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This touches on a question I have been evaluating. I am suspicious of
the fibs rating forumla in the way it accounts for match length. I have
collected a lot of match results and checked empirically whether the
winning probability as predicted by the FIBS rating formula actually
matches the observed winning probability for a given match between
players of known ratings. I sampled the players ratings before recording
any matches so that the random errors in the ratings would be uncorrelated
with with the outcome of the observed games. Only matches where both
players had at least 1000 experience points were included. Currently
the number of recorded results is as follows:
1 point matches 19926
3 point matches 12036
5 point matches 8621
1, 3, and 5 account for 90% of all matches.
I then took the fibs ratings formula for win probability:
P = 1/(1 + 10^(D*sqrt(N)/2000))
Rather than using the match length for N, I used an effective
match length where the effective match length was chosen so
that the formula gave the best fit with the observed data.
The results were what I expected only more extreme. The effective
match lengths which gave the best fit were as follows:
match length effective match length
---------------------------------------------------------
1 1.6
3 1.6
5 2.1
Due to the limited number of matches recorded, the standard error
on these effective match lengths is about 0.25 . If anyone notices
zbest lurking on fibs, he is collecting more data to try to get
a more accurate fix on these numbers.
These numbers suggest that a 3 point match has exactly the same
skill component as a 1 point match, and a 5 point match only
slightly more.
I am at a loss to explain these numbers, but the implication is
that if you want to increase you rating, play 1 point matches
agains the weakest opponents you can find, and play long matches
against the strongest opponents you can find. It also suggests
that if we want to make backgammon more a game of skill and less
a game of luck, we should eliminate the doubling cube.
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