http://andrewgelman.com/2015/07/09/hey- ... -hot-hand/

Relevant since we've had several discussions of streakiness on the boards.

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I must be really stupid, because the article is too technical for me.

What does it all mean?

Any real discussion of the question is going to be technical. Math is involved, because necessary to calculate the expectation of streaks (winning or losing) based on the null hypothesis "just chance"

Let me give you an example how naive thinking about the problem can lead us astray (NOT the same question, but you will be able to see why "math matters")

Suppose we start with 64 contestants and a knock out tournament of six rounds. It isn't unlikely that somebody will win six games in a row. It is CERTAIN. Doesn't matter if the individual contests had the winner decided by skill/outcome of the game or pure random chance like the flip of a coin. SOMEBODY (and exactly one somebody) will win six in a row.

Not only that, but the worst possible losing streak is one game.

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The article is particularly unclear and unhelpful. Look at the table on page 5 of the actual paper and you should understand what's going on. Basically because you're flipping a coin 4 times in a row, and looking at streaks only in those 4. Then repeating again, you add some bias to your experiment. There is nothing particularly surprising or that requires deep maths to understand.

Well, that's the way that I would approach the problem, looking for streaks. Maybe I missed something in the discussion on Gelman's site, but my impression was that neither the original researchers, who failed to find evidence for the "hot hand", nor the current researchers, took that approach. Apparently the current researchers found a flaw in the original methodology. Without having read either of the papers, I hesitate to say more, but maybe somebody can fill us in.

Edit: Here is a quote from Gelman's site, quoting the new researchers about the methodology of the old researchers:



Computing the relative frequency of heads on certain flips is not the same thing as checking the frequency of streaks of different lengths. I don't know why they did not take that simple minded approach, but apparently none of the researchers did.

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The "flawed methodology" is simply calculating probabilities with an incorrect weighting of the data. In the coin flipping experiment, the correct probability can be calculated by considering each occurrence of HX as an independent trial, with possible results HH (success) or HT (failure). What the authors seem to want to do instead is to consider each sequence of four flips as a trial, calculate the probability of HH versus HT independently for each such trial, then average these probabilities over all trials. This procedure is mathamatically incorrect -- giving each trial sequence equal weight when averaging leads to a biased and incorrect result. The correct result can be obtained by giving each trial sequence a weight equal to the number of HX occurrences in that sequence.