OR2017_curlingRating.dvi
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1 1998 (World Curling Federation, WCF) 1959 Scotch Cup (5 5) 5 WCF : (World Curling Federation, WCF) Scotch Cup[8] (5 5) 5 WCF ( ) ( ) 1
2 2. 1 1: Major international competitons of curling Competition Name Gender From Teams in latest event World Curling Championships (WCC) Men 1959( 1) 12 Women European Curling Championships (ECC) Men Women European Curling Championships Men C Division (ECC-C)( 2) Women 21 8 Pacific-Asia Curling Championships (PCC) Men Women Winter Olympic Games (WOG)( 3) Men Women Winter Olympic Qualifying Event Men (WOQ)( 3) Women ( 1): The competition is named as Scotch cup ( ), and Silver Bloom ( ). ( 2): be separeted from European Curling Championships. ( 3): be held once every four years Scotch Cup C ( ) WCF (Pacific Asia Championship) (1998 ) Olympic Qualifying Event 54 2
3 (1) ( ) WCF [7] ( ) i ( i )r i ij i ( )p i,j p i,j = 1 1+e (r i r j ). (3.1) 2 2: Notations N T Number of teams r = (r 1,,r NT ) T Rating vector N G Number of games i,j,s i,s j Result of one game. Team i and j scored s i and s j points in a game. N G tuples are stored in database. ǫ th Threshold value K Parameter used in rating update k Iteration index, 1 Column vector composed of zeros and ones with suitable dimensions x Euclidean norm of vector x 1. r () = ǫ th > K > 1 3 k = N G i,j,s i,s j 2. 3
4 3. i,j,s i,s j 4. r i r j p = 1 ( ), s = 1 (if s 1+e r (k) i r (k) i > s j ), (if s i < s j ) (3.2) j p = 1 ( ), s = s i, (3.3) 1+e r (k) i r (k) j s i +s j r (k+1) i = r (k) i +K(s p), r (k+1) j = r (k) j +K((1 s) (1 p)). (3.4) 5. r (k+1) r (k) < ǫth r (k+1) k k Bradley-Terry (BT )[3, 1] ( ) [4] BT ( ) (Elo rating)[2] WCF 6 [6] WCF [7]Web
5 ( ) 4.1. () r r r (maxr) 1 (4.1) 3 4 ( ) Ward[5] ( ) (12 ) (1 ) ( ) ( ) ( ) ( ).5 ( )
6 ( ) ( ) ( ) ( ) [1] Roger R. Davidson. On extending the bradley-terry model to accommodate ties in paired comparison experiments. Journal of the American Statistical Association, Vol. 65, No. 329, pp , 197. [2] Arpad E. Elo. Ratings of Chess Players Past and Present. Harper Collins Distribution Services, hardcover edition, [3] L. L. Kupper and P. V. Rao. Ties in paired-comparison experiments: A generalization of the bradley-terry model. Journal of the American Statistical Association, Vol. 62, No. 317, pp , [4] Stefani Ray. The methodology of officially recognized international sports rating systems. Journal of Quantitative Analysis in Sports, Vol. 7, No. 4, 211. [5] Joe H. Ward Jr. Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, Vol. 58, No. 31, pp , [6] World Curling Federation. Men s & women s world rankings referred in 216/11. [7] World Curling Federation. Results & statistics referred in 216/11. [8] World Curling Federation. Scotch cup referred in 216/11. 6
7 Number of teams [M] ECC C ECC WOG WOQ PCC WCC Year Number of teams [W] ECC C ECC WOG WOQ PCC WCC Year 1: Number of teams in major international competitons of curling 7
8 Number of matches [M] ECC C ECC WOG WOQ PCC WCC Year Number of matches [W] ECC C ECC WOG WOQ PCC WCC Year 2: Number of matches in major international competitons of curling 8
9 Rating (win/lose), Men Europe North America Pacific Asia Year 3: Rating history (men) 9
10 Rating (win/lose), Women Europe North America Pacific Asia Year 4: Rating history (women) 1
11 Top Teams Rating (win/lose), Men All Teams Rating (win/lose), Men : Rating distribution (win/lose, men) 11
12 Top Teams Rating (scoring ratio), Men All Teams Rating (scoring ratio), Men : Rating distribution (scoring rate, men) 12
13 Top Teams Rating (win/lose), Women All Teams Rating (win/lose), Women : Rating distribution (win/lose, women) 13
14 Top Teams Rating (scoring ratio), Women All Teams Rating (scoring ratio), Women : Rating distribution (scoring rate, women) 14
15 Men Women Rating (win/lose) Rating (scoring ratio) Men Women : Rating clustering 15
16 Correlation coefficient Prediction using rating on win/lose Men Women Year Correlation coefficient Prediction using rating on scoring ratio Men Women Year 1: Correlation coefficients bewteen predicted and real results 16
17 Men Women Rating (win/lose) : Rating clustering of volleyball national teams 17
vballOlympicPredictionLondon01.dvi
1 ( 1 ) a 2016 6 14 FIVB ( ) 1 1 ( ) ( ) ( ) ( ) ( ) [1] [2] (point exchange) (Elo rating)[3] [4] (ranking) (rating) a 1-501 konaka@meijo-u.ac.jp 2 1. 2. 1. 1. 2. 2. 1. ( ) ( [5, 6, 7, 8, 9, 10] ) [11]
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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] (
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