Author: Chris Carson
Date: 06:15:56 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 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. > >> >> >>>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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