Author: Walter Koroljow
Date: 05:08:56 04/17/02
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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 > > >>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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