1998 (World Curling Federation, WCF) 1959 Scotch Cup (5 5) 5 WCF : 1. 1998 (World Curling Federation, WCF) 1959 2 Scotch Cup[8] (5 5) 5 WCF ( ) ( ) 1
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 1979 12 European Curling Championships (ECC) Men 1975 26 Women 1975 2 European Curling Championships Men 21 11 C Division (ECC-C)( 2) Women 21 8 Pacific-Asia Curling Championships (PCC) Men 1991 8 Women 1993 5 Winter Olympic Games (WOG)( 3) Men 1998 1 Women 1998 1 Winter Olympic Qualifying Event Men 213 8 (WOQ)( 3) Women 213 7 ( 1): The competition is named as Scotch cup (1959 1967), and Silver Bloom (1968 1985). ( 2): be separeted from European Curling Championships. ( 3): be held once every four years. 1959 Scotch Cup 12 1975 1979 1 2 3 21 C ( 216 35 13 ) WCF (Pacific Asia Championship) 199 3 (1998 ) 214 213 Olympic Qualifying Event 54 2
3. 2 1. 2. (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
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 +1 2. 3.1. Bradley-Terry (BT )[3, 1] ( ) [4] BT ( ) (Elo rating)[2] 1 4.2 4. WCF 6 [6] 6 214 29 214 WCF [7]Web 2166 7 1 4
2 12526 ( 734 5492 ) 4.1. () r r r (maxr) 1 (4.1) 3 4 ( ) 2 6 5 8 215 Ward[5] 9 1..1 1 4.2. 3 4 ( ) 1 5 8 (12 ) (1 ) 1985 1 1. 215.6 ( ) 1 1985.269 215.354 ( ) 9 1 1 ( ) ( ).5 ( ) 1 11 5
11 9.74 5. ( ) ( ) 1959 12 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. 317 328, 197. [2] Arpad E. Elo. Ratings of Chess Players Past and Present. Harper Collins Distribution Services, hardcover edition, 1979. [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. 194 24, 1967. [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. 236 244, 1963. [6] World Curling Federation. Men s & women s world rankings. http://www.worldcurling.org/rankings-men-and-women, 216. referred in 216/11. [7] World Curling Federation. Results & statistics. http://results.worldcurling.org/, 216. referred in 216/11. [8] World Curling Federation. Scotch cup 1959. http://results.worldcurling.org/championship/details/5, 216. referred in 216/11. 6
Number of teams [M] 35 3 25 2 15 1 5 ECC C ECC WOG WOQ PCC WCC 196 197 198 199 2 21 22 Year Number of teams [W] 35 3 25 2 15 1 5 ECC C ECC WOG WOQ PCC WCC 196 197 198 199 2 21 22 Year 1: Number of teams in major international competitons of curling 7
Number of matches [M] 15 1 5 ECC C ECC WOG WOQ PCC WCC 196 197 198 199 2 21 22 Year Number of matches [W] 15 1 5 ECC C ECC WOG WOQ PCC WCC 196 197 198 199 2 21 22 Year 2: Number of matches in major international competitons of curling 8
Rating (win/lose), Men 4 6 8 1 12 Europe North America Pacific Asia 196 197 198 199 2 21 22 Year 3: Rating history (men) 9
Rating (win/lose), Women 4 6 8 1 12 Europe North America Pacific Asia 196 197 198 199 2 21 22 Year 4: Rating history (women) 1
Top Teams Rating (win/lose), Men.5 1 1.5.5 215 29 23 1997 1991 1985 1979 1973 1967 1961 3 5 1 15 2 All Teams Rating (win/lose), Men 4 6 8 215 29 23 1997 1991 1985 1979 1973 1967 1961 1 1 2 3 4 5 5: Rating distribution (win/lose, men) 11
Top Teams Rating (scoring ratio), Men.2.4.6.8 215 29 23 1997 1991 1985 1979 1973 1967 1961 1 5 1 15 2 All Teams Rating (scoring ratio), Men.5 1 1.5.5 215 29 23 1997 1991 1985 1979 1973 1967 1961 3 1 2 3 4 5 6: Rating distribution (scoring rate, men) 12
Top Teams Rating (win/lose), Women.5 1 1.5.5 215 29 23 1997 1991 1985 1979 3 5 1 15 2 All Teams Rating (win/lose), Women 4 6 8 215 29 23 1997 1991 1985 1979 1 1 2 3 4 5 7: Rating distribution (win/lose, women) 13
Top Teams Rating (scoring ratio), Women.2.4.6.8 215 29 23 1997 1991 1985 1979 1 5 1 15 2 All Teams Rating (scoring ratio), Women.5 1 1.5.5 215 29 23 1997 1991 1985 1979 3 1 2 3 4 5 8: Rating distribution (scoring rate, women) 14
Men Women Rating (win/lose) 4 6 8 1 1 2 3 4 5 Rating (scoring ratio).5 1 1.5.5 Men Women 3 1 2 3 4 5 9: Rating clustering 15
Correlation coefficient 1.8.6.4.2 Prediction using rating on win/lose Men Women 196 197 198 199 2 21 22 Year Correlation coefficient 1.8.6.4.2 Prediction using rating on scoring ratio Men Women 196 197 198 199 2 21 22 Year 1: Correlation coefficients bewteen predicted and real results 16
Men Women Rating (win/lose) 4 6 8 1 1 2 3 4 5 11: Rating clustering of volleyball national teams 17