By now you’ve probably seen the viral video of Steph Curry draining 105 3-pointers in a row during practice. You’re probably thinking “that guy can shoot well!”, but it’s a lot more than that. Historically, he’s shot an amazing 65% during the NBA 3-point shootout competition, but let’s be generous and say that his 3-point shooting percentage during practice is 80%. To put that in perspective, there are only a few hundred NBA players in history who have a career free throw percentage that high. So, what are the chances, you ask, that someone who shoots with an accuracy of 80% would make 105 in a row? About 1 in 15 billion. Yeah, it was a lucky streak.
Now, there is another explanation which traditionally hasn’t been taken seriously by people in the data wonk profession: the Hot Hand. It’s even been called the Hot Hand Fallacy. There have been several studies concluding that there is no evidence that those of us who feel like we’re on a “hot streak” aren’t deluding ourselves and being fooled by randomness. They have a point that randomness is much streakier than we expect, but I’ve always thought that if we had a controlled environment, the evidence for the Hot Hand would become clear (and not just because I somehow made 32 free throws in a row once). After examining the NBA Three-Point Shootout data, Gary Smith and I showed in our latest book that, given the relatively few contests in history, the mere existence of Craig Hodges 1991 streak of 19 consecutive baskets provides strong evidence in favor of the hot hand hypothesis.
Now, cherry-picking extreme examples is normally not a good way to gather statistical evidence. However, it can be considered compelling if you appropriately take into account how large the number of events there were from which you were cherry-picking. In the Hodges case, this means looking at how many participants there have been in the history of the NBA Three-Point Shootout. There simply haven’t been enough shooters in the contest’s history to expect a shooting streak like that if there’s no such thing as a Hot Hand!
Some other NBA news today indirectly provided another reason to believe in the Hot Hand. Curry just broke the Warriors franchise record for most consecutive free throws made in a row: 61. The NBA all-time record is 97 straight. That’s an amazing number, but how can the all-time streak of consecutive makes from 15 feet be smaller than the number of consecutive makes on Curry’s highlight reel of 3-pointers, more than seven feet further away from the basket?
Once again, I argue that the Hot Hand is the answer. In the NBA, free throws are usually shot in pairs, so players don’t have a chance to settle in and establish a hot streak. Shooting free throws is more in line with the statisticians assumption that each shot is an independent event; whether or not you made your last free throw 10 minutes ago doesn’t affect the likelihood that you’ll make the free throw you’re shooting now.
In order to decide whether or not Curry’s videotaped shooting streak is evidence that the Hot Hand is real, we need to account for the universe of attempts from which his 3-point shooting streak was cherry-picked. Let’s say there are 500 trillion basketball players in the world and that they all shoot 50% from behind the 3-point line (the NBA average is 35%). Now, let’s assume that they’ve each made a videotaped attempt at Curry’s feat once per day for the 13.8 billion year history of the universe (never mind that 3-pointers were invented only 40 years ago). How many times would you expect to see Curry’s feat replicated? About 0.00006 times. Of course, that’s if you assume the Hot Hand is a fallacy.
