Hi On 27 Feb 2004, John Smith wrote:
> The ELO system does indeed give reasonably accurate estimates of the > probability of winning. A simple logit model based on the difference > in ELO rating will give a reasonable estimate of the probabilities of > players winning. > > I suppose what I am asking, in a sense, is could this prediction be > improved by somehow accounting for the head-to-head record of the two > participants in addition to the ELO rating difference. One challenge is separating your criterion variable from your predictor. In the above logit model, for example, would not the probability of players winning in a given pair be equivalent to the head-to-head record? One approach might be to separate your database into predictor and criterion sets, with the predictors being generated from certain "trials" and the criterion from the other set of "trials. In doing the separation, you would need to ask whether you are interested solely in temporal prediction from past to present/future, or simply in whether given the universe of pairings across time you want to know whether head-to-head adds to elo ranking. If not temporal, then you could randomly divide your observations into the two sets, calculate elo and head-to-head within each of the sets, and then regress (using multiple regression) probability of winning in set A (i.e., head-to-head?) on the elo and head-to-head scores from set B, and vice versa. If you are interested in temporal prediction you would want to divide the observations into historical and "current" sets and do the same calculation. In either of these approaches (and presumably for your logit model), you need somehow to create pairs of players who have met enough times to provide meaningful data for both of your predictors and the criterion. Elo would be less of a problem than head-to-head in that respect. That is, presumably many of the possible pairings of your 600 players ( 600!/(598!2!) = 300 x 598 = 179,400 possible pairs ) have never occurred or occur infrequently enough that you would not have reliable information. And it would probably simplify the statistics to have unique pairs, rather than individuals appearing in multiple pairs. Having 1-2, 1-10, 5-10, ... would seem to introduce some complex dependencies among the observations. So one way would be to see if you could generate a data set of the following sort with sufficient numbers of observations to allow the regressions described above (this assumes H2H is a good proxy for your criterion of probability of winning). ELO here would be the difference in the two players ELO rankings (1-2 or vice versa) and H2H would be the probability one (arbitrarily specified?) player won (e.g., p first player won). Pair ELO-A H2H-A ELO-B H2H-B 1-2 3-5 ... Certainly gets messy as you think about the details, so perhaps there is a more elegant approach. There was at least one link to the mathematics of ELO rankings in google, but it appeared to be unavailable. Best wishes Jim ============================================================================ James M. Clark (204) 786-9757 Department of Psychology (204) 774-4134 Fax University of Winnipeg 4L05D Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED] CANADA http://www.uwinnipeg.ca/~clark ============================================================================ . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
