i s e q u i v a l e n t t o the s c a l e 1 and 2 i n S.R. S c a l e 2 (Fair) The served b a l l was passed near the t a r g e t area and c l o s e to the s e t t e r , but not very a c c u r a t e l y ( i . e . , 1 or 2m away form the s e t t e r ) . T h i s i s e q u i v a l e n t to the s c a l e 3 i n S.R. 102 S c a l e 1 (Poor) The served b a l l was a c c u r a t e l y passed t o the t a r g e t area ( i . e . , d i r e c t l y t o the s e t t e r ) . T h i s i s e q u i v a l e n t to the s c a l e 4 i n S.R. S c a l e 0 (Error) Serve e r r o r or any t e c h n i c a l f a u l t . SERVE RECEPTION (SR) AND FIELD RECEIVE (DIG) The main purpose of these s k i l l s i s t o d e l i v e r a b a l l t o the next person, e i t h e r a s e t t e r or a p l a y e r so t h a t he can connect the d e l i v e r e d b a l l to a s p i k e r f o r an a t t a c k . Thus, these s k i l l s are e v a l u a t e d by the degree of t h e i r accuracy to the next person i n order f o r him t o set up an o f f e n s i v e p l a y or a c o u n t e r a t t a c k . T h i s can occur from a spike or from a serve or from a b l o c k . Although here the performance of the serve r e c e p t i o n and d i g are e v a l u a t e d based on the same c r i t e r i a , they are s e p a r a t e l y recorded, analyzed and i n t e r p r e t e d a c c o r d i n g l y . S c a l e 4 ( E x c e l l e n t ) The b a l l was passed or dug up very a c c u r a t e l y i n the t a r g e t area ( s e t t e r ' s p o s i t i o n ) , c l o s e t o the net, w i t h a s u i t a b l e h e i g h t , speed, and p a r a b o l i c t r a j e c t o r y . The s e t t e r c o u l d have f u l l o p t i o n s on the d i r e c t i o n and type of set t h a t c o u l d be made as a r e s u l t of t h i s q u a l i t y of pass. * By the s e t t e r ' s p o s i t i o n , i t i n d i c a t e s the area t h a t i s about 3m from the r i g h t s i d e l i n e on the c o u r t and about one f o o t away f o r the net. S c a l e 3 (Good) The b a l l was passed or dug up e i t h e r away (about lm behind the s e t t e r or 2m i n f r o n t of the s e t t e r ) from the t a r g e t area or t r a v e l l e d a h i g h e r (>10ft), or a lower ( s e t t e r ' s shoulder l e v e l ) t o the t a r g e t area than i t s h o u l d be. - The s e t t e r might have l i m i t e d o p t i o n s t o set up a m u l t i p l e a t t a c k i n terms of d i r e c t i o n and type of s e t . 103 - A good s e t t e r c o u l d d e a l w i t h t h i s pass as much as he c o u l d with the s c a l e 4 pass with h i s a g i l i t y and a sense t o p r e d i c t the d i r e c t i o n and path of the b a l l . S c a l e 2 (Fair) The b a l l was passed or dug up e i t h e r behind 10 f t l i n e or extreme s i d e o f the net ( i . e . , the b a l l near the s i d e l i n e s a l ong the n e t ) . - The b a l l was high enough but was hard f o r the s e t t e r t o connect to a m u l t i p l e a t t a c k . - The b a l l was passed t i g h t l y t o the top of the net ( i . e . , the s e t t e r i s f o r c e d to do a s i n g l e - h a n d s e t ) . S c a l e 1 (Poor) The b a l l was passed or dug up very unexpectedly with very poor accuracy. - The b a l l near the s i d e l i n e s or e n d l i n e , or the o u t s i d e o f the c o u r t . - The b a l l passed with very low t r a j e c t o r y and with unexpected d i r e c t i o n which f o r c e d the s e t t e r t o contact the b a l l w i t h underhand ( i . e . , the s e t t e r i s i n a hurry to get under the b a l l ) . * The pass d i r e c t l y over the net i s recorded as "Over" under the s c a l e 1 which means t h a t the b a l l went d i r e c t l y over the net as an easy (free) b a l l f o r the opponent. Sc a l e 0 (Error) The b a l l h i t the f l o o r d i r e c t l y or i n d i r e c t l y (touched by a r e c e i v e r ) . - R a l l y was ended r i g h t a f t e r f i r s t or second c o n t a c t . - Any t e c h n i c a l f a u l t r e s u l t i n g i n l o s i n g a p o i n t or a s i d e -out . * In the case of a d i g , when the b a l l h i t s the f l o o r d i r e c t l y from a spike or from a b l o c k , i t i s not recorded on the s c a l e 0 as a mistake i n the d i g s e c t i o n . But i t i s re c o r d e d as an e r r o r i n the case o f serve r e c e p t i o n . 104 SET The main purpose of t h i s s k i l l i s t o connect a passed b a l l t o the s p i k e r a c c u r a t e l y . However, i n modern v o l l e y b a l l , the s e t t e r who i s a s p e c i a l i s t i n s e t t i n g i s r e q u i r e d t o possess f a r more a b i l i t i e s than j u s t accuracy of the s e t . For example, the s e t t e r has to be a b l e to s e l e c t the s p i k e r best a b l e t o take advantage of any weakness i n the opponent's b l o c k . In a d d i t i o n , he must a l s o work on d i s g u i s i n g h i s set so t h a t the opponent's b l o c k e r ( s ) cannot read the d i r e c t i o n of the intended s e t . These a b i l i t i e s can be the f a c t o r s t h a t d i s c r i m i n a t e between the good s e t t e r and the o u t s t a n d i n g s e t t e r . However, s i n c e these a b i l i t i e s , d i s t r i b u t i o n a l s t r a t e g y and d i s g u i s i n g technique, are not p o s s i b l y measured d i r e c t l y from the s e t t e r ' s performance, the number of b l o c k e r s a g a i n s t the s p i k e r who i s g i v e n a set by the s e t t e r i s used to e v a l u a t e those a b i l i t i e s . T h e r e f o r e , a type of set g i v e n t o a s p k i e r i s e v a l u a t e d by i t s accuracy i n r e l a t i o n to the s p i k e r ( i . e . , p o s i t i o n , t r a j e c t o r y , d i s t a n c e from the net, and the timing) , and the c o n d i t i o n of the opponent's b l o c k a g a i n s t t h a t s p i k e r ( i . e . , the number of b l o c k e r s : 1 or l e s s , incomplete 2 b l o c k e r s , and 2 or 3 b l o c k e r s ) . T h i s i s summarized i n the f o l l o w i n g t a b l e . Accuracy # of b l o c k e r Scale ; of Set 3: very accurate 3: one or l e s s 2: moderate accu. 2: incomplete 2-1: poor accu. l:two or more -man Scale 4= Scale 3= Scale 2= Scale 1= Scale 0= 33. 32,23,22. 31,21. 11,12,13 e r r o r * F i r s t p r i o r i t y i s g i v e n t o the accuracy of the s e t . * I t i s assumed t h a t the serve cannot be s e t . Scale 4 ( E x c e l l e n t ) A c c u r a t e set and one or l e s s opponent's b l o c k e r . - The set was a c c u r a t e as t o the h e i g h t above the net, d i s t a n c e from the net, t r a j e c t o r y of the b a l l and c o o r d i n a t i o n w i t h the s p i k e r and p r o v i d e d a one-man or l e s s b l o c k to the s p i k e r . - Because of the d e c e p t i v e motion or good choice of the s e t t e r , the opponent's b l o c k e r ( s ) c o u l d not f o l l o w or jump p r o p e r l y to the s p i k e r which allows the s p i k e r t o h i t the b a l l w i t h l e s s d i f f i c u l t y . 105 S c a l e 3 (Good) Accurate set and incomplete two-man b l o c k . Or moderate set and one-man or incomplete two-man b l o c k . - Although the set was accurate as i n the s c a l e 4, i t was more p r e d i c t a b l e than i t was i n the s c a l e 4 so t h a t the opponent's b l o c k e r s c o u l d f o l l o w the set and set up t h e i r incomplete two-man b l o c k . - Set was s l i g h t l y lower, or s l i g h t l y h igher, or s l i g h t l y longer or s l i g h t l y o f f the net than i t should be so t h a t the s p i k e r had l i m i t e d o p t i o n s on h i s s p i k i n g d i r e c t i o n and t e c h n i c a l s p i k i n g . However, because of the s e t t e r ' s a b i l i t i e s ( d i s t r i b u t i o n s t r a t e g y or d e c e p t i v e motion), the opponent's b l o c k e r ( s ) were faked so t h a t they c o u l d not set up a s o l i d two-man bl o c k a g a i n s t the s p i k e r . * By incomplete b l o c k , one of the b l o c k e r s jumped i n the wrong spot to block or was l a t e t o set up a s o l i d two-man b l o c k a g a i n s t the s p i k e r . * By moderate set, i t means t h a t : - h i g h s e t ; a b a l l was up near the 10ft l i n e ( i n s i d e ) or p l a c e d s l i g h t l y o u t s i d e o f the s i d e mark along the net, - medium or quick s e t ; a b a l l was s l i g h t l y o f f from where i t should be i n r e l a t i o n t o the s p i k e r i n terms of the h e i g h t , t r a j e c t o r y , p l a c e along the net, and d i s t a n c e from the net. S c a l e 2 (Fair) Set allowed the opponent's b l o c k e r s to set up a s o l i d b l o c k a g a i n s t the s p i k e r who was g i v e n t h a t s e t . - Set was d e l i v e r e d good enough f o r the s p i k e r t o h i t , but t h e r e was a s o l i d two-man or three-man block a g a i n s t the s p i k e r which means t h a t the intended set by the s e t t e r or another p l a y e r was very p r e d i c t a b l e . * High, slow sets f a l l mostly i n t h i s s c a l e . * The success of the s p i k e w i t h t h i s set i s l a r g e l y dependent upon the s p i k e r ' s t e c h n i q u e s t o handle i n a c c u r a t e s e t s and t o d e a l with the opponent's block, r a t h e r than t h a t o f the s e t t e r . 106 S c a l e 1 (Poor) Set t h a t f o r c e d the s p i k e r t o g i v e an easy or down b a l l , or a f r e e b a l l t o the o p p o s i t i o n r e g a r d l e s s o f the c o n d i t i o n s o f the opponent b l o c k i n g . - Medium s e t was d e l i v e r e d so i n a c c u r a t e l y and unexpectedly t h a t the s p i k e r was not able t o h i t the b a l l p r o p e r l y or was f o r c e d t o g i v e an easy or f r e e b a l l t o the o p p o s i t i o n due to i t s poor accuracy. - High set was up f a r away from the a t t a c k zone ( i . e . , on the middle of cou r t or f a r o u t s i d e of the s i d e marks). Or set i s given t o a s p i k e r who i s i n an i n a p p r o p r i a t e s p i k i n g p o s i t i o n . * Set d i r e c t l y c r o s s i n g over the net i s reco r d e d as "over" under the s c a l e 1. * Miscommunication between the s e t t e r and a s p i k e r r e s u l t i n g i n g i v i n g a f r e e or easy b a l l t o the opponent i s c o n s i d e r e d as a s e t t e r ' s f a u l t and giv e n a s c a l e 1. That i s , any time an s p i k e r does not a t t a c k the b a l l , the s e t t e r gets the s c a l e 1. * Save: E i t h e r the s e t t e r or another p l a y e r c o u l d o n l y t r y to save the b a l l up, wit h overhand s e t or underhand s e t , i n the a i r r a t h e r than t r y i n g t o set i t t o a c e r t a i n area or p o s i t i o n (no types o f set i s r e c o r d e d ) . S c a l e 0 (Error) A d i r e c t s e t t i n g e r r o r or a set which f o r c e s the s p i k e r t o make a d i r e c t mistake. The s p i k e r i s not charged with an e r r o r i n the case. - Any t e c h n i c a l f a u l t . In t h i s case the type o f set i s not recorded. - Set under the top of the net or m i s s i n g the s p i k e r . - A mistake i n team-play i n which a b a l l drops d i r e c t l y on the f l o o r a f t e r the s e t . 107 SPIKE (ATTACK) The spike i s p u t t i n g the b a l l over the net i n t o the opponent's c o u r t , u s i n g f o r c e and/or techniques from above the top of the net i n order t o score a p o i n t or r e g a i n the serve. T h e r e f o r e , the spike i s e v a l u a t e d by the degree of i t s e f f e c t i v e n e s s . * When a b a l l i s a t t a c k e d i n t o the net, and subsequently p l a y e d over the net by a teammate, the a t t a c k w i l l be recorded as a s c a l e 1. * I t i s assumed t h a t the serve w i l l not be a t t a c k e d . * There are as many types o f sp i k e s as there are s e t s . S c a l e 4 ( K i l l ) The s p i k e r gets a p o i n t or achieves a s i d e - o u t . - The b a l l h i t s the opponent's d i r e c t l y or i n d i r e c t l y ( i . e . , a f t e r contact w i t h a d i g g e r ( s ) . In t h i s case, the opponent's b l o c k w i l l a u t o m a t i c a l l y be given a s c a l e 1 ( i . e . , opponent's b l o c k e r ( s ) c o u l d not touch the b a l l ) . - The b a l l was out of p l a y a f t e r c o n t a c t with a b l o c k e r ( s ) on the opponent's team ( i . e . , wiped). - A f t e r the spi k e , the b l o c k e r committed a t e c h n i c a l f a u l t . S c a le 3 (Good) The s p i k e r a t t a c k e d i n such a way t h a t h i s team c o u l d repeat the a t t a c k . - The spike was e a s i l y r e j e c t e d by the block, which d e f l e c t e d the b a l l upward ( i . e . , easy r e j e c t i o n ) . - The b a l l r e t u r n e d t o the s p i k i n g team immediately from a digger on the opponent's team (over bump from the opponent's digger) or the opponent's c o u l d not set up a c o u n t e r a t t a c k and send the b a l l back t o the s p i k i n g team as a f r e e b a l l . S c a l e 2 (Fair) The s p i k e r attempted t o k i l l , but the s p i k e was dug up by the opponent's d i g g e r r e g a r d l e s s o f the q u a l i t y o f t h a t d i g ( i . e . , 2 or 3 or 4) . - The s p i k e r d i d not p r o v i d e any b e t t e r s i t u a t i o n f o r h i s team with h i s s p i k e r . 108 S c a l e 1 ( P o o r ) Down b a l l o r e a s y b a l l o r f r e e b a l l . - The s p i k e r j u s t t r i e d t o s e n d t h e b a l l o v e r t h e n e t t o t h e o p p o n e n t ' s t e a m due t o e i t h e r a p o o r s e t o r a l a c k o f c o n f i d e n c e t o h i t o r b e i n g i n an i n a p p r o p r i a t e s p i k i n g p o s i t i o n . - The s p i k e d b a l l d i r e c t l y r e t u r n e d t o t h e o p p o n e n t ' s c o u r t f r o m t h e a t t a c k c o v e r a g e a f t e r b e i n g b a d l y r e j e c t e d downward b y t h e o p p o n e n t ' s b l o c k . * The b a l l s e n t o v e r t h e n e t w i t h o u t a n a t t a c k ( i . e . , u n d e r h a n d o r o v e r h a n d c o n t a c t o r down b a l l ) . I n t h i s c a s e , n o t h i n g i s r e c o r d e d f o r o p p o n e n t ' s b l o c k (on a t t e m p t t o b l o c k ) . S c a l e 0 ( E r r o r ) The s p i k e r made a m i s t a k e r e s u l t i n g i n l o s i n g a p o i n t o r a s i d e - o u t . - The s p i k e was s t u f f b l o c k e d . - S p i k i n g e r r o r ( i . e . , h i t o u t , h i t i n t o t h e n e t ) , o r any t e c h n i c a l f a u l t ( i . e . , n e t v i o l a t i o n , f o o t f a u l t e t c . , ) . I n t h i s c a s e , n o t h i n g w i l l be r e c o r d e d on t h e o p p o n e n t ' s b l o c k . B L O C K The b l o c k i s t h e f i r s t d e f e n s i v e s k i l l a g a i n s t t h e o p p o n e n t ' s s p i k e . The m a i n o b j e c t s o f t h i s s k i l l a r e : (1) t o a t t e m p t t o s t u f f t h e o p p o n e n t ' s s p i k e f o r m a b o v e t h e n e t , (2) t o a t t e m p t t o r e d u c e t h e f o r c e o r s p e e d o f t h e s p i k e f o r t h e r e c e i v e r s by d o i n g s o f t b l o c k a g a i n s t t h e s p i k e a n d (3) t o a t t e m p t t o c o v e r a c e r t a i n a r e a a b o v e t h e n e t s o t h a t t h e d i g g e r s c a n s e t up a d e f e n s i v e f o r m a t i o n more e f f e c t i v e l y . T h e r e f o r e , t h e b l o c k i s e v a l u a t e d b y t h e d e g r e e o f i t s e f f e c t i v e n e s s t o d e a l w i t h t h e o p p o n e n t ' s s p i k e . S c a l e 4 ( S t u f f ) B l o c k e r ( s ) s c o r e d a p o i n t o r g a i n e d a s i d e - o u t . - R a l l y was e n d e d r i g h t a f t e r t h e b l o c k , e i t h e r r e s u l t i n g f r o m an a t t a c k - c o v e r a g e e r r o r b y t h e s p i k i n g team, o r b y t h e b a l l d i r e c t l y h i t t i n g t h e f l o o r . 109 * In t h i s case, the s c a l e 0 w i l l a u t o m a t i c a l l y be g i v e n to the opponent's s p i k e . S c a l e 3 (Good) Block performed i n such a way t h a t the b l o c k i n g team c o u l d set up a c o u n t e r a t t a c k . - The speed and power of the s p i k e was slowed down due t o the b l o c k and thus the b a l l came t o the b l o c k i n g team ( i . e . , s o f t block). In t h i s case, a s c a l e 2 i s given a u t o m a t i c a l l y t o the opponent's s p i k e ( i . e . , s p i k i n g attempt). - The opponent's s p i k e was b a d l y r e j e c t e d downward by the b l o c k ( i . e . , bad r e j e c t i o n ) . In t h i s case, a s c a l e 1 i s given a u t o m a t i c a l l y t o the opponent's s p i k e . S c a l e 2 (Fair) The spiked b a l l came back t o the s p i k i n g team a f t e r the b l o c k so t h a t another a t t a c k c o u l d set up f o r the s p i k i n g team. - The spike was r e j e c t e d upward by the b l o c k ( i . e . , easy re j e c t i o n ) . In t h i s case, the s c a l e 3 i s g i v e n a u t o m a t i c a l l y to the opponent's s p i k e . S c a l e 1 (Missing) The attacked b a l l came d i r e c t l y over the net e i t h e r between or around the block without a p p r e c i a b l e c o n t a c t w i t h the b l o c k . - The b l o c k e r ( s ) was faked by the opponent's s e t t e r so t h a t he c o u l d not f o l l o w p r o p e r l y or jumped at the wrong p l a c e or missed the b l o c k . - The b l o c k e r ( s ) c o u l d not p r e d i c t the intended set o f the s e t t e r so t h a t he was l a t e or missed the b l o c k . - The e f f e c t of the b l o c k c o u l d not make any d i f f e r e n c e i n r e d u c i n g the speed and power o f the s p i k e though the s p i k e was touched the b l o c k . * When a s p i k e d b a l l d i r e c t l y h i t the f l o o r , although the b l o c k e r ( s ) attempted t o b l o c k , the s c a l e 1 w i l l be a u t o m a t i c a l l y g i v e n t o the b l o c k . * In the case t h a t the b l o c k e r ( s ) d i d not attempt t o jump on purpose because of an easy or f r e e b a l l coming over, n o t h i n g w i l l be recorded i n b l o c k s e c t i o n . * To d i g t h i s b a l l , which d i r e c t l y comes over the net without 110 c o n t a c t with the b l o c k , i s l a r g e l y dependent upon the d i g g i n g a b i l i t y o f an i n d i v i d u a l p l a y e r on the team. S c a l e 0 (Error) The b a l l went out of p l a y a f t e r the b l o c k d e f l e c t e d the s p i k e d b a l l r e s u l t i n g i n l o s i n g a p o i n t or a s i d e - o u t . - R a l l y ended r i g h t a f t e r the b l o c k ( i . e . , wiped o f f ) . In t h i s case, the s c a l e 4 w i l l be a u t o m a t i c a l l y g i v e n t o the opponent's s p i k e . - Any t e c h n i c a l b l o c k i n g f a u l t ( i . e . , S h i f t key & Wiped key). In t h i s case, the opponent's s p i k e w i l l a u t o m a t i c a l l y be g i v e n a s c a l e 4 except t h a t i t happened be f o r e the opponent's sp i k e b e i n g taken p l a c e . I l l Appendix C Letter to the Coaches Dear . . . I have e n c l o s e d a b r i e f d e s c r i p t i o n o f the 5-point s c a l e f o r each of s i x s k i l l s and a r e c o r d i n g sheet as w e l l as an e d i t e d v i d e o tape which I would l i k e you t o watch i n order t o q u a n t i f y the s k i l l performance based on 5-point s c a l e . I do have a more complete d e s c i p t i o n of each s k i l l performance, but I am not supposed t o present them t o you because the main purpose of g e t t i n g feedback i s t o see whether an expert i n the v o l l e y b a l l f i e l d ( y o u r s e l f ) has commonly agreeable o p i n i o n s when e v a l u a t i n g the performance of these s k i l l s based on 5-p o i n t s c a l e . I t w i l l take you about 30 minutes t o f i l l the r e c o r d i n g sheet out while watching the videotape. When you d i s p l a y the tape, i n s t r u c t i o n s w i l l appear on the screen, please f o l l o w the i n s t r u c t i o n s . The e d i t e d tape i s Canada v s. Korea from the 3rd F.I.V.B. Korean cup, h e l d Seoul Korea l a s t November. Here are steps t o f o l l o w : 1. Read over the c r i t e r i a of o b s e r v a t i o n s f o r each s k i l l 2. Watch vi d e o i n s t r u c t i o n s e c t i o n 1 and s k i l l a c t i o n s f o r secton 1. 3. Record the s c a l e f o r the s k i l l s on the r e c o r d i n g sheet. - you may want t o re - l o o k at those s k i l l s and probably r e f e r t o the d e s c r i p t i o n f o r each s k i l l . 4. P l e a s e c o n t i n u e the same process t o s e c t i o n 19. 6. When completed, p l e a s e note any suggestions or comments on the s c a l e s or p o s s i b l e r e - s c a l e f o r each s k i l l . 7. P l e a s e m a i l the r e c o r d i n g sheet and your comments or suggestions t o my address. yours t r u l y Han Joo Eom cont'd 112 A B r i e f Descriptions for Each S k i l l Serve: Since the s c a l e of the serve r e c e p t i o n was d e f i n e d by how w e l l the serve was passed, a s c a l e o f serve i s g i v e n a u t o m a t i c a l l y through the computer program i n the f o l l o w i n g manner. 4: when the s c a l e of serve r e c e p t i o n i s 0. 3: when the s c a l e of serve r e c e p t i o n i s 1 or 2. 2: when the s c a l e of serve r e c e p t i o n i s 3. 1: when the s c a l e of serve r e c e p t i o n i s 4 0: serve e r r o r Serve Reception and Dig: The same c r i t e r i a i s used t o e v a l u a t e these two s k i l l s because the main purpose o f these s k i l l s to d e l i v e r a b a l l t o the next person, e i t h e r a s e t t e r or a p l a y e r , so t h a t he can connect the d e l i v e r e d b a l l t o a s p i k e r f o r an a t t a c k . 4: ac c u r a t e pass t o the t a r g e t area ( s e t t e r ' s p o s i t i o n ) . 3: 1 or 2m away form the s e t t e r 2: b a l l was up near the 10ft l i n e or extreme s i d e or middle of the c o u r t . 1: b a l l was up out s i d e o f the court or near the e n d l i n e o f the c o u r t . 0: pass e r r o r . In the case of Dig, no e r r o r i s re c o r d e d u n l e s s a f r e e b a l l from the opponent, or easy b a l l from a s o f t block i s given t o a d i g g e r . Set: The q u a l i t y o f set i s determined by both i t s accuracy i n r e l a t i o n t o the s p i k e r and the c o n d i t i o n of the opponent's b l o c k a g a i n s t t h a t s p i k e r ( f i r s t p r i o r i t y i s a c c u r a c y ) . 4: ac c u r a t e and none or one b l o c k e r . 3: moderate accuracy and one or incomplete two-man b l o c k . 2: a c c u r a t e and s o l i d tow-man b l o c k . 1: poor accruacy r e g a r d l e s s o f the number o f b l o c k e r s . 0: s e t t i n g e r r o r . cont'd 113 Spike: The spike i s evaluated by the degree of i t s e f fec t iveness . 4: k i l l 3: easy r e j e c t i o n by block or b a l l came back as a free b a l l 2: spike was dug up or softblocked. 1: easy, free, downball, or spike i s badly re jec ted by the b lock . 0: spike error Block: The f i r s t p r i o r i t y i n block i s s tu f f block, then soft block, and t h i r d l y , covering a cer ta in area above the net. 4: s t u f f b lock. 3: soft block, or bad r e j e c t i o n of opponent's sp ike . 2: easy r e j e c t i o n of opponent's spike. 1: missed to block the spike or the spiked b a l l came through the block (between or around) without appreciable contact with the block. 0: wiped out or block e r r o r . 114 Appendix D Keyboard Layout THE KEYBOARD Serve & # of B l o c k e r E r r o r High Sets Q W E R T Y U I O P one incom.2 two L.B L.F M R.F R.B Scal e s Medium Sets A S D F 6 H J K L : 4 3 2 1 0 L.S 33 X.F X.B R.S Block Types Save Quick Sets T.F Z:4 X:3 C:3 V:2 B:0 N M , / S t u f f Bad.R Sof t Easy.R Wiped 31 51 61 j j — I S h i f t | Space Bar: CANCEL I I I I NOTES: S h i f t key w i t h : Serve ; Spin serve Scale 1; Free b a l l (over-bump or over-set) Wiped ; B l o c k i n g T a c h n i c a l F a u l t Other keys: Space bar; Cancels the p r e v i o u s l y p r e s s e d key. Minus s i g n ( - ) ; Side-out P l u s s i g n ( + ) ; P o i n t E r r o r ; Serve e r r o r T.F; T e c h n i c a l F a u l t Escape key; Q u i t See Appendix A f o r a b b r e v i a t i o n s of the types o f s e t 115 Appendix E An Example of the Computer Screen Display and Data f i l e Screen Display Game #1 Canada 1 : Korea 0 Canada i s s e r v i n g CAN: f l o a t serve KOR: S.R s c a l e 3 KOR; l e f t h i g h s e t s c a l e 2 KOR: spi k e with 2 b i o . CAN: wiped s c a l e 0 (types o f serve?) (S.R q u a l i t y ? ) (type o f s e t / # of bl o c k e r s ? ) (set q u a l i t y ? ) (# o f blocker?) (spike q u a l i t y / b l o c k type?) Game #1 Canada 1 : Korea 0 Korea i s s e r v i n g KOR: s p i n serve CAN: S.R s c a l e 3 CAN: r i g h t backrow set s c a l e 3 CAN: spike w i t h incom. 2 bio. KOR: s o f t b l o c k s c a l e 3 KOR: d i g s c a l e 4 KOR: 51 set s c a l e 3 KOR: spi k e w i t h 1 or 0 b i o . KOR: k i l l s c a l e 4 (types of serve?) (S.R q u a l i t y ? ) (types o f s e t / # of blocker?) (set q u a l i t y ? ) (# o f blocker?) (spike q u a l i t y / b l o c k type?) (dig q u a l i t y / s e t / s p i k e ? ) (type o f set/# o f blocker?) (set q u a l i t y ? ) (# o f blocker?) (spike q u a l i t y / b l o c k type?) Game #1 Canada 1 : Korea 1 Korea i s s e r v i n g (type o f serve?) Quit input cont'd 116 Data F i l e ^ 0. CAN: serve f l o a t 2 1. KOR: r e c e i v e 3 2. KOR: se t h i g h l e f t 2 3. KOR: spi k e #blo>=2 4 4. CAN: bl o c k 0 5. KOR: serve s p i n 2 6. CAN: r e c e i v e 3 7. CAN: set B.R. r i g h t 3 8. CAN: spike # blo=1.5 2 9. KOR: bl o c k 3 10. KOR: d i g 4 11. KOR: set 51 3 12. KOR: spike # blc<=l 4 13. CAN: b l o c k 1 14. KOR: no input a: T h i s data f i l e i s co r r e s p o n d i n g t o the example of the screen d i s p l a y . 117 Appendix F P l a y i n g P a t t e r n s o f I n d i v i d u a l S k i l l Based on the r e s u l t s found i n the i n d i v i d u a l s k i l l a n alyses, the performance of each of the e i g h t s k i l l s were f u r t h e r examined with the a i d o f a d d i t i o n a l d e s c r i p t i v e i n f o r m a t i o n ( i . e . , p r o p o r t i o n o f each s c a l e ) i n terms of the p l a y i n g c h a r a c t e r i s t i c s of the s k i l l s . Since no s i g n i f i c a n t u n i v a r i a t e ANOVAs were found f o r the fou r v a r i a b l e s ; serve (SE), serve r e c e p t i o n (SR), s e t (SAP) and spi k e (SKAP), i n both the Team and Game Status, i n a d d i t i o n t o no n o t i c e a b l e d i f f e r e n c e i n the p a t t e r n o f the p r o p o r t i o n i n each s c a l e , the o v e r a l l observed frequency and p r o p o r t i o n of each s c a l e ( c o l l a p s e d over the Team and Game Status) f o r the fou r s k i l l s are p resented i n Table F - l . Serve (SE). The mean performance (1.76) of the serve (SE) suggested t h a t i t d i d not pr o v i d e d i r e c t advantage f o r the s e r v i n g team over the o p p o s i t i o n . T h i s low mean value suggested t h a t the main r o l e o f the serve s t i l l seems t o be to i n i t i a t e a p l a y , even though at hig h l e v e l s of c o m p e t i t i o n teams o f t e n t r y to use the serve as a f i r s t o f f e n s i v e weapon. Of the t o t a l SEs, about 30% ( s c a l e 3 and 4) were performed i n such a way t h a t i t f o r c e d the o p p o s i t i o n t o have d i f f i c u l t y i n p a s s i n g the b a l l a c c u r a t e l y t o the s e t t e r , thus r e d u c i n g the number of o p p o r t u n i t i e s f o r the o p p o s i t i o n t o set up a m u l t i p l e o f f e n s i v e p l a y . However, t h i s seemed t o occur with a c o n s i d e r a b l e e r r o r r a t e (7.8%), about 3 e r r o r s per game, as opposed t o the low success r a t e (2.4%) which was l e s s than one ace per game. Serve r e c e p t i o n (SR). The mean performance (2.94) i n the serve r e c e p t i o n (SR) i n d i c a t e s t h a t the serve from the o p p o s i t i o n was g e n e r a l l y w e l l r e c e i v e d and passed t o the s e t t e r . As can be seen i n the p r o p o r t i o n o f Sc a l e 3 and 4, 67.7% o f the t o t a l SRs were passed a c c u r a t e l y or at l e a s t near the t a r g e t area which allows a s e t t e r t o be abl e t o set up any type o f set i n any d i r e c t i o n . In a d d i t i o n , the low p r o p o r t i o n o f e r r o r r a t e (2.6%) i n S c a l e 0 suggests very few u n f o r c e d a b s o l u t e e r r o r s being made at the i n t e r n a t i o n a l l e v e l of men's co m p e t i t i o n . 118 Table F - l Observed Frequency and P r o p o r t i o n f o r SE, SR, SAP and SKAP S k i l l S c a le Grand Mean s4 s3 s2 S i sO T o t a l SE 1.77 64 735 587 1085 209 2690 P 2.4 27.4 21.9 40.5 7.8 100.0 SR 2.94 1085 587 475 260 64 2471 P 43.9 23.8 19.2 10.5 2.6 100.0 SAP 2.76 675 603 809 152 24 2263 P 29.8 26.6 35.7 6.7 1.1 100.0 SKAP 2.77 1180 217 359 160 315 2231 P 52.9 9.7 16.1 7.2 14 .1 100.0 P r o p o r t i o n of each s c a l e (%) • Set (SAP) . 56.4% of the SAPs (Scale 3 and 4) were ; not only a c c u r a t e l y d e l i v e r e d t o the s p i k e r , but a l s o gave u n c e r t a i n t y t o the opponent's b l o c k e r ( s ) as to the i n t e n d e d d i r e c t i o n and p l a c e o f the s e t . T h i s would p r o v i d e the s p i k e r w i t h a s i t u a t i o n i n which he c o u l d have l e s s d i f f i c u l t y i n h i s spi k e , assuming t h a t every p l a y e r at the i n t e r n a t i o n a l l e v e l has the a b i l i t y t o s p i k e w e l l when fa c e d w i t h an incomplete b l o c k . However, 42.4% of the SAPs (Scale 1 and 2) was e i t h e r i n a c c u r a t e or p r e d i c t a b l e f o r the opponent's b l o c k e r s t o f o l l o w and form a s o l i d b l o c k a g a i n s t the s p i k e r . The e r r o r r a t e (1.1%) again i n d i c a t e d very few a b s o l u t e s e t t i n g e r r o r at t h i s l e v e l o f c o m p e t i t i o n . Spike (SKAP). T h i s i s the s k i l l which ends an i n i t i a l o f f e n s i v e p l a y f o r a team. Of the t o t a l SKAPs, 52.9% r e s u l t e d i n winning a r a l l y , but 14.1% of the SKAPs were e i t h e r s t u f f b l o c k e d by the opponent's block, or a s p i k i n g e r r o r , thus l o s i n g a p o i n t . Together, 67% o f the SKAPs te r m i n a t e d a r a l l y i n e i t h e r a success or a f a i l u r e , w h i le 33% of them c o n t i n u e d a r a l l y t o a c o u n t e r a t t a c k p r o c e s s . Of the t o t a l , 7.2% (Scale 1) o f the SKAPs was t u r n e d t o be a f r e e b a l l f o r the o p p o s i t i o n due t o e i t h e r the s p i k e r b e i n g g i v e n an i n a c c u r a t e set or h i s l a c k of c o n f i d e n c e i n the s p i k i n g . O v e r a l l , the magnitude o f the mean v a l u e (2.77) i n d i c a t e s the advantage of the s p i k i n g team over the o p p o s i t i o n i n t h i s s k i l l . 119 The frequency and p r o p o r t i o n o f the f o l l o w i n g f o u r s k i l l s were examined s e p a r a t e l y under Win-Lose and Top-Bottom c a t e g o r i e s . Block (BLO). C o n s i d e r i n g t h a t the b l o c k i s the f i r s t d e f e n s i v e s k i l l which attempts to stop the opponent's sp i k e at the net, the b e t t e r performance i n the b l o c k i n d i c a t e s the l e s s e f f e c t i v e n e s s i n the opponent's s p i k e . However, as shown i n the p r o p o r t i o n of Scale 1 and 0, o v e r a l l 72% of the t o t a l b l o c k s were performed i n such a way t h a t i t e i t h e r d i d not c o n t a c t w i t h the s p i k e d b a l l at the net or was wiped out by the s p i k e r . In a d d i t i o n t o t h i s , the low mean va l u e s suggest a predominant c h a r a c t e r i s t i c of the s k i l l o f the s p i k e i n the i n t e r a c t i o n with the b l o c k at the net (see Table F-2). The d i f f e r e n c e i n the performance of the b l o c k between the winning and l o s i n g games across the p r o p o r t i o n of each s c a l e showed an almost i d e n t i c a l p a t t e r n w i t h t h a t between the top 4 and bottom 4 teams. That i s , the performance of the top 4 teams and winning games on the b l o c k was s u p e r i o r t o t h a t of the bottom 4 teams and l o s i n g games i n a l l s u b c a t e g o r i e s of the b l o c k , thus r e s u l t i n g i n a s i g n i f i c a n t d i f f e r e n c e i n the marginal means. A g r e a t e r p r o p o r t i o n of S c a l e 3 and 4 f o r the top 4 teams and winning games, f o r example, i n d i c a t e d t h a t the block more f r e q u e n t l y stopped the opponent's spike at the net or r e f l e c t e d i t i n t o the b l o c k e r ' s c o u r t . Table F-2 Observed Frequency and P r o p o r t i o n f o r B l o c k Group S c a l e Marginal Mean s4 S3 s2 s i sO T o t a l Win 1.53 175 265 100 814 298 1652 P 10.6 16.0 6.1 49.3 18.0 100.0 Lose 1.34 129 180 53 939 269 1570 P 8.2 11.5 3.4 59.8 17.1 100.0 Top 1.50 172 256 105 774 313 1620 P 10.6 15.8 6.5 47.8 19.3 100.0 Bottom 1.37 132 189 48 979 254 1602 P 8.2 11.8 3.0 61.1 15.9 100.0 Dig. The marginal means as w e l l as the p r o p o r t i o n of each s c a l e between the winning and l o s i n g games showed no n o t i c e a b l e d i f f e r e n c e (see Table F - 3 ) . However, the d i f f e r e n c e between the top 4 and bottom 4 teams looked to be 120 apparent. The top 4 teams outperformed the bottom 4 teams i n r e c e i v i n g spiked b a l l s by the opponent's s p i k e r and p a s s i n g them more a c c u r a t e l y t o the s e t t e r . However, the p r o p o r t i o n of Scale 3 and 4, i n average, was only about 12.5% and 11.5%, r e s p e c t i v e l y . O v e r a l l , about 75% of the t o t a l DIGs were performed i n such a way t h a t the b a l l was dug up i n the middle of the court, r a t h e r than d e l i v e r i n g i t d i r e c t l y to the s e t t e r at the net. This c o u l d l i m i t the s e t t e r ' s options i n terms of the type or d i r e c t i o n of the s e t . U n l i k e the performance o f the other s k i l l s , the p l a y i n g c h a r a c t e r i s t i c s of the d i g do not l e a d t o a c l e a r d e s c r i p t i o n of the performance. Given non s i g n i f i c a n t r e s u l t s between the winning and l o s i n g games, the s i g n i f i c a n t d i f f e r e n c e between the top 4 and bottom 4 teams i n the d i g seems t o show an i n c o n s i s t e n t p a t t e r n of the performance. Examination o f the c e l l means f o r the d i g showed t h a t the mean value f o r the top 4 teams i n the winning games was 2.17, as opposed to 2.08 i n the l o s i n g games. However, t h i s p a t t e r n was not t r u e f o r the bottom 4 teams. The mean v a l u e i n the winning games (1.8 9) was s m a l l e r than t h a t i n the l o s i n g games (2.00) f o r the bottom 4 teams. Therefore, averaged over the Game St a t u s , t h i s l e d a g r e a t e r marginal mean f o r the top 4 teams (2.14) than t h a t f o r the bottom 4 teams (1.96), but not f o r the winning (2.07) and l o s i n g (2.03) games when averaged over the Team St a t u s . Table F-3 Observed Frequency and P r o p o r t i o n f o r D i g Group S c a l e Marginal Mean s4 s3 s2 s i sO T o t a l Top 2.14 91 90 292 184 4 661 P 13.8 13.6 44.2 27.8 0.6 100.0 Bottom 1.96 70 87 362 232 7 758 P 9.2 11.5 47.8 30.6 0.9 100.0 Win 2.07 82 96 330 211 3 722 P 11.4 13.3 45.7 29.2 0.4 100.0 Loss 2.03 79 81 324 205 8 697 p 11.3 11.6 46.5 29.4 1.1 100.0 121 Set (SCP). As can be seen i n Table F-4, the main cause o f the s i g n i f i c a n t d i f f e r e n c e i n the SCP between the teams was due t o the g r e a t e r p r o p o r t i o n i n Scale 4 and 3 and the s m a l l e r v a l u e i n Scale 2 shown by the top 4 teams, given approximately same r a t e of i n a c c u r a t e s e t s (Scale 1) and e r r o r r a t e (Scale 0). When c o n s i d e r i n g t h a t the SCP i s supposed t o be f o l l o w e d by the d i g , i t i s u n c l e a r , however, whether t h i s s i g n i f i c a n t d i f f e r e n c e i s due t o the b e t t e r perrormance i n the SCP per se, or due t o the b e t t e r performance i n the d i g s t a r t e d w i t h . On the other hand, g i v e n no s i g n i f i c a n t d i f f e r e n c e i n the d i g between the game Sta t u s , the s i g n i f i c a n t d i f f e r e n c e between the winning and l o s i n g games suggests t h a t the s e t t i n g performance i n the winning games was s u p e r i o r t o t h a t i n the l o s i n g games. O v e r a l l , u n l i k e the SAP, the performance of the SCP d i d not seem t o p r o v i d e the s p i k e r with an optimal s i t u a t i o n i n h i s s p i k i n g . Of the t o t a l SCPs, about 80% were performed i n such a way t h a t i t was e i t h e r p r e d i c t a b l e f o r the opponent's b l o c k or i n a c c u r a t e f o r the s p i k e r . Thus, the success i n the s p i k e w i t h t h i s type o f set i s r a t h e r dependent upon the s p i k e r ' s a b i l i t y t o handle a s o l i d b l o c k and i n a c c u r a t e s e t s . Table F-4 Observed Frequency and P r o p o r t i o n f o r SCP Group S c a l e M a r g i n a l Mean s4 s3 s2 s i sO T o t a l Top 2.11 67 60 303 123 8 561 P 11.9 10.7 54.0 21.9 1.4 100.0 Bottom 1.97 52 49 405 146 9 661 P 7.9 7.4 61.3 22.1 1.4 100.0 Win 2.11 73 55 348 131 5 612 P 11.9 9.0 56.9 21.4 0.8 100.0 Loss 1.97 46 54 360 138 12 610 p 7.5 8.9 59.0 22.6 2.0 100.0 Spike (SKCP). An almost i d e n t i c a l p a t t e r n of d i f f e r e n c e was shown i n the examination o f the p r o p o r t i o n i n each s c a l e f o r both the Team and Game Status (see Table F-5). The d i f f e r e n c e i n the p r o p o r t i o n o f each s c a l e between the Team Status and between the Game Status i s i n favo r o f the top 4 teams and winning games. The success r a t e f o r the t o p 4 teams and winning games (43.1%, 44.8%) was much g r e a t e r than t h a t 122 (36.2, 33.8%) f o r the bottom 4 teams and l o s i n g games. When c o n s i d e r i n g the s k i l l o f SKCP i s aimed at s c o r i n g a p o i n t , the g r e a t e r success r a t e and s m a l l e r e r r o r r a t e shown by the top 4 teams and winning games would s u r e l y make a s i g n i f i c a n t d i f f e r e n c e i n d e t e r m i n i n g team success. Indeed, these were the main sources r e s p o n s i b l e f o r the s i g n i f i c a n t d i f f e r e n c e i n the mean performance f o r the teams and games. Table F-5 Observed Frequency and P r o p o r t i o n f o r SKCP Group Scale M a r g i n a l Mean s4 s3 s2 s i sO T o t a l Top 2.50 P Bottom 2.22 P 236 43.1 235 36.2 46 8.4 53 8.2 95 17.3 124 19.1 88 16.1 118 18.2 83 15.1 120 18.5 548 100.0 650 100.0 Win P 2.53 270 44 .8 201 33.8 49 8.1 50 8.4 110 16.6 119 20.0 99 16.4 107 18.0 85 14.1 118 19.8 603 100.0 595 100.0 Loss P 2.19 123 Appendix 6 Decomposition of L^ - for Transition from Set to Spike P a r t i a l A s s o c i a t i o n Marginal A s s o c i a t i o n ( c o n d i t i o n a l t e s t ) ( u n c o n d i t i o n a l t e s t ) E f f e c t df L2 P L2 P Spike(K) 4 1392.69 <.0001 Set (S) 3 695.31 <.0001 Game(G) 1 8.05 .0045 Team(T) 1 22.47 <.0001 Process (P) 1 328.50 <.0001 KS 12 917.51 <.0001 1028.46 <.0001 KG 4 18. 95 .0008 25.85 <•0001 KT 4 2.23 .6927 1.28 .8643 KP 4 4.29 .3678 105.32 <.0001 SG 3 14.90 .0019 24.70 <.0001 ST 3 2.75 .4316 4.54 .2086 SP 3 390.87 <.0001 489.75 <.0001 GT 1 395.81 <.0001 395.42 <.0001 GP 1 8.23 .0041 2.13 . 1449 TP 1 13.92 .0002 1. 64 .2002 KSG 12 12.90 .3762 18.11 .1124 KST 12 11.86 .4569 17.10 . 1460 KSP 12 20.27 .0622 21.64 .0418 KGT 4 3.63 .4579 4.66 .3236 KGP 4 3.26 .5155 5.05 .2818 KTP 4 .86 . 9301 5.24 .2636 SGT 3 8.11 .0439 9.19 .0269 SGP 3 .35 .9503 1.98 .5764 STP 3 20.65 .0001 24. 62 <.0001 GTP 1 .99 .3194 .31 .5791 KSGT 12 16.22 .1812 13.84 .3112 KSGP 12 13.96 .3035 12.93 .3744 KSTP 12 12.01 .4448 10.92 .5361 KGTP 4 9.00 .0610 4.52 .3408 SGTP 3 3.06 .3826 2.08 .5566 KSGTP 12 16.01 .1908 T o t a l 159 124 Appendix H Decomposition of l£ f o r Transition from Reception to Spike P a r t i a l A s s o c i a t i o n Marginal A s s o c i a t i o n ( c o n d i t i o n a l t e s t ) ( u n c o n d i t i o n a l t e s t ) E f f e c t d f L2 P L2 P Spike(K) 4 1419.10 <.0001 Reception(R) 3 403.80 <.0001 Game(G) 1 5.70 .0170 Team(T) 1 18.64 <.0001 Process (P) 1 312.73 <.0001 KR 12 297.11 <.0001 376.73 <.0001 KG 4 31.53 <.0001 27.08 <.0001 KT 4 2.44 .6557 .83 .9344 KP 4 24.39 .0001 103.17 <. 0001 RG 3 4.96 .1747 3.88 .2743 RT 3 4.91 .1785 3.32 .3454 RP 3 591.60 <.0001 673.71 <.0001 GT 1 415.27 <.0001 411.24 <.0001 GP 1 6.81 .0090 5.57 . 0183 TP 1 1.32 .2498 -.03 1.0000 KRG 12 7.55 .8194 6.84 .8679 KRT 12 18.31 .1067 18.83 .0927 KRP 12 15.22 .2296 15.87 .1973 KGT 4 5.89 .2076 7.74 .1016 KGP 4 3.18 .5274 2.57 .6320 KTP 4 2.63 . 6211 6.29 . 1786 RGT 3 1.93 .5869 1.92 .5901 RGP 3 2.20 .5313 1.43 . 6984 RTP 3 14.36 .0025 15.22 .0017 GTP 1 1.33 .2482 .57 .4488 KRGT 12 14.48 .2710 12.91 .3754 KRGP 12 8.90 .7117 12.66 .3944 KRTP 12 6.70 .8768 8.58 .7383 KGTP 4 7.17 .1270 4.71 .3186 RGTP 3 6.36 .0952 4.87 .1816 KRGTP 12 11.55 .4826 T o t a l 159 Note: Reception r e f e r s t o both serve r e c e p t i o n and d i g , but they are d i s t i n g u i s h e d by the Process f a c t o r 

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