Hot hands: You gotta believe!

The NBA playoffs are heating up (and The Heat are at 1 to freakin’ 3 which, in my book, is an awful bet but what do I know?) and sports fans everywhere start hearing about the “hot hands” phenomenon. Who’s “hot?” What player can carry his team to the championship? Who’s playing way above the norm at this critical time of the year?

This topic actually pops up everywhere. Hockey goalies seem unbeatable – they just know where the puck is heading and stop anything thrown at them. Quarterbacks are on fire – pass after pass finds down-field receivers clean in stride. But it’s in basketball that the effect is most prominent. It’s tough to miss those moments where a player can seemingly do no wrong. He’s in a state of grace, on fire, cannot miss. He’s draining 22 footers like they were layups, nailing ‘em from the corners, all net from the top of the key.

Are these moments real? That is, real in the sense that when they occur they are mathematically or metaphysically special? I’m not trying to split hairs; this is a serious question. When an all-pro quarterback seems to be in that ‘zone’ is he really in a zone or is this just the kind of performance we expect to see on a statistically determinable basis? When a guy drains 7 of 8 from downtown is this something special, something transcendental or merely an event that will pop up with predictable frequency?

People who play sports or follow them with any passion swear these effects are real. Basketball coaches issue instructions: “Get Joey the ball; he’s got the ‘hot hand’.” Baseball managers manipulate their lineups to get the guy with the ‘hot bat’ an extra turn at the plate. Golfers enter extra tournaments when they think that they’re ‘striking the ball’ good. Poker pros play more hours or enter more events when they’re ‘running good.’ But is there really a hot hands phenomenon? Are bats really hot? Do poker players really run good? Maybe. Then again, maybe not.

The psychologist Amos Tversky took a look at this issue some years back. He reasoned that if Joey really had a hot hand, then we should see a statistically aberrant performance, one where he made more shots with more regularity than his norm. So Tversky analyzed every shot taken by several dozen NBA basketball players over a full year looking for evidence of a hot hands effect. He found little. Players got ‘hot’ about as often as a random number generator got ‘hot.’

If Joey’s a 42% shooter, we expect to see runs of shots made and shots missed – and we can calculate just how long they should be, distributed over the full year. If another player makes 47% of his shots we should see a different pattern but one consistent with his level of skill. And this is what Tversky found. Sure, there were occasions where Joey hit nine in a row and seemed to be ablaze for an entire half. But these rushes happened about as often as we would expect given that Joey is, overall, a good player who makes a tad better than forty percent of his shots from the floor. So, no hot hands.

Other psychologists did similar analyses in a host of sports and found pretty much the same thing. Quarterbacks got hot about as often as their long term statistics suggest they should. Sure an all-pro like Tom Brady seems to have the hot hand more often than a journeyman backup but, statistically speaking, he should.

But as usually happens in science, when a topic is interesting people do deeper analyses. Follow-up studies suggested that there might be something that Tversky missed. Long runs of baskets or completed passes or shutouts in hockey were occurring more often than one might expect, statistically speaking. But, and here’s the fun part, it wasn’t clear what was causing them. It’s difficult, if not impossible, to tease apart a real hot hands moment from the belief that others have that one is occurring because the latter can produce the former.

If Joey seems to be on fire and if his team mates believe he’s got the hot hand, their behavior changes. They start setting effective picks, trapping opponents allowing him to get free, passing to him in optimal spots on the court. The likelihood of Joey continuing to make shots goes up and his stats defy expectations.

Do we want to conclude that Joey really had a hot hand or that everyone else, by virtue of their beliefs, changed how they play so that it looked like he did? If the hot hands effect is real it’s likely based on a conspiracy of beliefs of the participants.

I like Miami but not at 1-3, no matter how ‘hot’ LeBron is….

Comments

[npc]

First, there's a difference between the "hot hand" and the "better team". The number on the heat seems pretty fair to me based on my math models.
At the same time, the Gilovich and Tversky paper (which can be downloaded here.) is one of my favorite research articles of all time. It did fundamentally new research, it countered the prevailing wisdom, it generated loads of controversy, it spawned dozens of follow-up articles, and it withstood the storm. Tversky has his hand in a lot more important research than this piece, yet this one is special to me.

[Arthur S. Reber]

npc:
I only knew Tversky glancingly. We met at a cog sci meeting where he stunned a room full of very smart people by gently asking a question about an equation that a presenter had put up. A moment of stunned silence followed as we all realized that Amos had dug deeper than any of us and saw a fatal flaw in what looked like, on the surface, to have been a really neat model. It was done without ego and in the spirit of doing good science. He became one of my favorite people that day. He died too soon and would have shared the Nobel with his good friend Danny Kahneman.

There have been some good follow-ups on "hot hands" using Baysean statistics that show that the effect may be stronger and more reliable than Tversky thought. My approach to this was to point out that, while this may be statistically real, it doesn't tell us what factors are responsible.

And, yeah, Miami's a damn good team. I just hate giving odds like those. I'd rather sit on the sidelines and watch the game..... which is what I do anyway. I'm basically a play poker these days.
Thanks for your comment.
AR

[Russ]

You seem to have gone silent in the past year or so in applying Psychological principles and research to gambling topics...

I would really like to see some discussion of cognitive biases and Thoroughbred Handicapping...the Hot Hand applies to the way the Public perceives certain trainers...but frankly, the streaks are *not* an illusion, some trainers have undoubtedly found ways to cheat, and seem unbeatable on some of the circuits.
Still, when it comes to evaluating the true EV of betting on a certain horse/trainer we have to take into account the Odds (determined by the Public's beliefs and biases) and the true probabilities based upon the trainer's, jockey's and horse's skills.
Do you have any energy/interest in discussing this stuff, and writing some guest Blogs or doing some actual research on a website which I will be launching soon?