Author: Drexel,Michael
Date: 10:40:17 11/21/03
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On November 21, 2003 at 11:25:20, Dieter Buerssner wrote: >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 Yes formally, but are the results still a good approximation? Michael
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