Author: Dieter Buerssner
Date: 13:11:46 03/17/04
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On March 17, 2004 at 15:08:55, Christophe Theron wrote: >Someone at the Israeli Chess Federation screwed up and I guess that now they are >forced to keep this formula for reasons that have more to do with >historical/political reasons than mathematical ones! :) I don't think so. Actually, their formula is slightly better in the range from 20% to 80% winning expectation on average, also the maximum error is smaller. >I think my formula is more accurate. And actually it's not _my_ formula. I have >found it somewhere, but I do not remember where. Your formula is more accurate close to 50% winning percentage. >The real elo formula has the interesting property to be close to linear in the >20%-80% winning percentage range, hence the 80% validity limit. Close to 20%/80% it is already signigicantly non linear, which favors a higher multiplier to average this out a bit. The best multiplier for the 20-80 range would be 7.55. But with pocket calculators, it is no problem to use the better forumla rating_differnce = -400 * log10(1/match_result-1) where match_result is the "winning-percentage"/100. That formula is correct, if the elo system uses the "logistic distribution" and almost correct, if it uses the normal distribution (only in the extreme tails, say < 5% or > 95% it will make a difference). I am not sure, which it really uses. The German Chess Ferderation seems to use the normal distribution, while USCF seems to use the logistic distribution. In the FIDE handbook, I just find the tables. At the tails of the given table, it does not fit either distribution totally accurately. I found one article of Glickman once, which mentioned, that FIDE switched to the logistic distribution, but actually numbers calculated from the normal distribution fit the given table better ... Regards, Dieter
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