Analysis of the 1962 world chess championship, Curacao
R. K. S. Hankin
To cite the hyper2 package in publications, please use Hankin (2017).
This file creates likelihood functions H and H_coll, which appear
in the package as interzonal and collusion respectively. It also
presents some analysis of the datasets using the hyper2 package.
jj <- read.table("stockholm1962.txt",header=FALSE)
results <- as.matrix(jj[,-(1:2)])
players <- as.character(jj$V1)
nationality <- as.character(jj$V2)
rownames(results) <- players
colnames(results) <- players
points <- rowSums(results,na.rm=TRUE)Now some comparison between stockholm1962.txt (results) and
stockholm1962_matches.txt (results2):
H <- hyper2(pnames=c("white","draw",players))
H_coll <- hyper2(pnames=c("white","draw","collusion",players))
restab <- read.table("stockholm1962_matches.txt",header=FALSE)
stopifnot(all(unique(sort(c(as.character(restab$V1),as.character(restab$V2)))) == sort(players)))
results2 <- matrix(0,length(players),length(players))
rownames(results2) <- players
colnames(results2) <- players
diag(results2) <- NA
for(i in seq_len(nrow(restab))){
white_player <- as.character(restab[i,1])
black_player <- as.character(restab[i,2])
match_result <- as.character(restab[i,3])
nw <- which(players==white_player)
nb <- which(players==black_player)
if(match_result == "1-0"){ # white win
results2[nw,nb] <- 2
results2[nb,nw] <- 0
H[c(white_player ,"white" )] %<>% inc()
H[c(white_player,black_player,"white","draw")] %<>% dec()
if(nationality[nw]=="USSR" & nationality[nb]=="USSR"){
H_coll[c(white_player ,"white" )] %<>% inc()
H_coll[c(white_player,black_player,"white","collusion")] %<>% dec()
} else {
H_coll[c(white_player ,"white" )] %<>% inc()
H_coll[c(white_player,black_player,"white","draw")] %<>% dec()
}
} else if(match_result == "0-1"){ # black wins
results2[nw,nb] <- 0
results2[nb,nw] <- 2
H[c( black_player )] %<>% inc()
H[c(white_player,black_player,"white","draw")] %<>% dec()
if(nationality[nw]=="USSR" & nationality[nb]=="USSR"){
H_coll[c( black_player )] %<>% inc()
H_coll[c(white_player,black_player,"white","collusion")] %<>% dec()
} else { # collusion not playing
H_coll[c( black_player )] %<>% inc()
H_coll[c(white_player,black_player,"white","draw")] %<>% dec()
}
} else if (match_result == "1/2-1/2"){ # draw
results2[nw,nb] <- 1
results2[nb,nw] <- 1
H[c( "draw")] %<>% inc()
H[c(white_player,black_player,"white","draw")] %<>% dec()
if(nationality[nw]=="USSR" & nationality[nb]=="USSR"){
H_coll[c( "collusion")] %<>% inc()
H_coll[c(white_player,black_player,"white","collusion")] %<>% dec()
} else { # collusion not playing
H_coll[c( "draw")] %<>% inc()
H_coll[c(white_player,black_player,"white","draw")] %<>% dec()
}
} else {
stop("not possible")
}
} # i loop closesSo, results [from the square matrix] and results2 [from the
3-column dataframe] should match:
stopifnot(all(results[!is.na(results)] == results2[!is.na(results2)]))Now some maximum likelihood estimation.
H_maxp <- maxp(H)
H_maxp## white draw Fischer Geller Petrosian Korchnoi Filip
## 2.5868e-02 7.0232e-02 1.5282e-01 8.2099e-02 3.3356e-02 5.2589e-02 5.2522e-02
## Gligoric Benko Stein Uhlmann Portisch Pomar Olafsson
## 4.2981e-02 4.4059e-02 8.0256e-02 8.1948e-02 5.7431e-02 3.1393e-02 4.7111e-02
## Bolbochan Barcza Bilek Bisguier Yanofsky Bertok German
## 2.4104e-02 2.4101e-02 3.7777e-02 1.3022e-02 1.3680e-06 1.0005e-06 9.8650e-03
## Schweber Teschner Cuellar Aaron
## 1.0165e-06 1.5749e-02 1.3010e-02 7.7004e-03small <- 0.01
maxlike_free <- maxp(H_coll,startp=c(small,small,small/2,rep(small,22)),give=TRUE)
print("l")## [1] "l"dput(maxlike_free$value)## -239.374896808407jj <- maxlike_free$par
maxlike_free <- maxp(H_coll,startp=jj,give=TRUE)
dput(maxlike_free$value)## -239.374896799213H_coll_maxp <- maxlike_free$valuesamep.test(H_coll,c("draw","collusion"))##
## Constrained support maximization
##
## data: H_coll
## null hypothesis: draw = collusion
## null estimate:
## white draw collusion Fischer Geller Petrosian Korchnoi
## 2.7002e-02 6.8445e-02 6.8445e-02 1.4541e-01 7.6341e-02 2.7828e-02 4.7145e-02
## Filip Gligoric Benko Stein Uhlmann Portisch Pomar
## 4.8519e-02 3.9705e-02 3.9243e-02 7.4762e-02 7.6348e-02 5.3070e-02 2.6904e-02
## Olafsson Bolbochan Barcza Bilek Bisguier Yanofsky Bertok
## 4.2533e-02 2.2722e-02 2.1418e-02 3.3990e-02 1.2726e-02 4.5531e-06 3.5002e-06
## German Schweber Teschner Cuellar Aaron
## 1.0188e-02 2.4565e-05 1.6079e-02 1.2783e-02 8.3612e-03
## (argmax, constrained optimization)
## Support for null: -241.87 + K
##
## alternative hypothesis: sum p_i=1
## alternative estimate:
## white draw collusion Fischer Geller Petrosian Korchnoi
## 1.4467e-02 3.7671e-02 4.1164e-01 8.9348e-02 5.7870e-02 2.4014e-02 3.5589e-02
## Filip Gligoric Benko Stein Uhlmann Portisch Pomar
## 2.9569e-02 2.4518e-02 2.3834e-02 5.3810e-02 4.6322e-02 3.2258e-02 1.6879e-02
## Olafsson Bolbochan Barcza Bilek Bisguier Yanofsky Bertok
## 2.6655e-02 1.2392e-02 1.2623e-02 2.1161e-02 7.1505e-03 1.0000e-06 1.0001e-06
## German Schweber Teschner Cuellar Aaron
## 5.2761e-03 1.0002e-06 8.4737e-03 5.8633e-03 2.6095e-03
## (argmax, free optimization)
## Support for alternative: -238.3 + K
##
## degrees of freedom: 1
## support difference = 3.5767
## p-value: 0.0074821Package dataset
Following lines create interzonal.rda, residing in the data/
directory of the package.
interzonal <- H
interzonal_maxp <- H_maxp
collusion <- H_coll
collusion_maxp <- H_coll_maxp
save(interzonal,collusion,interzonal_maxp,collusion_maxp,
file="interzonal.rda")References
Hankin, R. K. S. 2017. “Partial Rank Data with the
hyper2 Package: Likelihood Functions for Generalized Bradley-Terry Models.” The R Journal 9 (2): 429–39.