I knew it. Admittedly, I always objected on other grounds, namely that basketball shots are not all alike. Sometimes the “hot hand” is just a defensive breakdown leading to wide open threes. Also, it seemed wildly implausible that someone getting fouled hard would have no effect on subsequent free throws, and so on.
Miller and Sanjurjo’s table arriving at 5/12s seems bogus. To quote someone on r/slatestarcodex:
Anyone can easily check there are eight post-heads results available. Four of them are heads, four tails. That's 50%. I think the authors reached 5/12 by averaging the "proportion of Hs on recorded flips" in each scenario, which just seems wrong.
Maybe that commenter is wrong. I'm open to persuasion.
You are totally right about the proportion of H after an H overall. But the question you would face if you throw your coin three times is what's happening in the specific sequence you observed. You observe only one sequence, so it is like sampling one sequence of these 8. In that sequence you are less likely to observe H after H. I appreciate that it is not intuitive at all. By all means, try it by yourself.. The footnote contains Stata and R code. You can run (repeatedly) the R code in this applet: https://rdrr.io/snippets/. The mean estimated in each simulation is around 46%.
I knew it. Admittedly, I always objected on other grounds, namely that basketball shots are not all alike. Sometimes the “hot hand” is just a defensive breakdown leading to wide open threes. Also, it seemed wildly implausible that someone getting fouled hard would have no effect on subsequent free throws, and so on.
Miller and Sanjurjo’s table arriving at 5/12s seems bogus. To quote someone on r/slatestarcodex:
Anyone can easily check there are eight post-heads results available. Four of them are heads, four tails. That's 50%. I think the authors reached 5/12 by averaging the "proportion of Hs on recorded flips" in each scenario, which just seems wrong.
Maybe that commenter is wrong. I'm open to persuasion.
You are totally right about the proportion of H after an H overall. But the question you would face if you throw your coin three times is what's happening in the specific sequence you observed. You observe only one sequence, so it is like sampling one sequence of these 8. In that sequence you are less likely to observe H after H. I appreciate that it is not intuitive at all. By all means, try it by yourself.. The footnote contains Stata and R code. You can run (repeatedly) the R code in this applet: https://rdrr.io/snippets/. The mean estimated in each simulation is around 46%.
The crux is that you leave out the THH by conditioning on H.