# NCAA Stars Really Can Have a "Shooting Streak", Mathematicians Argue

The Oregon Ducks are having a very good NCAA tournament, thanks in part to the skills of star guard Tyler Dorsey. The sophomore is performing the best he has all season, shooting at a 62.4 percent average from the field and at 57.8 percent from the three-point range. Some might say that Dorsey has a developed a “hot hand”, as he seems to get better every game. A pair of economists are on a mission to prove that it’s not such an improbable thing, even though other statisticians have argued that having a shooting streak is a mathematical fallacy.

In an article published Sunday in *The Conversation*, professors of economics Joshua Miller and Adam Sanjurjo discuss their 2016 working paper, which argues that the hot hand fallacy may be, in itself, a fallacy.

Here’s the backstory: For the past three decades, mathematicians and behavioral economists have argued that having a hot hand isn’t possible and what people are actually seeing when they watch basketball are just imaginary patterns within randomness. Even the NCAA hosts an article on its website that says winning streaks are “simply illusions in sports.” Those who dispute the idea of a hot hand compare it to flipping coins: With a fifty-fifty chance, flipping a heads five times in a row isn’t that difficult *if* you flip that coin 700 times. An occasional streak doesn’t mean that an actual pattern is forming and has the momentum to keep moving.

But Miller and Sanjurjo argue that this way of thinking is *also* prone to selection bias.

In their review and analysis of a 1985 paper that famously first made the case that streak shooting in basketball wasn’t real, they take issue with the idea that a 100 shot outcomes from a player could equal a point-or-no-point in the same way a coin would show heads or tails. In *The Conversation*, they write:

Our surprising finding is that this appealing intuition is incorrect. For example, imagine flipping a coin 100 times and then collecting all the flips in which the proceeding three flips are heads. While one would intuitively expect that the percentage of heads on these flips would be 50 percent, instead it’s less. . . To visualize this, imagine the researcher taking these collected flips, putting them in a bucket, and choosing one at random. The chance the chosen flip is a heads — equal to the percentage of heads in the bucket — we claim is less than 50 percent.

Once they eliminated the assumption that the chances of getting heads or tails in a coin toss are really fifty-fifty, they were free to interpret the basketball data as showing that when players make three shots in a row, their odds of making the next basket increase by six percentage points. That’s not a *huge* difference — but it does support the idea that a hot hand isn’t a fallacy. Still, this type of “winning streak” is still a contentious topic in statistical circles today, but at least now you can say someone like Dorsey has a hot hand and have actual research to back it up.