Paige Miller <[EMAIL PROTECTED]> wrote in message > I dislike binning numbers that are essentially on a continuous > scale. I think methods designed to treat the ELO ratings as > continuous will be more powerful statistically than methods based on > binning. But for the sake of my understanding of your proposal, > let's go with bins.
I defer to your knowledge here, it was just an idea as I don't really know how to proceed otherwise! > Oooh, average of ratios. Another not-so-good idea. Better to compute > a ratio of the total number of wins divided by the total number of > games of everyone in the bin. Would this not just give me some sort of discrete approximation to ELO pdf? > Now you're coming close to stating an hypothesis, without actually > stating one. Of course, figuring out what the distribution of this > "binned-ratio-difference of series" statistic could be a difficult > problem. Thanks ;-) I'll try the example route you suggest Lets take three players; Tom, Dick and Harry who have elo ratings of 1600,1500 and 1400 respectively. Now according to http://tournaments.tantrix.co.uk/ratings/simple.shtml , the ELO ratings can be interpreted probabilistically as follows: Tom would be expected to beat Dick 57% of the time and Harry 64% of the time. Dick would also expect to beat Harry 57% of the time. Now lets imagine they had played each other 100 times, so that the following table could be drawn up: Tom v Dick - Tom has 57 wins, 43 losses Tom v Harry - Tom has 50 wins, 50 losses Dick v Harry - Dick has 57 wins, 43 losses It can be seen that, mirable dictu, Toms record against Dick and Dicks record against Harry are in line (exactly!) with the expected win/loss record. The 'anomaly' seems to be Toms record against Harry - we would expect 64 wins and 36 losses, but we have a 50:50 record. Is this just chance, or is there a 'head to head effect'? If there is an effect, a follow-on question might be how can one modify the probabilistic interpretation of ELO above to account for this new effect. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
