vballOlympicPredictionLondon02.dvi

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1 1 (2) a FIVB ( ) 1 1 ( ) ( ) ( ) ( ) ( ) [1] [2] (point exchange) (Elo rating)[3] [4] (ranking) (rating) a [email protected]

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 3

4 )[15] ( ) /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, 17] 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) 4

5 Probability r 1 Won-lost sets probability i,j *1 [4] [18] 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) (3) * % 5

6 1 ( ) (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 *2 6

7 1. r (0) = 0 ǫ th > 0 K > k = 0 N S i,j,s i,s j 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 ,+ 2 ( ) r r r (maxr) 1 (8) Bradley-Terry (BT )[19, 20] BT i j i j *3 p i,j π i,π j > 0 p i,j = π i π i +π j (9) p i,j = π i π i +π j = 1 1+ πj π i = 1+exp 1 1 ( ) = log πj 1+exp(logπ j logπ i ) π i (10) r i = logπ i (11) (1) *

8 [1] BT [16, 17] a i b i θ j j j p i,j p i,j = 1 1+exp( 1.7a j (θ i b j )) k i j i j p i,j p i,j = 1 1+exp( a k (r i r j )) a k > 0 ( )BT (1) (12) (13) 3 ( ) FIVB ( ) ( ) ( ) ( ) ( ) ( )

9 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

10 ( ) 3, ((1)) ( ) 5 Probability/Scoring rate by set 5 Prediction ALL JPN Probability/Scoring rate Konakalab 0 Rating Gap 2 Rate difference and scoring rate in each set (London Olympic 2012, Women) 3 Regression and correlation coefficients based on proposed rating method Regression coefficient Correlation coeficcient by Set by Game by Set by Game Dataset Dataset Dataset Dataset

11 5 5 Probability/Scoring rate by game Probability/Scoring rate Prediction ALL JPN 2016 Konakalab 0 Rating Gap 3 Rate difference and scoring rate in each game (London Olympic 2012, Women) 3.3 ( ) (1) ( ) 3 1 ( ) ( ) 11

12 5 Probability/Scoring rate by set 5 Prediction ALL JPN Probability/Scoring rate Konakalab 0 Rating Gap 4 Rate difference and scoring rate in each set (Rio WOQT 2016, Women) FIVB 4 1( ) FIVB FIVB FIVB FIVB 4 ( 1 3) ( ) ( ) 3 3*( ) 12

13 5 5 Probability/Scoring rate by game Prediction ALL JPN Probability/Scoring rate Konakalab 0 Rating Gap 5 Rate difference and scoring rate in each game (Rio WOQT 2016, Women) 4 Correlation coefficients: FIVB ranking and scoring rate FIVB ranking gap by Set Correlation coefficient FIVB ranking point gap by Game by Set by Game Dataset Dataset 1* Dataset Dataset Dataset 3* Dataset *: except GBR

14 5 Probability/Scoring rate by set 5 Prediction ALL Probability/Scoring rate Konakalab Rating Gap 6 Rate difference and scoring rate in each set (London Olympic 2012, Men) ( ) ( ) *4 1 (FIVB 3 ( )) ( 2 3 ) ( 2 ) ( 2 ) 4 ( 3 ) 2 ( 23 ) (3 ) (3 ) *4 14

15 5 5 Probability/Scoring rate by game Probability/Scoring rate Prediction ALL 2016 Konakalab Rating Gap 7 Rate difference and scoring rate in each game (London Olympic 2012, Men) FIVB ( ) (12) (24) (12) (28) 5 ( ) ( ) 15

16 5 Probability/Scoring rate by set 5 Prediction ALL JPN Probability/Scoring rate Konakalab Rating Gap 8 Rate difference and scoring rate in each set (Rio WOQT 2016, Men) 16

17 5 5 Probability/Scoring rate by game Prediction ALL JPN Probability/Scoring rate Konakalab Rating Gap 9 Rate difference and scoring rate in each game (Rio WOQT 2016, Men) 17

18 5 Probability/Scoring rate by set 5 Probability/Scoring rate Rankig Gap 10 FIVB ranking difference and scoring rate in each set (Rio WOQT 2016, Men) 5 Probability/Scoring rate by set 5 Probability/Scoring rate Rankig Point Gap 11 FIVB ranking point difference and scoring rate in each set (Rio WOQT 2016, Men) 18

19 5 Probability/Scoring rate by game 5 Probability/Scoring rate Rankig Gap 12 FIVB ranking difference and scoring rate in each game (Rio WOQT 2016, Men) 5 Probability/Scoring rate by game 5 Probability/Scoring rate Rankig Point Gap 13 FIVB ranking point difference and scoring rate in each game (Rio WOQT 2016, Men) 19

20 5 Numer of teams Competition name Teams Men Women Basketball FIBA Basketball World Cup 24 Basketball FIBA Women s Basketball World Cup 16 Basketball 2016 Summer Olympics Hockey Hockey World Cup Hockey 2016 Summer Olympics Football FIFA World Cup 32 Football FIFA Women s World Cup 24 Football 2016 Summer Olympics Handball World Men s Handball Championship 24 Handball World Women s Handball Championship 24 Handball 2016 Summer Olympics Rugby (sevens) Rugby World Cup Sevens Rugby (sevens) 2016 Summer Olympics Ice Hockey IIHF Ice Hockey World Championships 16 Ice Hockey IIHF Ice Hockey Women s World Championship 8 Ice Hockey 2014 Winter Olympics 12 8 Curling World Curling Championships 12 Curling World Women s Curling Championship 12 Curling 2014 Winter Olympics

21 A IOC 3 [21] 6 Rating: Dataset 1 (just befor London Olympic Games, Women) RUS USA NED ARG CAN EGY BRA PER GBR ITA PUR FRA CHN ALG SVK SEY TUR ROM UKR DEN POL GER BUL TPE AUT MEX POR SWE JPN KEN HUN CHI THA AZE ISR HON SRB CRO GRE GEO CUB ESP CRC KOR DOM CZE VEN BIH TTO BEL COL URU [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. [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),

22 7 Rating: Dataset 2 (just before Rio WOQT, Women) BRA CHN USA SRB RUS NED GER THA JPN ITA TUR BEL CZE POL KOR PUR BUL DOM CAN ARG KAZ CRO CUB PER KEN VEN COL CMR EGY TUN ALG CHI BOT UGA [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): , [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] R. Hambleton. Fundamentals of Item Response Theory (Measurement Methods for the Social Science). Sage Publications, Incorporated, new. edition, [17] R. J. de Ayala. The Theory and Practice of Item Response Theory (Methodology in the Social Sciences). Guilford Pr, 1 edition, [18] World Rugby. World rankings confirm Japan s victory as biggest shock referred in 2016/6/14. [19] L. L. Kupper P. V. Rao. Ties in paired-comparison experiments: A generalization of the bradley-terry model. Journal of the American Statistical Association, 62(317): , [20] Roger R. Davidson. On extending the bradley-terry model to accommodate ties in paired comparison experiments. Journal of the American Statistical Association, 65(329): , [21] International Olympic Committee. List of all national olympic committees in IOC protocol order. 22

23 8 Rating: Dataset 3 (just befor London Olympic Games, Men) GER POL IRI SVK GBR GRE BRA LAT NED AUT FRA FIN HUN ISR USA KOR PUR COL RUS JPN VEN MKD BEL ITA CHN EGY CMR PAK DOM CHI CZE POR UKR BIH CUB ESP MNE TOT AUS SLO DEN GHA BUL EST ALG CRC ARG SRB TUN TUR ROM CRO GEO CAN IND MEX Committees/List-of-National-Olympic-Committees-in-IOC-Protocol-Order.pdf. referred in 2016/6/15. 23

24 9 Rating: Dataset 4 (just before Rio WOQT, Men) FRA BRA GER USA POL SRB ITA IRI RUS ARG JPN BEL TUR MNE KOR BUL CZE CAN AUS NED CUB EGY ESP CHN GRE SVK ALG FIN POR TUN VEN CHI PUR KAZ MEX CMR COL CGO COD NGR

5 2:02:29 1 1:58:03 2 1:59:43 3 1:59:55 5 K s-y ITC 1:51: :02:07 18 ITC2:02:43 28 NTT NTT 2:03:54 40 TEAM KEN S A&A2:07:14 1 1:49:32 2 SUI 1:49:

5 2:02:29 1 1:58:03 2 1:59:43 3 1:59:55 5 K s-y ITC 1:51: :02:07 18 ITC2:02:43 28 NTT NTT 2:03:54 40 TEAM KEN S A&A2:07:14 1 1:49:32 2 SUI 1:49: 2 POL 1:56:46 2005 3 1:57:47 5 1:58:44 3 5 7 1:59:11 8 1:59:40 1 AUS 2:07:56 2 2:08:45 1 NZL 2:00:39 3 ITC 2:09:09 2 2:00:59 4 2:09:32 3 NTT NTT 2:01:31 6 NTT NTT 2:02:50 10 TEAM KEN S A&A2:04:36 18 2:11:02