I started reading the book “Thinking, Fast and Slow“, by the Nobel laureate Daniel Kahneman some months ago, and, even if I am slow progressing with it, I find it extremely interesting.

A recurring topic when reading about how our psychology deceives us is when thinking about probabilities. In this post I wanted to write about a paper he refers to in the book: “The Hot Hand in Basketball: On the Misperception of Random Sequences” [PDF, 1MB], by Thomas Gilovich of Cornell University (1985).

If you have actually made the exercise of coin-tossing several dozens times or have gone several to a casino and watched roulette results, you will believe without effort that seeing long streaks of a certain event (several heads for the coin, over a dozen reds or three 32 in a row for the roulette) is part of the randomness of those games. Basketball players and fans get it consistently wrong when believing in hot hands, and that is precisely what the paper from Gilovich is about and it is a wonderful reading.

It starts with a survey among basketball fans, who no doubt believe in hot hands being behind streaks: 91% believed a player has a better chance of hitting after having converted 2 or 3 throws. They even ventured into assigning probabilities. For a player with 50% in field throws they said the chances of :

• hitting after a converted throw were 61%,
• missing after a missed a shot, 42%.

Then he studied the performance of Philadelphia 76ers players (Julius Erving among them) during the season, carefully analyzing the chances of a each player hitting or missing a throw after having missed or hit the previous one, two or three consecutive throws. The results are clear, they do not support the existence of such “hot hands”, they are random. In fact, on average, the chances of hitting after a hit were always lower than the field score % of the team while chances of hitting after a miss were higher and higher than the ones of the supposedly hot hands.

He analyzed the numbers of runs (streaks, like the several heads or tails in a row for the case of a coin) and were not different that what could be expected randomly.

He went on to analyze whether the different players had more cold or hot nights than what can be expected by statistics… also discarded.

Of course, in field throws the author understood that there were many variables at play: for instance, if a player had hit 2 consecutive throws the defense might be harder on him… to eliminate those possible factors influencing results, he went to study free throws, in this case taking the figures from Boston Celtics (Larry Bird among them) and NY Knicks. Guess what? No hot hand in free throws either: there were even more players scoring after a miss than the other way around (but again, nothing statistically significant).

He went even further: he made a controlled experiment with college players in which they threw 100 shots from a distance in which their scoring success was 50% (different distance for each one). Throws were made without opposition but from different position each time. Players got paid according to the hits and could bet higher or lower money each time depending on whether they believed that they were having a hot hand… this, again, proved that there were no hot hands and what’s more: players did believe in those hot hands and were completely unreliable in predicting their next throw chance of success.

The paper has only 21 pages: I encourage anyone who likes psychology, statistics or basketball to read it, its wonderful.

I thought that to conclude this post with a funny note, I could link the following short video of Shane Battier’s “clear” hot hand in the first game of this year’s NBA finals:

Impressive, 3 consecutive 3pt-throws converted in the first quarter!

A difference between now and 1985, when the professor wrote his paper, is that now we don’t need to ask the team statistician about the figures, but NBA site records all of them. I went to check what happened to Shane and his hot hand in that match. After those 3 throws converted, he attempted other 3 in that match: he missed 2.

Still, he had a 66% on 3pt throws that night… what could be a hot night. I went to check his percentages during the season and career. During the finals he made a 0.577%, remarkable; during the whole of the play offs, 0.382% in 3pt. And guess what is his average career (13-years) percentage score for 3pt throws: the same 0.382% he showed in the play-offs. That streak you saw was nothing but the random streak expected from Shane.