Author: Richard Pijl
Date: 09:07:45 01/15/03
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> >How can it be? The order of the games is going to influence the rating >significantly since more recent games have more weight than earlier games. > That is not what he suggested. The difference in calculating is very small, but in extreme cases a very different result What Miguel suggested is to calculate the expected result for each game for an assumed rating, and then add all those expected results together. If the real result is higher than this sum, try again with a higher assumed rating, if it's lower, try again with a lower assumed rating until the best approximation is found. The advantage is quite clear when using an extreme example: Suppose you play: 9 games against a 1000 player with 50% 1 game against a 2000 player with 0 % score 45% with average opposition 1100 -> TPR just below 1100 Let's say we play 5 more games against the 2000 player. Score is now 33%, average opposition 1400 -> TPR rises to somewhere around 1250 if I'm not mistaken. Now compare with Miguels scheme. Start with the assumed rating of 1000: 9x against 1000 -> expected result 4.5 1x against 2000 -> expected result 0.01 (or something like that, very small) This is very close to the real result. Now the additional games: again assume a rating of 1000 9x against 1000 -> exp. result 4.5 6x against 2000 -> exp. result 0.06 Again, quite close to the real result. As far as I know rating calculation for established ratings is done in a similar way to Miguels suggestion; not taking the average of the opponent's rating, but base it on the sum of expected results instead. Richard.
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