On 14 Mar 2002 01:51:06 -0800, [EMAIL PROTECTED] (John Smith) wrote: [snip, earlier notes. Concerning, predicting who will Win.] > > I understand that this is not necessarily realistic, or at the very > least a simplistic analysis. I suppose there is an underlying > assumption that there is a single number (a 'strength' parameter) > which characterises the likelihood of winning a match.
Right. Your question implies that there is a single score for each competitor. And then, given two scores, there must be a known description of the 'gradient' between them -- the rate than one beats the other, given score A and B. What is the metric of that distance function, A vs. B? If A has a stated chance of beating B, while B can beat C, what is additive: the Odds Ratio? Normal distances? Actually, you could say that it would be one of the very special cases if it works out to be additive. So are you trying to assume one of the very special cases, too? > > Am I being naive in thinking that a situation where A>B (i.e. beats > B), B>C and C>A happens in three individual matches, is not > inconsistent with the simple model - it is just a question of the > probability of A>B, B>C and C>A over one sample is not representative > of the underlying probability? I am not sure of your question. I was saying, it is quite consistent with a physical model - but not with your presumed models - that A beats B most of the time, B beats C most of the time, and C beats A most of the time. See discussion of 'intransitive dice.' For example, http://www.louisville.edu/~seedge01/514/dice.html -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
