Author: Eelco de Groot
Date: 17:25:16 08/02/01
Go up one level in this thread
On August 02, 2001 at 19:53:15, Eelco de Groot wrote: >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 Sorry, I'm not following my own rules; the rating of the opponents should stay 2000 in calculating a TPR so a winner would then get a TPR of 2000 + infinity, a losing player 2000 - infinity, this is also approximately minus infinity and not exactly the same as zero. Well I think that's what my calculator would say if only it could work with infinities. Eelco
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