Re: [Bug-gnubg] Ratings as random walks

[Joern Thyssen]

On Sun, Jun 15, 2003 at 06:54:09AM -0700, Rod Roark wrote
> Joern, I'm realizing that the standard deviation of a FIBS
> rating increases with the number of matches played, so it's
> not going to be meaningful to publish it in isolation.
> 
> For some theory behind this, consider that the rating is a
> type of one-dimensional random walk[1], since each new rating
> must be close to the previous one.  There's some academic
> discussion at http://www.chm.uri.edu/urichm/chm531/walk/walk.html,
> and in particular the statement:
> 
>   Equation (35) implies that the standard deviation of
>   the random walk probability distribution function grows
>   as the square root of the number of steps.

Yes, but to get the 95% confidence interval you should devide by the
square root of the number of steps (following the discussion last week).

> And the latest numbers, in case you are interested:
> 
> Number of samples  : 1245
> Lowest             : 1945.040000
> Highest            : 2116.510000
> Mean               : 2029.861751
> Standard Deviation : 29.786614

Hence the 95% confidence interval is around 1.7.

Jørn