Author: Robert Hyatt
Date: 09:52:42 01/15/03
Go up one level in this thread
On January 15, 2003 at 12:07:45, Richard Pijl wrote: >> >>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. > As I have said, that is not a realistic happening for _normal_ rating scenarios. But on ICC it is likely and the problem is that we are now rating _matches_ between a rated and unrated player. Unfortunately there is no real alternative other than to make new players play in a couple of "rating tournaments" before playing individual players in matches, which is doable and would have a better result than any attempt at fixing the provisional scheme which is not broken. >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. Play the 2000 players first. Now what?? > >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. How can you know the expected result _prior_ to having any results to base it on? That is what the provisional rating period tries to establish, and it does so pretty well overall. The above scheme is just as sensitive to who plays who when, while the current provisional rating doesn't care about the order for the first 20 games, to get a baseline established. > >Richard.
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