Tuesday, October 27, 2015

More on Miller & Sanjurjo

Edit: Jonathan Miller was nice enough to explain my error in interpreting their claim. See below. 

I wrote last week about Miller & Sanjurjo (2015), a working paper which shows how taking unweighted averages of ratios of conditional proportions of success (conditional on previous success) can lead to a biased estimate of the true conditional probability. I then claimed that this result does not extend meaningfuly to the context that they're trying to extend it to: the "hot hand" in basketball, particularly Gilovich, et al. (1985).

Various people smarter than me, notably Andrew Gelman, disagree. They think that the Sanjurjo & Miller critique matters even for the sample sizes considered by Gilovich et al.

Tuesday, October 20, 2015

Are coin flips memoryless?

There's a working paper going around by Miller and Sanjurjo, cited in a New York Times article, that seems to be arguing the impossible: that, in a sequence of flips of a fair coin, the probability of flipping heads is smaller than 1/2 if the previous flip was heads.

The working paper argues that this is relevant to the "hot hand" debate. E.g., is a basketball player more likely to hit his next shot if he hit his previous shot? The seminal paper in this literature, Gilovich, Vallone, and Tversky (1985), found that the conditional probability of success given previous success was close to the unconditional probability of success, concluding that each shot was roughly independent. But if the laws of probability as we know them are wrong, and independence would somehow imply a decline in the conditional probability of success given previous success, then a finding of conditional probability equal to unconditional would actually be evidence in favor of the hot hand hypothesis.

This claim, for lack of a better word, appears to be wrong.

Edit: See my most recent entry for why I was misunderstanding Miller & Sanjurjo's claim with respect to the Gilovich, et al. study. Basically, I was looking at the wrong part of the Gilovich paper! My exposition of the Miller & Sanjurjo result is still valid, though.