Rich Ulrich <[EMAIL PROTECTED]> wrote in message > It has been my impression that the chess rating system is one > of the best developed and best documented "rating systems" > of competition that there is, and it works very well for predictions. > I think you are asking, in one version of the question: > How much information might there be concerning a 'second > dimension' of skill? > Or, How big are the residuals, if you take victories as predicted > by the scores? > > - You don't have much information if you don't have the same > people playing several times. If you are not starting out with > any notion of what the second dimension *is*, you don't have > much leverage, either. > > - Any statistical approach is probably going to have trouble > with 'scaling' here: > First, do you accept the differences to be logistic? or Normal? > > Either one seems *somewhat* reasonable, except for the > following: > After you decide on that, What do you do with zeroes in > the data? - since 0% doesn't exist on either scale.
What about the following approach: I bin the data in terms of the ELO ratings difference, e.g -100 to -90,-90 to -80 etc Within each bin I separate winners from losers to make two 'sub-bins' I average the win/loss head-to head ratio in each of these sub-bins. I now have a series of figures, two for each bin, one is the average previous win% against that opponent where player 1 wins the match and the other for where player 1 loses the match. Some kind of difference measaure then between the two 'series' would indicate how much separate effect there is? Alternatively, bin the data according to head to head records and average the ELO ratings. Any thoughts or comments? . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
