Yes, Virginia, There Is A Hot Hand

Dateline: 12/21/97

The 76ers' Sunk Cost

My basic numbers show that Philadelphia got the best of their recent trade with Detroit. Jerry Stackhouse was not producing in the pros as he did in college. Eric Montross has never gained confidence to score. On the other hand, Theo Ratliff has been a positive surprise and Aaron McKie has a role as a three-point bomber... An ESPN poll says the Sixers gave up on Stackhouse too quickly. Coincidentally, I recently received a scientific study indicating that NBA teams give high draft picks like Stackhouse too long to develop, ignoring their liabilities. More on that later...

DEAR EDITOR: I am 8 years old. Some of my friends say there is no Hot Hand. Papa says, "If you see it in The Game, it is so." Please tell me the truth, is there a Hot Hand?
-- Virginia

VIRGINIA: Your little friends are wrong. They have been affected by the skepticism of a skeptical age. They do not believe except that which they calculate. They think that nothing can be which is not supported by their little numbers. All minds, Virginia, whether they be men's or children's are little. In this great game of ours, man is a mere insect, an ant in his intellect, as compared with the boundless world about him, as measured by the intelligence capable of grasping the whole of truth and knowledge.

Yes, Virginia, there is a Hot Hand. It exists as certainly as love and home court advantage and Michael Jordan exist, and you know that they abound and give to your life its highest beauty and joy. Alas! how dreary would be the world if there were no Hot Hand! It would be as dreary as if there were no Virginias. There would be no childlike faith then, no autographs, no hero worship to make tolerable the excesses of sport. We should have no enjoyment, except in sense and sight. The eternal light with which childhood fills the world would be extinguished.

Not believe in the Hot Hand! You might as well not believe in zone defense! You might get your papa to hire men to count all of the shots of the Philadelphia 76ers, but even if they did not see a streaky shooter, what would that prove? Nobody sees a Hot Hand, but that is no sign that there is none. The most real things in the world are those that neither children nor men can see.

No Hot Hand! Thank God, it lives, and it's on a roll. A thousand years from now, Virginia, nay, ten times ten thousand years from now, it will continue to make glad the heart of basketball fans.

...Skepticism of a Skeptical Age...

Amos Tversky's study on whether streak shooters exist was built on the classic skepticism of a scientist. It is a scientist's job to doubt the existence of something unless overwhelming proof can be generated in support of it. In this way, Tversky did not prove that streaks don't exist. He just stated that there was no proof that they do exist.

In our leap to the conclusion that streaks do not exist, we demonstrate our susceptibility to the skepticism of a skeptical age.

...It Exists As Certainly As Home Court Advantage...

In fact, there is no denying that a home court advantage exists. The reasons for it may not be fully known, but its presence cannot be denied.

Just as having the home court helps a team win, there are real factors that help a player shoot. If Eddie Johnson covers Michael Jordan, you know that Jordan will take him to school. If Eric Montross covers David Robinson, you know that Robinson is going to get a lot of points. You might even say that Robinson is hot when Montross is guarding him.

...If They Did Not See A Streaky Shooter, What Would That Prove? ...

Though Tversky saw no evidence of a hot hand, that does not mean it does not exist. I can generate a sequence of shots where the offense knows a player is hot, but the sequence itself would show no evidence of streakiness.

First of all, let's agree on a test for streak shooting, one that is different from Tversky's:

When you watch a game and you think someone is hot, keep track of their shots and it should show them shooting better than their average. If you think someone is cold, keep track of their shots and it should show them shooting worse than average. Regardless of whether Tversky's tests show that streaks exist, if you can really see when a player is hot and cold, there is information there that we can take advantage of and that teams probably do take advantage of.
This test explicitly evaluates whether we see something real. If we can see something that tips us off that a player is hot, then it exists.

Such a test can lead to a sequence of shots that, by Tversky's test, is not a streak. If what we see occurs somewhat randomly -- like Montross covering Robinson until he picks up enough fouls to go out of the game and a better defender comes in to replace him -- then, even though a team recognizes a streak (recognizes a mismatch), the stats of Tversky's test won't see it.

As a concrete numerical example, say that a team knows when a player is hot, hot meaning that he hits 65% of his shots during this time. He is hot only 40% of the time he shoots the ball. The rest of the time (60% of the time), he hits only 40% of his shots. If the times at which a player is hot is random due to the defense playing him differently, that is immaterial to the strategy of getting the ball to a hot hand. When you simulate this type of sequence, it looks random. It looks like the player shoots 50% and without streaks according to Tversky's test. (An interactive demo is probably more than most people could understand, but if you write to me, I can send you one or the algorithm to do it yourself in a spreadsheet.)

...Making Glad The Heart of Basketball Fans...

In the first round of the NCAA Tournament a few years ago, I began to sense my own hot streak. Every shot seemed to hit the mark. Every pass of mine was converted and returned later. The game felt completely natural. Ours was a great team, better than the sum of the parts. I'd dream at night of how well everything was working, enough that I was only half asleep yet completely rested. I'd dream of playing again the next day.

When I had to stop playing a few months later, the streak ended. It was a fantastic few months. I'd like to believe that there was a reason for the streak and that I can get it back. Calling it just dumb luck doesn't seem to do justice to the many little reasons that made the streak feel so good.

Acknowledgements

Excerpts obviously drawn from the classic Christmas editorial by Francis Church.