Author: Walter Koroljow
Date: 10:38:38 04/17/02
Go up one level in this thread
On April 17, 2002 at 12:42:12, Miguel A. Ballicora wrote: >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 > Miguel, I do not like the TPR calculations as they are done for the same reason you do not. For my personal use, I define my TPR as the rating of a player that would be expected to achieve the result I achieved. This is, of course, highly non-linear, a lot of trouble to use, etc. I believe, however, that the term "TPR", in public discussions, means precisely the linearized formula I used above. It is unfair to use a private definition in such a discussion. So I used the usual definition in my post above. By the way, I have done a little analysis on this issue. My result is that the linear approximation is very good up to about a difference of 300 points, and then it breaks down very badly. So I do not think the difference in definitions is significant for the computer-Smirin match (if you are willing to say computers are between about 2400 and 3000). I am a little pressed for time, but I will try to dig up my notes and post them. Best regards, Walter > > > > >> >>> >>> >>>>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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