On 26 Feb 2004 01:31:11 -0800, [EMAIL PROTECTED] (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? > > any help appreciated, with thanks in advance
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. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html "Taxes are the price we pay for civilization." . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
