Author: Uri Blass
Date: 20:12:36 04/26/02
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On April 26, 2002 at 16:48:10, Osorio Meirelles wrote: >On April 26, 2002 at 09:29:26, Gian-Carlo Pascutto wrote: > >>Given a score from a series of games, y, we can calculate >>the ELO difference between the two players as: >> >>x = -400*log((1-y)/y) >> >>My question is now, how do we calculate the error margins >>on this value? >> >>-- > >Gian-Carlo, I would recomend that first we get the standard deviation for y, >which is : > > std(Y) = square_root( y*(1-y)/ n ) where n is the number of games. > > A 95% confidence interval for y is: > > [ y - 1.96*std(Y) , y + 1.96*std(Y)] > > make h1 = y - 1.96*std(Y) this is the y lower bound > make h2 = y + 1.96*std*(Y) this is the y upper bound > > Since x = -400*log((1-y)/y), the confidence interval for x would be: > > -400*log( (1-h1)/h1) ) lower bound > > -400*log( (1-h2)/h2) ) upper bound It is truth when there are no draws and when the number of games is big. Draws reduce the standard deviation of y and if the number of games is not big the distribution of y is not close to be normal and it cause the formula to be wrong. I did not consider draws in my previous post in this subject. Uri
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