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Subject: Re: ELO performance?

Author: Peter Fendrich

Date: 11:22:26 05/22/99

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Sorry, I forgot to answear the 95% question... :)

To estimate the standard deviation of the Performance Rating there are
lots of options, giving about the same result. You need the individual results
to know the the error margin and that's what this is all about. There is a
difference between a result of only wins and losses compared to a result with a
lot of draws. The SSDF method is best described as:
       (1) s=SQRT(W(1-m)**2 + D(0.5-m)**2 + L(0-m)**2/(n-1))
       (2) A=1.96 * s/SQRT(n)

       where s is estimated standard deviation
             n     is number of games
             m     is score/n
             W,D,L is number of Wins, Draws and Losts respectivelly
             A     is the margin of error (for score, not rating points)
             1.96  is fethed from the Normal Distribution table to get
                   95% reliability
             SQRT  is the square root
             **    is used as 'the power of'

    Now we have an 95% interval of *scores* from m-A to m+A

    Compute the ratings for each m-A and m+A and here we go!
    These ratings are the end points in the interval.

//Peter




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