{"id":1528,"date":"2015-11-10T23:20:20","date_gmt":"2015-11-11T05:20:20","guid":{"rendered":"http:\/\/blogs.ams.org\/blogonmathblogs\/?p=1528"},"modified":"2015-11-10T23:47:08","modified_gmt":"2015-11-11T05:47:08","slug":"fallacy-of-the-fallacy-of-the-hot-hand","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/blogonmathblogs\/2015\/11\/10\/fallacy-of-the-fallacy-of-the-hot-hand\/","title":{"rendered":"Hot Hands and Tuesday’s Children"},"content":{"rendered":"
\"Image:<\/a>

Image: Neon Tommy, via Flickr. CC BY-SA 2.0.<\/p><\/div>\n

People, especially sports fans, seem to believe that players can get \u201chot,\u201d that they will hit more baskets (or succeed in whatever metric is of interest in their sport) more after a series of hits than after a series of misses. We statistics-savvy types are far too sophisticated to believe something like that, though, which is why we call it the fallacy of the hot hand<\/a>. In 1985, Thomas Gilovich, Amos Tversky, and Robert Vallone wrote a paper suggesting\u00a0that the \u201chot hand\u201d doesn\u2019t exist; it\u2019s just a misinterpretation of the natural streakiness of independent events. But a few months ago, Joshua B. Miller and Adam Sanjurjo published an article that claims to find an important flaw in the 1985 paper. Perhaps there is a hot hand after all!<\/p>\n

I\u2019ve read several posts and articles about the fallacy of the fallacy of the hot hand recently. Jordan Ellenberg was on the case for Slate<\/a> with a good explanation of the flaw (the moral of the story: averaging ratios is a dicey prospect), and George Johnson wrote about it for the New York Times<\/a>. I also enjoyed the G\u00f6del\u2019s Lost Letter<\/a> post about the problem, complete with a suggestion for fixing it.<\/p>\n

Andrew Gelman has the most extensive coverage of the hot hand with four<\/a> posts<\/a> about<\/a> it<\/a> in the past few months and a nice one from 2014<\/a> as well.<\/p>\n

One thing I really like about Gelman\u2019s writing in general is thefact that he emphasizes effect size so much. He wrote,\u00a0\u201cA better framing is to start from the position that the effects are certainly not zero. Athletes are not machines, and anything that can affect their expectations (for example, success in previous tries) should affect their performance\u2014one way or another.\u201d To me, this puts the hot hand question into better perspective. (On the other hand, it also makes me want to give up\u2014how can we possibly untangle all the contributing factors to any aspect of human behavior or performance? I suppose that\u2019s why I\u2019m in math and not psychology.)<\/p>\n

The problem Miller and Sanjurjo\u00a0found with the earlier research boils down to a fairly simple observation about probability, so posts about it eventually spill into questions about coin flips and boys and girls born in different families. Steven Landsburg writes about boys, girls and hot hands<\/a>, comparing the problem with the Gilovich, Tversky, and Vallone\u00a0paper to a probability question about the ratio of boys to girls in a village where families stop having children when they get a boy. I\u2019m not sure I quite agree with him that the situations are analogous, but he has a good explanation of the hot hand issue, and there are some interesting threads in the comments.<\/p>\n

It seems that these probability discussions tend to\u00a0spill into the dreaded questions about boys born on Tuesdays. I have always bristled at these types of puzzles\u00a0because they feel like semantics exercises rather than probability exercises. Once again, Jordan Ellenberg writes about them for Slate<\/a>, leading off with this hilarious exchange:<\/p>\n

Toby and Marla are playing a game with coins, because that\u2019s what people in math problems do. Toby flips a fair coin three times, out of Marla\u2019s view. \u201cDid you get any heads?\u201d Marla asks
\n\u201cYes,\u201d Toby says. \u201cFor instance, the second coin came up heads.\u201d (Because that\u2019s how people in math problems talk.)
\n\u201cI\u2019ll bet you the next flip after that came up tails,\u201d Marla says.
\nIs this a good bet?<\/p><\/blockquote>\n

Ellenberg\u2019s point is that puzzles like this are<\/em> psychological to some extent rather than mere exercises in probability\u2014the right answer depends on our assumptions about how people communicate about coin flips or children and when they were born (mod 7). He also points to a great post\u00a0by Tanya Khovanova about sons born on Tuesday<\/a>\u00a0which she followed up with an invented dialogue about the problem<\/a>. I think I will refer to her posts the next time someone tries to trick me with a riddle from that genre.<\/p>\n

Do you have any sons born on Tuesday? If so, what is the probability that you also have a daughter? Does she tend to make more baskets after\u00a0making a few in a row, or does her basketball shooting record support the null hypothesis?<\/p>\n

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People, especially sports fans, seem to believe that players can get \u201chot,\u201d that they will hit more baskets (or succeed in whatever metric is of interest in their sport) more after a series of hits than after a series of … Continue reading →<\/span><\/a><\/p>\n

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