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Suggested Idea for Performance Grading

Posted By: Timothy Chow
Date: Monday, 6 October 2014, at 10:42 p.m.

In Response To: Suggested Idea for Performance Grading (mamabear)

mamabear wrote:

I realize this is just an example you are using, but to me the significant issue is that one player who tends to play more games of types the bot misevaluates at the lower ply, where it now evaluates the luck, will be affected for good or ill more than one who doesn't. That will never converge until the bot is made perfect--and then VRR will work fine.

I don't understand your argument here. In your scenario, the VRR will still be correct on average for both players. The convergence to the average will be slightly slower for the misevaluated player, meaning that the variance in the bot estimates will be larger. But there will be no systematic bias against anyone. The person who gets affected for good more will also get affected for ill more, in a way that balances out. This is just what it means, mathematically, when we say that luck is unbiased. It is unbiased even if the bot is imperfect.

This is not true for PR, which can systematically discriminate against some players if the bot is not perfect.

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