Re: [Bug-gnubg] Ratings as random walks

[Rod Roark]

On Sunday 15 June 2003 01:44 pm, Douglas Zare wrote:
...
> Of course the ratings after subsequent matches are correlated, hence the
> observed standard deviation is not accurate. This is also a random walk
> with a restoring force, not an unbiased random walk.

Yes that is clearly the case, and a good way of expressing
it.

> See the discussion of Kevin Bastian's statistics in the appendix of
> http://www.gammonvillage.com/backgammon/news/article_display.cfm?
> resourceid=764 . That article also has a description of the stable
> distribution, assuming that one's opponents are correctly rated. The actual
> standard deviation should be higher.

Like Joern, I do not have access to this.

> Since what you have observed is much
> lower, I don't think you have a representative sample.

Agreed, as SD has been increasing steadily during the 11
days that I've been keeping logs.  Obviously the "restoring
force" will eventually impose a consistent value.  I would
be very surprised to see the bot produce any ratings below
1850 or above 2200.

-- Rod