Author: Walter Koroljow
Date: 07:48:03 04/17/02
Go up one level in this thread
On April 17, 2002 at 09:15:56, Chris Carson 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)*400/2 = 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 > >This shows the spread 2300 to 3100 with a 2700 average. Nice simple example. > >You left off the "/2" in your last two examples (check right hand side of "=" in >the next to last example, I put ** next to each). This did not make a >difference since the "win-loss" was 0, but would if that were not the case. > Well, we are both half-right! I left off the /2 in the first statement, but the word "average" implies the /2 in the second statement. By the way, congratulations on your degree and your new profession. Best of luck to you. >> >>> >>> >>>>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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