Author: Jeff Lischer
Date: 05:58:26 08/08/03
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On August 08, 2003 at 02:04:48, Axel Schumacher wrote: >Quite some interesting differences... eh? > >Another problem is still present, even with EloStat (Startvalue 2400). The lower >ranked engines are get still a much too high Elo. How to avoid that? I saw >several other lists, where the list-authors made it possible that the Elo-values >are lower. If I start with a lower start-value of e.g. 2000, than the top >engines are ranked far too low. Any suggestions? > >Axel I think this could have what Uri posted below about the problems associated with calculating Elo's based on the "average opponent". The problem comes from the non-linearity of the Elo formula. For example, if you had three players rated 2000, 1800, and 1600 play 100 games against each other, the expected outcome would be about: Elo2000 vs Elo1800: 76 - 24 Elo2000 vs Elo1600: 91 - 9 Elo1800 vs Elo1600: 76 - 24 If you put these results into Elostat, with an average Elo of 1800, you'll get the following: Player Estimated Elo Elo2000 1988 Elo1800 1800 Elo1600 1612 In the average opponent approach, high Elo's are underestimated while low Elo are overestimated. The problem is that in actuality, the 2000 rated player is expected to score differently in the following cases: 1) Individual opponent (100 games vs 1800 plus 100 games versus 1600) Total expected score: 167 - 33 2) Average opponent (200 games versus 1700) Total expected score: 170 - 30 and that difference affects the Elo calculations. The reason Elostat doesn't "like" Chess Tiger is that Chess Tiger played against weaker opponents. It has a much lower average opponent (80 points less than CM9000), so it got hurt more by the average opponent approach. The differences between the Fritz and Elostat ratings that you showed are consistent with Fritz calculating the Elo's based on the individual games. Does anyone know the details of how Fritz calculates the ratings?
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