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win probability for a PR difference and match length

Posted By: Maik Stiebler
Date: Friday, 21 September 2012, at 5:25 a.m.

In Response To: win probability for a PR difference and match length (Chuck Bower)

For one-point-matches it is simple: Between any two players, the winning probability (wp) of the favorite is a linear function of q=(the absolute value of their difference in average Snowie style ER)*(average number of plies in their matches).

I think replacing ER with PR doesn't make the statement about linearity totally incorrect for practical purposes.

Average number of plies in a match surely depends on the playing styles of the opponents to some degree. Between approximately equal opponents, my intuition is that the number of plies tends to be larger the weaker they are.

Elo difference is linear in ln(wp/(1-wp)), which is reasonably close to linear in wp for, I'd say, 0.4<wp<0.6.

Actually, wp=0.5+q/1000. This does mean that a surprisingly low upper limit of difference in average Snowie style ER is established at 500/(average number of plies).

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