John Smith wrote: > I was wondering if anyone could help me with what is probably a fairly > basic question. > > I want to investigate the significance of head-to-head records of > chess players, versus their ELO rating. In other words, does player A, > who has lost 3 of 10 games to player B and 7 of 10 games to player C, > have more of a chance of beating player B than player C, if their ELO > ratings were all equal? > > The counter-theory would I suppose be that the head to head ratings > will already be implicitly accounted for in the ELO ratings (along > with games against all other opponents), and that it is the ELO rating > that is therefore significant rather than the head-to-head rating. > > What sort of tests should I look to perform on a database of results > to test this hypothesis?
Statistical hypothesis tests are usually stated more formally, such as the parameter of interest is equal to X, against the parameter of interest is not equal (or less than, or greater than) X. By the way, how can you compare one hypothesis where you state "if their ELO ratings were all equal" to another hypothesis where ELO ratings don't have to be equal? That comparison, as you state it, doesn't make sense to me. Does the ELO system allow you to say that a superiority of 100 points over your opponent leads to a victory Z% of the time? What percent of the time would a superiority of 50 points over your opponent lead to a victory? Before you can test an hypothesis, you will need to be more specific about what the hypothesis is, and what the ELO system predicts. By the way, I don't think the ELO system was set up to be predictive of wins, I believe it was set up to rank players' relative strengths based on past experience, so that they could be seeded into tournaments. -- Paige Miller Eastman Kodak Company paige dot miller at kodak dot com http://www.kodak.com "It's nothing until I call it!" -- Bill Klem, NL Umpire "When you get the choice to sit it out or dance, I hope you dance" -- Lee Ann Womack . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
