I'd welcome pointers to statistical models of the following vaguely-specified situation I play tennis. There are probably plenty of people who also play tennis whom I could defeat, if they were chosen at random amongst all players who know how to play and have a racket. However, I could easily point to a tennis player X whom I would little chance (essentially zero) of defeating. (S)he in turn could point to a player Y with the same property. And Y could point to player Z. I'm sure that for a middling tennis player such as me, there must be at least five levels, and perhaps many more, of players with this transitive "I'd have little chance of defeating that person" property Eventually we'd reach Novak Djokovic at the top of the world tennis rankings. There are probably only ten players who have any reasonable chance of beating him in a match today. What I'm looking for is a statistical model of such a situation, which I view as somewhat in common in competitive sports. The closest thing I can think of is the ELO chess rating system. I'm interested in answering questions like this. Say I have two randomly chosen worldwide tennis players X and Y. Let's say X defeats Y twice in two matches. What is the chance X will defeat Y in a third match, if no other information is provided? I'm also interested in (again vaguely-defined) "churn" parameter (ie the mixing of player skill levels over time). For example, in chess it seems to be possible for a player to play at specific level for many years. In tennis, most players begin to fade by their thirties if not sooner -- Thane Plambeck tplambeck@gmail.com http://counterwave.com/