# Computer Chess Club Archives

## Messages

### Subject: Re: A question about statistics...

Author: Peter Fendrich

Date: 17:55:33 01/04/04

Go up one level in this thread

```On January 04, 2004 at 17:44:08, Dieter Buerssner wrote:

>I think, I understand the issue you rise. However, 17-3 will be more significant
>than the other results independent of draw. So, still some truth there. I really
>wonder, how exactly Elostat calculates the +/- margins to the calculated rating.
>Does anybody know an URL, where one can read this?

I don't know how Elostat is working but it should be close to:

s=SQRT(W(1-m)^2 + D(0.5-m)^2 + L(0-m)^2/(n-1))
A=1.96 * s/SQRT(n)

where s is estimated standard deviation
n     is number of games
m     is score/n
W,D,L is number of Wins, Draws and Losses respectivelly
A     is the margin of error (for score, not rating points)
1.96  is fethed from the Normal Distribution table to get
95% reliability
SQRT  is the square root

Now we have an 95% interval of scores from m-A to m+A

Compute the ratings for m-A and m+A and that's it.

http://remi.coulom.free.fr/WhoIsBest.zip
and read about why draws doesn't count when finding out who is best. (That's
something else than computing ratings where draws definitely counts)

/Peter

```