## Bayes Rule and Hot Hand

https://www.thecut.com/2016/08/how-researchers-discovered-the-basketball-hot-hand.html

The well known Hot-Hand is the event where if someone experiences a successful outcome, it is supposedly more likely for them to experience success in later attempts. Over the years, researchers such as Tom Gilovich (Cornell University), have dismissed the phenomenon as fallacious. The idea of the hot hand phenomenon comes from basketball, where we some of the best shooters in the game often go on remarkably successful shooting streaks, and basketball fans such as myself often believe that if he’s got the ball again, he’ll likely make another shot. However when professor Gilovich was a graduate student he and two professors, showed that there was no evidence for a such a pattern, the probability of making a shot given that you made a few in a row just before, does not increase. « past success doesn’t predict future success, and that hot streaks can end, randomly, on any shot attempt. » The experiment run in the paper was replicated several times until recently, in « a paper presented at the 2014 MIT Sloan Sports Analytics Conference by Andrew Bocskocsky, John Ezekowitz, and Carolyn Stein. » The trio observed that « All else being equal, they found that an NBA player who hits four shots in a row is about 2 percent more likely to hit his next one than one who has hit just two of his last four shots », in other words, 45% FG shooter turns into a 46% shooter after 4 made shots. Another paper from researchers in Europe, adjusts the numbers from Gilovich’s original paper to account for conditional probabilities of finite shot attempts, and they observed that: the estimate of the hot hand effect in the 26 collegiate players studied by Gilovich and his co-authors went from effectively zero to “around 12 percentage points” Which can be the difference between an average NBA player, and a world class shooter. The underlying concept of this fallacy is conditional probability, are shots independent from each other, or can a series of successful shots after the probability of success of the following one. We used Bayes’ Rule to study human decision making, given the information they have, and in some of the papers mentioned in the article, it is said that players on a shooting streak tend to take tougher shots due to higher confidence, and defenders tend to beef up their defense because they also believe the shooter has a « hot hand», which I believe is a type of information cascade.