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Just Wondering...

Posted By: Timothy Chow
Date: Thursday, 27 August 2015, at 4:17 p.m.

In Response To: Just Wondering... (Stick)

Stick wrote:

Do you know how many games/matches you'd have to play to have a meaningful outcome if the difference in PR is .3 or less?

By a "meaningful outcome," I take you to mean a meaningful separation of PR values, not a meaningful win rate. To estimate the answer to your question, one needs some kind of model of the variance in PR from one match to the next. I made a crude stab at such a model a while back. I concluded that the probability that a PR 6.0 player could average under 4.0 after ten 7-point matches was less than 2%. I'm in a rush right now, but later I could try re-running the numbers with PR 3.3 and PR 3.0. A PR difference of 0.3 is much less than a PR difference of 2.0, of course, but presumably the PR variance of a 3.x player is much lower than the PR variance of 6.0 player.

Without running the numbers, my guess is that a moderately large number of matches is required, but not nearly so many as you seem to be implying.

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