Author: Chris Carson
Date: 08:16:30 04/17/02
Go up one level in this thread
On April 17, 2002 at 10:48:03, Walter Koroljow wrote: >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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