Author: Eelco de Groot
Date: 16:53:15 08/02/01
Go up one level in this thread
On August 02, 2001 at 14:59:58, Vicente Fernández wrote: >Suppose two players meet in a 24 game match. How does one calculate the final >ratings? Is it correct to calculate the ratings change after each game result? >Shall I calculate all 24 games according to the initial rating of both players? >Suppose we have a match between two players rated 2000; if player 1 wins all the >games, shall I rate him 24 wins against a 2000 player or should I take into >account the rating changes after each round? > >I tried both ways on the CERN Chess Club Elo rating calculator, >http://chess.cern.ch/ratings/elocalc.en.shtml using a progress coeficient of 24, >and the results change in about 6 point. The performance rating is completely >diferent. > >Thanks Vicente, Sometimes we have some very bright mathematicians over here who might answer this but if I would have to say something about it, without knowing what the official rules are, I'd say that you have a problem especially with 100 %, or if you like 0 %, scores. If you make no assumptions about how the ratings are distributed in the population, id est every rating is equally likely, then the winners would all be concentrated around infinity. This would be both their TPRs AND their "most likely ratings" assuming you had a very long match; for calculating the TPR you don't have to know anything about the length of a match. But if the match becomes shorter for the "most likely ratings" you have to go look at the reliability of the original ratings. If these were based on 1000 games (against some "standard" calibrated opposition) and the match just 24 games the TPRs would still approach infinity and zero but the "most likely ratings" would be a lot closer to the originally calculated ratings. If you make other assumptions about how the ratings are distributed in the population the "most likely ratings" will go vary too. For example to calculate the chance that the winner is actually 2400 if the beaten player is 2000 you first have to calculate 1. the chance of finding a 2400 player in the population and then 2. the chance that he could win all 24 games. And for the "most likely rating" 3. the chance that this 2400 player had acquired only a 2000 rating first. Point 2 is straightforward and always the same if you follow the standard elo calculations, but point 1 depends on what population or "pool' of players you are working with. Point three depends also on the pool AND on the number of games used for calculating the first rating AND on the method of doing such a rating calculation AND on the possibility that ratings may change over time... So this "most likely rating" becomes an elusive property if you don't know these characteristics exactly, even if you knew that the elo-system for the rest was a very accurate description of chessplaying abilities. That has nothing to do with the TPRs: with a 24-0 results as far as I know these should be infinity and zero respectively for winner and loser following standard elo-method, not the lineair or some other approximation of it. Probably I have lost all my readers by this point and they'll never read anything I write again! Sorry about my dense formulations this is just a personal and non mathematically precise way I would describe it. Normally I think for TPR you should keep the original ratings of the opponents intact for calculating the average opposition, no matter what kind of approximation you will use then to calculate TPR. Kind regards, Eelco
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