Let's say I have a database of a lot of (thousands) chess games. In chess, every player have a rating, called Elo that gives an estimation how strong is this player. If we know the the Elo ranking of both players, we can give an estimation of the probabilities of the possible outcomes of the match. In theory, a player whose rating is 100 points greater than their opponent's is expected to score 64%.
This is theory. The player's true skill can be different. E.g. if he/she is really tired, or out of practice, his/her true skill will be lower than his/her Elo. So for every game I have an estimation (if we don't count the draw, it's pratcically a simple binomial experiment) of the probability of the different outcomes, and the outcome itself. Is there a statistic method, with which I can verify how accurate is this estimation?
I need something that can tell how accurate is the method of estimation not just disprove a null hypotesis that it doesn't have anything to do with player's true skills.