Author: Dieter Buerssner
Date: 08:25:20 11/21/03
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On November 21, 2003 at 08:50:50, Drexel,Michael wrote: >You might have a look at this page: > >http://en2.wikipedia.org/wiki/Elo_rating_system I wonder, if this is accurate. I read: --- Subsequent statistical tests have shown that chess performance is almost certainly not normally distributed. Weaker players have significantly greater winning chances than Elo's model predicts. Therefore, both the USCF and FIDE have switched to systems based on the logistic distribution. However, in deference to Elo's contribution, both organizations are still commonly said to use "the Elo system". --- With the logistic distribution, the formula is p = 1/(1+10^(-dp/400)) [1] while for the normal distribution it would be p = 0.5+0.5*erf(dp/400) [2] erf=error function, dp is the rating difference. When I now look at the (seemingly official?) table at http://www.fide.com/official/handbook.asp?level=B0210 I see: p dp using [1] using [2] 0.99 677 0.9801 0.9917 0.98 589 0.9674 0.9813 [First 2 columns from the link] So, using formula [1] gives a p, that is outside the rounding range, while using [2] it actually gives the number given in the table at FIDE to the given precision. Still, I have some doubt, because a better number dp for 0.99 would be 658, yielding in p=0.9900009 with [2]. >You can only calculate expected scores between two rated players if the >difference is not higher than 400 points. Why? Formally you can certainly calculate expected scores for a higher range. Regards, Dieter
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