On Fri, Feb 10, 2012 at 5:43 PM, Guy Haworth <g.haworth@reading.ac.uk> wrote:

Arpad Elo suggested that a 200-pt rating difference on the ELO chess scale should mean that the higher-rated player's expected score in a game should be 0.75 and the lower-rated player should expect 0.25.

Not sure that translates to a probability of the poorer player winning of 1 in 4.

In a game where draws are impossible, it does. Draws, which of course are common in chess, complicate matters. An expectation of .25 can mean I win one game in 4 and draw the rest, or I draw half the games and lose half, or anywhere in between.

 The appropriate cumulative distribution or logistic distribution curve can be consulted to see what the expectations are for larger Elo differences.

See, that's what I don't get. It seems to me (using backgammon instead of chess to simplify by avoiding the issue of draws), that the question "When A plays B, A wins 3 times out of 4. When B plays C, B wins 3 times out of 4. How often do we think A will win when playing C?" Is an empirical question, not a statistical one. What reason is there to expect that the answer given by the "logistical curve" is the correct answer? Why would we expect the answer to this to be the same whether the game is backgammon or tennis? Andy