Author: Eelco de Groot
Date: 13:49:48 04/26/05
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On April 26, 2005 at 14:41:25, Dieter Buerssner wrote: >Eelco, did you compare the numbers calculated with the approximation formula to >those given in the FIDE handbook? There was a larger difference than what you >have given as the error, when I tried it. I used a very accurate version of >erf() by Stephen Moshier (I think, 15 digits correct). I used the following >formulas: > >p = 0.5+0.5*erf(dp/400) > >and > >p = 1/(1+10^(-dp/400)) > >p is the expected score, dp the rating difference. IIRC, USCF uses the later >formula based on the logistic distribution. In the center (rating difference >small), both formulas give practically identical values. In the tails, they >differ (not much in absolute terms, but significantly taken into relation). The >numbers given on the FIDE site where in between. > >Regards, >Dieter Hi Dieter, Are we talking about the same approximation formula? The elo-numbers that Odd Gunnar Malin computed for the Hastings formula came out pretty well compared to what Excels own approximation of the normal distribution would give. http://www.talkchess.com/forums/1/message.html?422011 And Hastings best approximation could be found in the manuals for both Casio's and Texas Instruments programmable calculutors. (I have the Casio manual that came with my FX-501P calculator, bought that in 1980, it had no less than 128 programmable steps!) This approxiation is probably around since the 1950's but for calculator use (8 digits or thereabout) it should work well enough. Regards, Eelco
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