Statistics

# Yes, There Is A Hot Hand In Basketball

On the Second of March in the Year of Our Lord One Thousand Nine Hundred Sixty-Two, well before the sport became another venue for pencil-necked political correctness, a basketball player for the now-defunct Philadelphia Warriors named Wilton Norman “Wilt” Chamberlain scored a century of points against the New York Knickerbockers, a feat which propelled the Warriors to victory, triumphing 169 to 147, at the Hershey Sports Arena in Hershey, Pennsylvania, home of a famed chocolate firm.

In that same season, Wikipedia assures us, “Wilt the Stilt”—the gentleman was seven feet one inch tall—averaged over 50 points per game, which, if you don’t follow basketball, is said to be a lot.

By any definition, Chamberlain’s 100-point game, and many of his other games in that same year, are proof that at least one player at one time had a “hot hand” in basketball.

Therefore the hot-hand phenomenon exists.

The observation of Chamberlin’s performance is called (in technical terms) a “statistic”. Thus, statistics has proved the existence of a hot hand. Quod erat demonstrandum, as an sober Irishman once said.

That’s it, then. Except that isn’t it, because other authors, many of them learned and well-credentialed, say that statistics prove that a hot hand does not exist. Indeed, belief in a hot hand has been called a fallacy.

A prime difficulty with modern statistics, with its wealth of sophisticated methods, is temptation. Fancy, important-sounding models are used where they aren’t needed, and they are used wrongly. The lure of mathematics, the whiff of science, the feeling that something important is happening in the algorithms—occult truths are being revealed!

Well, sometimes. Usually, not so much.

The title of the 1985 Cognitive Psychology paper by Amos Tversky, Thomas Gilovich, and Robert Vallone which set off the hot-hand debate is revealing: “The Hot Hand in Basketball: On the Misperception of Random Sequences“. There are no such thing as random sequences in any ontological sense, so they cannot be misperceived, or even correctly perceived. There are only sequences which have causes, known or unknown.

In their abstract, they say:

Basketball players and fans alike tend to believe that a player’s chance of hitting a shot are greater following a hit than following a miss on the previous shot…The belief in the hot hand and the “detection” of streaks in random sequences is attributed to a general misconception of chance according to which even short random sequences are thought to be highly representative of their generating process.

This is important because later attempts by other authors to prove or disprove the existence of a hot hand rely on these same concepts.

The problem is that these concepts are all wrong. Again, there are no such things as “random sequences”, and there is no such thing as “chance” or probabilities of shots.

What fans and coaches see is a man is doing well, better than he usually does. They see that the player is, for the moment, “hot.” This happens for a variety of causes, all complex and compound; to include such things as what the player ate for lunch, where the opponents traveled from, the confidence of the player, the floor stickiness, and on and on. Every baseball fan has seen batters suffer slumps, just as they’ve seen others maintain streaks. Same thing happens in basketball but at a faster pace.

Coaches and other team players see these streaks and slumps and try to use or minimize them. So do opposing players and coaches. Opponents try to vary causes to stop the streaks, and to enhance the causes that bring slumps. The whole is dynamic.

Chamberlin’s is not the only record which proves the hot hand. Klay Thompson, who coincidentally played for the transplanted Warriors, once scored 37 points in a single quarter, which is the most ever. And then Ty Lawson of the Denver Nuggets scored 10 consecutive 3-point shots. There are many more such records.

Now it will also happen that an enthusiastic fan, or even coach, will see a performance that he calls a “hot hand”, but which isn’t. This is akin to somebody in the crowd in the middle of a fireworks show labeling the latest large burst the “Grand Finale!” Sometimes the number of points scored, or some other measure of performance, by a player is only average. The juiced fan will think he is seeing something spectacular, when what is on display is the mundane.

Because some fans err and label average performances hot hands does not prove that there are no hot hands, because as Chamberlin’s and the other records show, there are.

So why do some researchers theorize there is no hot hand? Because of the Deadly Sin of Reification. These folks fit probability models to data and make pronouncements about the value of parameters of these models, pronouncements which are said to confirm or disprove the hot hand. This does not work, though, because probability models can’t confirm or disprove cause (except in some trivial senses).

All of these attempts forget that probability is conditional, that it is not real. To say what is not real is real is the Deadly Sin of Reification.

What happens is something like this, with minor variations. A researcher gathers shot data from some time and place for some collection of players. The researcher will then say that this player (or collection) “had” this-and-such probability for making consecutive shots (or for other intervals between shots), and then the player also “had” a probability which is similar for making single shots. The researcher will then say that since these two probabilities aren’t sufficiently different, there is no hot hand.

Since probabilities are not real and are entirely conditional on the data selected, any sort of story can be told by careful selection of data. That is the probabilities all change every time the data does—which is fine, because probability doesn’t exist. If only average player data is selected when these average players are performing at their average, the research will say there are no hot hands. If instead the data is Wilt Chamberlin’s century game and Klay Thompson’s record game, the research will show there are hot hands.

It’s better, then, to use the coaches’ knowledge of what constitutes a hot hand, because coaches think in terms of causes and skill. And not probability, which is a distraction or is misleading.

Not every player has a hot hand, and even the best don’t have hot hands all the time. Hot hands may be rarer than commonly thought. In any case, shots taken by players aren’t “random”. They are caused, and the causes vary, and in proportion to the sequence of shots taken. It may well be these causes are not very predictable, but that is nothing. They still exist.

Categories: Statistics

### 3 replies »

1. Wilt was”in the zone.” So has Michael Jordan and many other athletes…where statistical probability takes a deep back seat to the psychology of human performance.

2. Thiago says:

“Opponents try to vary causes to stop the streaks, and to enough the causes that bring slumps.”

What?

–—————-

If it is true “that a player’s chance of hitting a shot are greater following a hit than following a miss on the previous shot”, this would seem to parallel the stock market, where a stock is more likely to go up after having gone up than after having gone down. There are other effects like this – I think this is called the “Matthew principle”.

Of course, in the stock market also, some people also seem to think that the stock market is also “random” in a reified sense, in what is called the “random walk hypothesis”.

3. Briggs says:

Thiago,

Another typo placed by my enemies. Change “enough” to “enhance”.

The stock market is only “random” in the sense of unpredictable. This is easily proved by noting that those who possess the best predictive information, i.e. “insiders”, are prosecuted.