TomR>I think the number of "levels" depends largely on how much variance we expect in performance from game to game, and how much the game counteracts that variance through "repeated measurement".

In Go, for instance, there are a lot of moves, and the poorer player thus has many more opportunities to make the mistakes that the stronger player can exploit. (I believe Go has many many more levels than almost any other board game.)

In the 50 meter dash, there is probably very little variance and thus one would also expect many levels.

In heads-up Texas Hold'em, on the other hand, the cards themselves introduce a far amount of variance, so there are probably fewer levels.

Tennis I know very little about; how hard is it for a random punter to steal a game from a much superior player?

Elwyn Berlekamp (world class) says that your level in Dots & Boxes is how many theorems you know. TomR>Things get fun when the "is-better-than" relation is not transitive; here, linear rating systems start to fail.

From personal experience in club-level table tennis, intransitivities are a fairly common consequence of incomplete "skill vectors" (e.g., loop, chop, sidespin, power, mobility,...), with the usual problem (e.g., Efron dice) of comparing incomparable vectors.

This is also why the idea if IQ is bogus. --rwg On Fri, Feb 10, 2012 at 10:19 AM, <rcs@xmission.com> wrote:

I'll add one more vaguely-specified question to Thane's list: He estimated that the spread of tennis skill is at least six steps of 'near certain victory', and maybe much higher.

What's the story for other games?

I think Chess has a smaller spread: IIRC, 400 Elo rating points is one Plambeck step, and the Elo spread is 1200 - 2900, only 4.25 Pbk. I'll guess that Go has a bigger spread, while soliciting more information from real players.

Rich

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Quoting Thane Plambeck <tplambeck@gmail.com>:

...

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