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PR differencies and winning ratios

Posted By: Rick Janowski
Date: Sunday, 6 May 2012, at 3:09 p.m.

In Response To: PR differencies and winning ratios (Maik Stiebler)

Maik, very interesting points you have made!

The main reason I think an approach adopting unequal METs is potentially superior to the normal ELO approach is the latter’s use of ”random walk” theory to determine the relative value of matches of length less than 25 points (the baseline value the elo model assumes is equivalent to a chess match). Random walk theory suggests that the relative value (or difficulty in winning) a match is proportional to the square root of the match length. Although this approach appears to be reasonable, it does not take into account the general effects of the doubling cube or the Crawford rule, which the MET approach does attempt to tackle.

With regard to the 52% - 48% edge predicted by the “Fish” MET for a 100 elo advantage at DMP (and 52.9% - 47.1% edge using elo formula), I definitely agree with you now I think of it. I don’t have any massive data, but from my own long-term data playing 1-point matches on GridGammon and FIBS, it would appear that a 3 pr edge (corresponding to 100 elo roughly) would tend to make the superior player a 53.5% favourite at DMP.

Interestingly, I checked through Danny Kleinman’s coverage of Norman Zadeh’s mid 1970s mathematical analysis of skewed match scores in “How Can I keep from Dancing” (Zadeh’s ground-breaking work is also discussed in "Can a Fish Taste Twice as Good?"). I carried out an analysis initially of the 15 away 15 away match scores (that’s the extent of the data) and matched these against equivalent points on the “Fish” METs to estimate corresponding elo differences for the Zadeh Charts. There appears to be very good correlation between the Zadeh and “Fish” METS for 7 to 15-point matches, but significant deviation for the lower match scores with Zadeh predicting larger edges for the superior player. For DMP, the Zadeh charts appear to predict the player with the 100 elo advantage winning 54.3% of games (cf. 52% from the “Fish” MET).

The construction of the “Fish” MET tables adopted a significant number of assumptions and a considerable amount of trial and error. I suspect the equity values for low match scores may be particularly sensitive to the assumed parameters/algorithms related to varying gammon rates (between favourite and underdog) and the assumed values for 2 away 2 away equities. This may partially explain the poor correlation between the Zadeh and “Fish” METs for short match scores.

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