There is an effect; there are tests you can do to see if it is statistically significant (I'm pretty sure it would be, in this case; you made it pretty extreme). But without some additional variable to attempt to explain it, I'm still at a loss to say what you could say about the effect other than Tom plays badly against Harry.
Why does Tom play badly against Harry? Does Tom have a style which is poorly matched to Harry's? Was part of the match played while Tom was drunk? Did Harry threaten to beat Tom up if he won? or what? Peter <<< 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. >>>>. Peter L. Flom, PhD Assistant Director, Statistics and Data Analysis Core Center for Drug Use and HIV Research National Development and Research Institutes 71 W. 23rd St www.peterflom.com New York, NY 10010 (212) 845-4485 (voice) (917) 438-0894 (fax) . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
