On 6/1/2023 8:42 AM, Bradley K. Sherman wrote:
> Even I don't know what my record would be against the bots
> in 11-pt matches, so let's not argue about that.
Yes, sorry, I got confused about the match length. What I
remembered was that you reported a 40% win rate against GNUBG,
but when I checked, I saw that you were talking about 5-point
matches, not 11-point matches.
On the other hand, the current issue of the USBGF PrimeTime
magazine has an interesting article by Art Benjamin, Richard
Stubbe, and Susan Martonosi, who collected approximately
19,000 matches from Backgammon Studio Heroes, courtesy of Terje
Pedersen. They ran the stats and came to the unexpected
conclusion that while PR difference does a pretty good job of
predicting the win rate, the *match length doesn't matter*.
If D is the PR difference, then their predicted win percentage
for the stronger player (if D >= 1) is
50.32 + 2.23 D
and the match length doesn't enter the formula. (But note that
they only considered match lengths from 5 points to 17 points.)
They don't claim to have the "correct" explanation for their
results. One obvious possibility is that 19,000 matches is not
enough data, or at least not enough high-quality data. Another
thing that's odd, and that I plan to ask Art about, is that they
say that they used GNUBG to calculate PR. I didn't know that
GNUBG was able to calculate PR (of course, it computes Snowie ER
and its own home-grown error rate measure, but PR is defined in
a different way). So maybe they made a mistake calculating PR
(though even so, they probably did calculate something close to PR).
Among their proposed explanations, the one that sounds most plausible
to me (if we assume that match length really doesn't matter much,
at least in the range between 5-pointers and 17-pointers) is that
errors don't affect your match-winning chances much until near the
end of the match. That means that the stronger player is only a
very slight favorite to be ahead by the time the match score gets
down to 5-away/X-away.
In any case, if we are to believe that the data from the 19,000
matches is reliable, then it suggests that your PR is around 5
and that your chances against Stick---assuming Stick's PR is
around 2---would be about 43%, whether it's a 5-pointer or an