Author: Robert Hyatt
Date: 18:44:52 01/15/03
Go up one level in this thread
On January 15, 2003 at 17:27:23, Miguel A. Ballicora wrote: >On January 15, 2003 at 15:25:41, Robert Hyatt wrote: > >>On January 15, 2003 at 13:03:16, Miguel A. Ballicora wrote: >> >>>On January 15, 2003 at 12:52:42, Robert Hyatt wrote: >>> >>>>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?? >>> >>>To be honest, I do not understand what you don't understand. >>> >>>4.5 + 0.06 = 0.06 + 4.5 >>> >>>What is the relevance of what game was played first? >> >>The way you are proposing, I assume that after playing 6 games, you are going to >>use >>_that_ as my "official rating". But what will it look like after 8 games? >>Until you > >You recalculate with 8. >Note that in the present scheme (USCF), a recalculation takes place, BUT, since >it is an average you can use an aritmethic trick not to recalculate. That is why >it was most probably chosen at the beginning. Today that is not a good excuse. > >Miguel The interesting question, whose answer might convince me your idea is better, is what I suggested earlier. Pick a tournament with some known players. Take one and pretend he started with _no_ rating. Take the tournament results he had, round by round, and calculate his rating _both_ ways. When you finish the tournament, see which rating is closer to his actual post-tournament rating as computed by the Elo formula used by FIDE. Do this for every player in the event, one by one, and do it for multiple events, so that abnormal/atypical results don't inflate anything. The approach with the smallest sum-of-square error term is the best one to use...
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