[Bug-gnubg] Ratings as random walks

[Rod Roark]

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.

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

Cheers,

-- Rod

[1] At least this seems intuitively obvious to me.  :-)

On Thursday 12 June 2003 11:30 am, Rod Roark wrote:
> On Sunday 08 June 2003 11:01 am, Rod Roark wrote:
> > On Wednesday 04 June 2003 01:09 am, Joern Thyssen wrote:
> > > ...
> > > It would still be nice to collect some statistics about the rating, so
> > > we can say: "gnubg playing at 2-ply 33% is rated 1900 +/- 40 at FIBS".
> >
> > Here are some stats for the past 4 days of ParlorBot matches:
> >
> > Number of samples  : 436
> > Mean               : 2027.279404
> > Standard Deviation : 19.468276
> > ...
>
> For the past 8 days:
>
> Number of samples  : 921
> Lowest             : 1945.040000
> Highest            : 2069.640000
> Mean               : 2019.892400
> Standard Deviation : 24.716409
>
> Again this is gnubg 0.13.0, 2-ply 33%, "narrow" move filters.
> I'll likely move to the 0.14 weights soon.
>
> -- Rod