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Variance reduction is unbiased but may be skewed

Posted By: Timothy Chow
Date: Saturday, 11 April 2015, at 4:19 p.m.

In Response To: Variance reduction is unbiased but may be skewed (Maik Stiebler)

Maik Stiebler wrote:

If the luck is skewed, it doesn't follow that the luck-adjusted aka varianced-reduced result is.

Yes, that's true. Still, my intuition is that the non-VR estimate will tend to be skewed, and it seems a bit optimistic that the skew will be perfectly cancelled out by subtracting off the luck.

Although as I think about it further, it occurs to me that perhaps the fact that what's unlucky for my opponent is lucky for me may cancel out most of the skew already.

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