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BGonline.org Forums
ELO
Posted By: Rich Munitz In Response To: ELO (Bob Koca)
Date: Wednesday, 16 December 2009, at 9:25 p.m.
"The Elo formula does not care in the least what the absolute ratings are - only relative ratings, and these two players must produce win percentages in the long run to match the Elo formula by definition." -- No. What may happen is that the ELO formula overstates the underdogs chances for a small ratings difference but overstates it for a large difference. There is no reason to think it is exactly correct for a given ratings difference. --
I cannot say whether or not you are correct here regarding the magnitude of relative rating differences. The formula assumes that squaring the match length has the same effect on expected winning chances as doubling the Elo rating difference. Clearly the match length assumption is just that. It is beyond dispute that lengthening the match favors the stronger player, but I don't quite follow why it should vary with the square root of the match length. So let's therefore say that all rated matches were exactly 25 points to eliminate a variable. As for Elo difference, the formula is defined recursively based on itself. I have no problem believing that a rating system would accurately predict win rates over the entire range of ratings differences if the ratings outputs were specifically designed to make this true. Under the 25-point match simplification, there is exactly one input to the formula: rating difference, and exactly one output: expected win %. Is the formula simply a self-fulfilling prophesy by design? I'll leave it to the mathematicians to determine if indeed this is true.
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