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Subject: Re: A question about statistics...

Date: 10:26:17 01/09/04

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```On January 09, 2004 at 08:53:58, Peter Fendrich wrote:

>On January 07, 2004 at 12:23:00, Dieter Buerssner wrote:
>> [...]But now assume Player A won all his games with white, and
>>additionally 20 games with black. No draws. Again m=0.51. W/D/L the same as
>>above.
>
>Just to check if I got it right: You mean that A plays 490 white games and 510
>black games?

No. Sorry, a typo above. I meant Player A won additionally *10* games with
black. The other numbers I cited were correct (I really did the simulatatian and
fit with wW=500, bW=10, bL=490, no draws, other numbers are fixed with these

>I think I've sent you the text describing it otherwise give me a hint.

Yes, I have it.

>>No problem with me, to disuss it in email. I just thought, I post an followup
>>here, and try to explain it a bit clearer. Perhaps, we are not the only 2
>>persons interested.
>
>Maybe so, I doubt there are more ...

You are more realistic than me :-) Ricardo and Andrew Dados (?) in the past also
were interested in such discussions. Also Christophe, and of course Remi (whose
paper and program I know).

>>I guess, you are referring to the Elo calculations.
>
>Yes
>
>>I think, the Elo just complicates things, without giving more insight.
>
>:-)
>I wouldn't put it that way. It's the other way around. The -400LG(x) formula is
>a simplification. But is it exact?

Perhaps I formulated bad, again. Actually, I don't think that the calculation of
the margins in "Elo-domain" is bad. But we will be able to do it easily - the
error margin in the score is more basic. About the Elo formula ("400LG").
Actually I thought until very recent, that the Elo formulas use a normal
distribution (and Elo's original approach did). Recently I learned (from
Glickman's (sp?) papers)  that USCF and FIDE use the logistic distribution
instead (the LG formula). I am still puzzled. There is only very little
differnece between the two -it can be seen in the tails, however (when rating
difference is huge - say over 400). I tried to calculate the tables given at
FIDE and at DSB (Deutscher Schach Bund). They neither totally agree with my
calculations (in the last given digit), whether I take the logistic distribution
or the normal distribution (I used a reliable erf() for the later, that has very
high accuracy). The numbers from the normal distribution, seem to fit slightly
better to the numbers given in the tables.

I used for the normal distribution:

p = 0.5 - 0.5*erf(rating_difference/400.)

and

p = 1-1/(1+10^(-rating_difference/400))

for the logistic distribution. The FIDE table is at
http://www.fide.com/official/handbook.asp?level=B0210

It does not mention, how the numbers were calculated (or I have overseen it).

Regards,
Dieter

```