Author: Jeff Lischer
Date: 19:50:08 01/22/01
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On January 22, 2001 at 17:53:10, Paulo Soares wrote:
>Jeff Lischer taught me the standard formula for the
>win expectancy (We) for a program x to win a
>program y, below placed:
>
>We = 1/(1 + 10^((delta rating)/400))
>where (delta rating) = rating y - rating x
>
>I remember another formula that considered a certain error
>margin. I am almost sure that that formula was already shown
>here several times for some people, perhaps Dann Corbitt,
>Bruce Moreland or Uri Blass?
>Does anybody remember that other formula?
>
>Thanks in avdanced,
>
>Paulo Soares, from Brazil
The simplest error margin formula that I have seen was given here by Walter
Koroljow in message 128346. The standard error for the win expectancy, We, would
be:
Sigma = sqrt[We*(1-We)/N - D/(4*N^2)]
where Sigma = standard error of the win expectancy,
We = win expectancy =(W + 0.5D)/N
D = number of draws,
N = total number of games
The first part of the equation is the standard formula for a binomial
distribution. The second term, with the D, accounts for the actual number of
wins, losses, and draws. As an example, a game score of +15 =10 -5 results in:
We = 0.667, Sigma = 0.068.
Therefore, the 95% margins (±1.96*Sigma) would be about [0.533, 0.800]. This is
simple theory that's assumes a normal distribution, but it works fairly well for
many cases.
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