Author: Dieter Buerssner
Date: 13:05:59 04/25/05
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Odd Gunnar, sorry for the slow response. Perhaps there is a small misunderstanding. I feel, that it is not best to use this approximation formula nowadays. Transcendental functions (like erf, log, pow) are easily and with very high accuracy available nowadays. No need to use the approximation. Even, when you cannot inverse (like it seems to be the case for erf(), which is needed when using the normal distribution - with the logistic distribution inversion is easy), one can easily do it with numerical methods and the "real" formula. IIRC more sophisticated math libraries (like Steven Moshier's cephes, that is freely available in source) can even inverse erf() with very high accurracy, very good perfomance, and just a function call. Of course the differences will only show in the tails (large Elo difference) and are rather theoretical. In these tails, the assumptions made are most probably not true anymore anyway - so it is a rather theoretical argument. Remi has done a model based on Bayesian statistics, which seems to make less assumptions (I don't understand it fully). Martin Glickman (the inventor of the Glicko rating system used on chess servers) seems to use Bayesian statistics in his newest publications, as well. Regards, Dieter
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