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Error Rates and Edges

Posted By: Daniel Murphy
Date: Tuesday, 25 May 2010, at 7:53 p.m.

In Response To: Error Rates and Edges (Matt Cohn-Geier)

Matt, I'm not sure what your "this" refers to but you mention a 400 point rating difference.

+400 Elo predicts a 91% win rate in backgammon 25-point matches. It's hard to imagine that any 1600 player would have a particular "style" that would enable him to do significantly better than some other 1600 player against a 2000 player. Likewise for 1500 vs 1900, 1400 vs 1800, etc.

Your question (elsewhere above) is also interesting.

Players A & B have the same true Elo.

• A is a 45-55 underdog in an 11 point match vs. the bot.
• B is a 40-60 underdog in an 11 point match vs. the bot.

My answer is certainly yes. Player A may be more successful in exploiting bot errors. But the key word there is "bot."

Suppose we talk instead of human players and pin down what level players we are talking about. A 60-40 edge in an 11 point match = 106 Elo difference. A 55-45 edge in an 11 point match = 53 Elo difference. And let's say a World Class player has Elo 2000. And let's say Player A and Player B are both truly rated 1894. If so, they should both win 40% against WC but Player A wins 45%.

So the question would then be: is it possible that Player A's "style" is such that he does significantly better than his Elo predicts against WC?

I doubt it. 2000 players have few exploitable weaknesses. To the extent that Player A can identify and use them, I'd say Player ought to be able to do the same (and more so) against Player B. But then Player A and B wouldn't be truly rated equally.

I think it more likely that if Player A is more successful against WC than Player B, it's because of psychological factors -- Player may play better against top competition, or Player B play worse, or WC for whatever reason (gets too cautious or rash?) doesn't play equally well against A and B (in the short run, well, we're all in the short run).

Perhaps it's more likely that A and B would do differently against C if C, instead of being world class, was truly rated, say, 1600, and A and B are rated 106 (or 53) Elo points lower. Now all three players have sizable weaknesses in their games, and I suppose it's quite possible that the particular strengths and gaps in their games fit better against some superior opponents than against others.

I believe (not having a copy with me) that Jake Jacob's Fish book, discussing rating systems, mentions the possibility of three players A, B and C, where A tends to beat B, B tends to beat C, but C tends to beat A. Do such eternal rating triangles exist in real life? Maybe, but imagine you are the captain of a team in charge of assigning Player X or Y to play Opponent Z. Thinking over all the players I have known, I think it very doubtful that there would be a Y who is worse than X but whom I would assign to oppose Z, barring any psychological factors that prevent X from bringing his "A" game to the table.

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