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Posted By: Maik Stiebler
Date: Tuesday, 8 May 2012, at 10:14 a.m.

In Response To: Thanks! +1 (Christian Plenz)

Let me try to summarize: Your data, like Rick's, confirm what I referred to as conventional wisdom: That Elo differences are magnified in one-pointers as opposed to longer matches under the FIBS formula. We might as well call them Elo_op and Elo_lm and regard them as different (although related) beasts. Another way to look at it would be that there is only one 'true' Elo difference and the FIBS formula is broken, mostly for one-pointers (and if I recall correctly, other servers have used corrected formulas for those), and maybe for other match lengths as well, if the random-walk model doesn't describe the reality well.

The other issue that you bring up is that of PR to Elo conversion for one-pointers and longer matches. It seems that after applying the correction factor, PR difference is of the same order of magnitude for one-pointers and longer matches, although in your case, the correction factor could be a bit higher than 1.5 to achieve a better matching. I don't know if the design goal of the correction factor actually was to achieve the best possible matching.

Anyway, if PR difference after the correction is roughly equal for one-pointers and longer matches, then by applying the same PR-to-Elo-conversion formula to both of them, you get roughly the same Elo difference, so it either has to be Elo_op or Elo_lm or something in between, but it can't be both at the same time. In reality, it seems to be close to Elo_lm. So to derive real Elo performance in one-pointers (Elo_op) from PR in one-pointers, you have to use the XG-corrected PR value, plug it in the 33*PR formula, and then apply a correction factor again for the difference between Elo_lm and Elo_op.

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