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Bearing In Lesson--eye opener for most

Posted By: Timothy Chow
Date: Friday, 27 June 2014, at 4:05 a.m.

In Response To: Bearing In Lesson--eye opener for most (Taper_Mike)

Just to remark again that this is the well-known Hiawatha debate all over again. If we assume that a long rollout is gospel (a somewhat questionable claim, but widely assumed), then a full rollout is an unbiased estimator of the gospel, whereas XGR++ is potentially biased but with lower variance. Neither unbiasedness nor low variance is what you really care about in the end; what you care about is something like the probability that the verdict you deliver is correct (where the verdict will be something like, "Plays A, B, and C are ranked in that order, with the equity differences to three decimal places being such-and-such"). Either approach could give you the higher probability depending on how badly biased the biased estimator is and how inefficient (i.e., high-variance) the unbiased estimator is.

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