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Answers @Bob, Dmitriy, Michael, Sebalotek: PR and luck in live matches
Posted By: Jeom In Response To: PR and luck in live matches (Jeom)
Date: Thursday, 21 September 2017, at 7:15 a.m.
@Michael: Interesting. Can I read about this somewhere? Is the difference in winning probability at PR-1 smaller or larger at low levels?
@Bob Koca: The reason for mixing up match lengths is simple: it was not possible to notice any significant difference in winning probability between samples with different match lengths. This is similar to the findings of other experiments I've seen on this forum, but is of course a result of too small samples (if we take for granted that the PR is a perfect reflection of skill). By the way, was your statement about the method sarcastic, or is it actually a natural thing to do? See my reasoning below.
@Dmitriy Obukhov: Yes, of course it sounds fishy, that's why I raised it as a concern. However, you can think about it this way: in each mach there is one winner and one loser. The way the matches were listed in Backgammon Studio is (probably) with the 'submitting player' as Player 1 and the 'opponent' as Player 2 (I do not know this). If running the model using the list of matches as is on BS, the probability of Player 1 winning at equal PR was something like 0.47. Of course, this means that the probability of Player 2 winning at equal PR was approx. 0.53. When adding them together, we get a mean of exactly 0.5 (which is basically what is done when adding a mirror to the dataset). One reason for the strange results might be that there is a bias toward submitting lost matches in which the submitting player have played good and lost? This would of course skew the results, but might also be a reason for why Player 1 in the original sample needs to play with a PR of approx. -2 to have equal winning chances as Player 2.
@sebalotek: Thank's a lot for this! Given that the PR is a perfect representation of skill, the results based on a large sample of matches should of course be exactly the same as the table you constructed. This renders any further work quite useless, if the purpose is not to challenge PR as measuring skill (which would be fun, but I doubt that there is anything to find there, and it would require a tremendous amount of data). However, given that the calculations posted here took an hour to produce, if given access to such data, I would of course give it a try!
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