Author: Christophe Theron
Date: 21:43:05 03/17/04
Go up one level in this thread
On March 17, 2004 at 16:11:46, Dieter Buerssner wrote:
>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.
Thank for pointing this out.
I have looked at this a little bit more and I think a reasonably "simple" elo
formula is:
1) if the winning percentage of the winner is above 80%, stop here (use a
scientific calculator with the REAL elo formula).
2) subtract 50 from the winning percentage of the winner.
3) if the winning percentage is 73% or below, multiply by 7 and you get the
approximate elo difference.
4) if the winning percentage is above 73%, multiply by 8 and you get the
approximate elo difference.
By using this "version 2" of the simplified formula you are never off by more
than 7.5%.
Another idea is to keep the formula of my previous message and to restrict it to
the 30%-70% range of winning percentages. It is still very simple and will be
very useful in many cases. The error in the worst case is 5% (an error of 7 elo
points on a 147 elo points difference).
Christophe
>>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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