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Subject: Re: ELO & statistics question

Author: Ratko V Tomic

Date: 15:01:48 04/26/02

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The error sqrt(N) is valid in the limit of large N
(where Stirling approximation for N! is usable). In
that case edge effects don't occur provided
1/sqrt(N)<<MIN(y,(1-y)).

For small N you have to use the exact combinatorics
to get probabilities of different outcomes of the
sequence of n rounds (e.g. the binomial distribution:
P(k)=Comb(N,k)*y^k*(1-y)^(N-k)) for k wins, where
Comb(N,k)=N!/[(N-k)!*k!]). The most probable value
for k is kmax=y*N. The next most probable values are
kmax+/-1, etc. Adding these probabilities around kmax
(in order of decreasing P(k)) until the sum reaches
say 0.95 will give you the most accurate error margins
for any desired confidence interval and any N. A small
C or Basic program can compute this quickly for any
practical match length.



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