vballOlympicPredictionLondon01.dvi

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1 1 ( 1 ) a FIVB ( ) 1 1 ( ) ( ) ( ) ( ) ( ) [1] [2] (point exchange) (Elo rating)[3] [4] (ranking) (rating) a konaka@meijo-u.ac.jp

2 ( ) ( [5, 6, 7, 8, 9, 10] ) [11] ( ) Massey [12] [13] [14] ( ) 1 1 ( ) ( ) 2

3 2 2.1 FIVB (FIVB) [2] 1 1 FIVB Ranking Point System Competition name Standing Olympic World Cup World Championship Men Women Tie Tie Tie Tie ( ) ( 4 ) ( ),12( ) (ATP )[15] ( ) 3

4 /3 ( ) ( ) 2.2 FIVB ATP FIVB i ( i ) r i i j i p i,j 1 p i,j = 1+e (ri rj). (1) [3] [16] r = r i r j 0,0.01,0.02,, , 2-3 r i r j = % [3] (1) p i,j = (r i r j ) 400 (2) i,j *1 * % 4

5 Probability r 1 Won-lost sets probability [4] [17] i,j s i,j = { 1 i win. 0 i lose. r i = r i +K(s i,j p i,j ) (4) r j (4) 1 ( ) (3) 5

6 (4) K 16 K r i (4) r i * ( (4) K) 1 (4) 2 2 Notations N T r = (r 1,,r NT ) T Number of teams Rating vector N S i,j,s i,s j ǫ th K k Number of sets Result of one set. Team i and j scored s i and s j points in a set. N S tuples are stored in database. Threshold value Parameter used in rating update Iteration index 0, 1 Column vector composed of zeros and ones with suitable dimensions x Euclidean norm of vector x 1. r (0) = 0 ǫ th > 0 K > k = 0 N S i,j,s i,s j 2. *2 6

7 3. i,j,s i,s j 4. r i r j p = 1 ( ),s = s i, (5) 1+e r (k) i r (k) j s i +s j r (k+1) i = r i (k)+k(s p), (6) r (k+1) j = r j (k)+k((1 s) (1 p)). (7) 5. r (k+1) r (k) < ǫ th r (k+1) k k ( ) FIVB ( ) ( ) ( ) ( ) ( ) ( ) ( )

8 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3, ( (1)) 8

9 ( ) 5 by set 5 JPN Rate difference and scoring rate in each set (London Olympic 2012, Women) 3 Regression and correlation coefficients Regression coefficient Correlation coeficcient by Set by Game by Set by Game Dataset Dataset Dataset Dataset ( ) (1) ( ) 9

10 5 by game JPN 0 3 Rate difference and scoring rate in each game (London Olympic 2012, Women) 3 1 ( ) ( ) 3.4 ( ) ( ) *3 *3 10

11 5 by set 5 JPN Rate difference and scoring rate in each set (Rio WOQT 2016, Women) 1 (FIVB 3 ( )) ( 2 3 ) ( 2 ) ( 2 ) 4 2 ( 2 3 ) (3 ) (3 ) [1] Stefani Ray. The methodology of officially recognized international sports rating systems. Journal of Quantitative Analysis in Sports, 7(4), [2] FIVB. FIVB volleyball world rankings. referred in 2016/6/14. 11

12 5 5 by game JPN Rate difference and scoring rate in each game (Rio WOQT 2016, Women) [3] Arpad E. Elo. Ratings of Chess Players Past and Present. HarperCollins Distribution Services, hardcover edition, [4] World Rugby. Rankings explanation. referred in 2016/6/14. [5] Han Joo Eom and Robert W. Schutz. Statistical analyses of volleyball team performance. Research Quarterly for Exercise and Sport, 63(1):11 18, PMID: [6] Eleni Zetou, Athanasios Moustakidis, Nikolaos Tsigilis, and Andromahi Komninakidou. Does effectiveness of skill in complex i predict win in men s olympic volleyball games? Journal of Quantitative Analysis in Sports, 3(4), [7] Lindsay W. Florence, Gilbert W. Fellingham snd Pat R. Vehrs, and Nina P. Mortensen. Skill evaluation in women s volleyball. Journal of Quantitative Analysis in Sports, 4(2), [8] Rui Manuel Araújo, José Castro, Rui Marcelino, and Isabel R Mesquita. Relationship between the opponent block and the hitter in elite male volleyball. Journal of Quantitative Analysis in Sports, 6(4), [9] Marco Ferrante and Giovanni Fonseca. On the winning probabilities and mean durations of volleyball. Journal of Quantitative Analysis in Sports, 10(2), [10] Tristan Burton and Scott Powers. A linear model for estimating optimal service error fraction in volleyball. Journal of Quantitative Analysis in Sports, 11(2), [11] Piotr Indyk and Rajeev Motwani. Approximate nearest neighbors: towards removing the curse of dimensionality. In Proceedings of the thirtieth annual ACM symposium on Theory of computing, pages ACM, [12] Ken Massey. Massey rating. referred in 2016/6/14. [13] Hope McIlwain Elizabeth Knapper. Predicting wins and losses: A volleyball case study. The College Mathematics Journal, 46(5): ,

13 5 by set Rate difference and scoring rate in each set (London Olympic 2012, Men) [14] Sam Glasson, Brian Jeremiejczyk, and Stephen R. Clarke. Simulation of women s beach volleyball tournaments. Australian Society for Operations Research, 20(2):2 7, [15] ATP World Tour. Rankings FAQ. referred in 2016/6/14. [16]. 2.., [17] World Rugby. World rankings confirm japan s victory as biggest shock referred in 2016/6/14. 13

14 5 by game Rate difference and scoring rate in each game (London Olympic 2012, Men) 5 by set 5 JPN Rate difference and scoring rate in each set (Rio WOQT 2016, Men) 14

15 5 5 by game JPN Rate difference and scoring rate in each game (Rio WOQT 2016, Men) 15

vballOlympicPredictionLondon02.dvi

vballOlympicPredictionLondon02.dvi 1 (2) a 2016 6 28 FIVB ( ) 1 1 ( ) ( ) ( ) ( ) ( ) [1] [2] (point exchange) (Elo rating)[3] [4] (ranking) (rating) a 1-501konaka@meijo-u.ac.jp 2 1. 2. 1. 1. 2. 2. 1. ( ) ( [5, 6, 7, 8, 9, 10] ) [11] (