Current Ratings
url = "http://216.119.100.169/history/rating/History/Allplayers
AllRatings = readHTMLTable(url, as.data.frame = T,
header = T, colClasses = c("integer", "character",
"character", "numeric", "character", "character"))
AllRatings = as.data.frame(AllRatings)
names(AllRatings) = c("ID", "Expire", "Name", "Rating",
"State", "LastPlayed")
nrow(AllRatings)
[1] 5600
summary(AllRatings$Rating)
Min. 1st Qu.
7
1010
Median
1440
Mean 3rd Qu.
1390
1770
Max.
2840
Distribution of Ratings
densityplot(~Rating, AllRatings, plot.points = F)
0.0008
Density
0.0006
0.0004
0.0002
0.0000
0
1000
2000
Rating
3000
David Marcus
Zermelo
Zermelo’s Playing Strengths
Player A has strength sA
Player B has strength sB
Probability that A beats B is
p(sA , sB ) =
sA
sA /sB
=
sA + sB
sA /sB + 1
Marcus Version of Zermelo Model
Player A has rating rA
Player B has rating rB
Probability that A beats B is
eα(rA −rB )
1 + eα(rA −rB )
α = 1/67
Probability of Win
1.0
Win Probability
0.8
0.6
0.4
0.2
0.0
−200
−100
0
Rating Difference
100
200
A rating is normal distribution
A rating is reported as a pair such as 1450 (65)
Long Ma (CHN)
Dan Seemiller (US)
3149 (37)
2430 (168)