Thanks for the reply Jim Im afraid I must be very stupid as I am having problems understanding what you are talking about - it isn't often I wish I was a statistician, but now might be one time ;-)
jim clark <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>... > 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. I don't quite know what you mean by this. In a sense the head-to-head is an estimate of the probability of winning, but is it a better estimate than the ELO ratings difference. Excuse my (probably lamentable!) ignorance, but what are the predictor and criterion sets? > 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 truth I am more interested in the 'temporal prediction', but I would have assumed the two were strongly related. If the H2H improves temporal prediction would it not by definition add to elo ranking, and vice versa? > 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. Correct, there are many examples of limited interactions between players. I am not sure what you mean by the last sentance? > 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 > ... I'm sorry, but my brain is confuddled here ;-) . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
