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Subject: Re: Proving something is better

Author: Peter Fendrich

Date: 08:03:14 12/20/02

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On December 20, 2002 at 04:10:35, Rémi Coulom wrote:

>On December 19, 2002 at 19:28:01, Peter Fendrich wrote:
>>
>>I did, some 15-20 years ago, in the Swedish "PLY" a couple of articles that
>>later became the basics for the SSDF testing.
>>A year or so ago you posted a question about how to interpret results with very
>>few games. In a another thread I posted a new theory for this as an answer
>>"Match results - a complete(!) theory (long)".
>>I also made a program to use for this that can be found at Dann's ftp site.
>>/Peter
>
>Hi Peter,
>
>If you had not noticed it, you can take a look at a similar program I have
>implemented:
>http://remi.coulom.free.fr/WhoIsBest.zip
>Basically, I started with the same theory as you did, but I went a bit farther
>in the calculations. In particular, I proved that the result does not depend on
>the number of draws, which is intuitively obvious once you really think about
>it. I also found a more efficient way to estimate the result. I checked the
>results of my program against yours and found that they agree.
>
>Rémi

Hi,
For me it's not so obvious that you can through the draws out.
I just took a short look at your paper and maybe I misunderstood some of it.

Take this example: A wins to B by 10-0
Compared with: A wins to B by 10-0 and with additional 90 draws.
Not counting the draws will get erronous results.

The results between our programs shouldn't agree, I think, because I heavily
relies on the trinomial distribution (win/draw/lose). One can use the binomial
function (win/lose) and add 0.5 to both n1 and n0 for draws. That will probably
give a fairly good approximate value but the only correct distribution is the
trinomial.

/Peter



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