Author: Miguel A. Ballicora
Date: 09:42:12 04/17/02
Go up one level in this thread
On April 17, 2002 at 08:08:56, Walter Koroljow wrote: >On April 16, 2002 at 21:13:40, Miguel A. Ballicora wrote: > >>On April 16, 2002 at 18:34:57, Walter Koroljow wrote: >> >>>Of course you can combine TPRs of different programs as per common sense. >>> >>>However, if you wish to be mathematically absolutely correct and precise, all >>>you need do is say, "The average of the programs' TPRs is ...". >>> >>>A little algebra will quickly show that the the average of the programs' TPRs is >>>exactly the TPR of the programs taken as a group. This change of wording gives >> >>Actually, that is not correct. >> >>Regards, >>Miguel >> >> >I believe it is correct. Here is a simple example: two programs play a human >rated 2700. Program 1 wins and program 2 loses. then: > >TPR1 = 2700 + (wins-losses)*400 = 2700+400 = 3100 >TPR2 = 2700 + (wins-losses)*400 = 2700-400 = 2300 >Average of two TPRs = (2700+400 + 2700-400)/2 = (2300 + 3100)/2 = 2700. > >Notice that this is just 2700 + average of 400*(wins-losses). > >On the other hand, the "team" TPR is: > >2700 +(wins-losses)*400/2 = 2700 + (1-1)*400 = 2700. > >This is also just 2700 + average of 400*(wins-losses). > >This illustrates the general case: in both cases the (wins-losses)*400 term is >averaged over all games. Hence the same answer. > >Best regards, > >Walter Yes, you are partially right because that is the way that USCF calculate (or at least used to be, I do not know whether it changed) the initial rating of a player. However, that is an aproximation. IMHO, it is a very gross aproximation. It assumes that the players are reasonably close in rating and the elo table is linearized in that area of the curve. You can have very distorted results when those assumptions are not correct. For instance, the initial rating of Anatoly Karpov in USA was ~2500. Probably still is. I am sure is because he played in an Amateur US ch (I remember this was 3-4 years ago), beat everybody but could not be more than the average of the opponents + 400. Generally, TPRs are not calculated as USCF does for the initial ratings. I have seen that many times that the average of the opponents is taken and the calculation is made, using the Elo table, like you play n games with an "average player" without introducing that 400 points constant. That is a better aproximation. With this type of calculation, your original statement is not correct. That is what I meant. Note that this is still not perfectly correct: What would you prefer if you are 2500? playing against two players 2500 and 500 or playing against two players that are 1500? The perfect way to do it is to estimate your TPR, calculate how many points you expect to get calculating it individually for each opponent and adding it all. Then you make sure that this number equals the points that you really obtained, otherwise, iterate. Nobody does it in this way for obvious reasons. Regards, Miguel > >> >> >>>you an unassailable mathematical position. And I think the common sense meaning >>>is not changed. If you don't want to bother with this distinction, I won't >>>mind. :) >>> >>>Cheers, >>> >>>Walter >>> >>>P.S. Chris - When you say TPR, it would be nice to say whose TPR - Smirin's or >>>the programs'.
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