Thursday, July 15, 2010

A Tale to Tell

People love to tell stories. It's something that I think is fundamentally built into the human psyche. Having others' attention and entertaining them with a good story is as strong a rush as there is. I've heard that the vast majority of criminals, when arrested, will simply confess because the urge to tell their story to a captive audience is just too strong.

This tendency manifests itself even when there is, quite literally, no story to tell. The clustering illusion denotes the human impulse to see significance in random patterns. Suppose a series of ten coin flips goes as follows: T, H, H, H, T, T, T, T, T, T. A lot of people (but hopefully not too many of my own readers) would see the coin as streaky, though how they would react to that perception might vary: Some might conclude that the coin was "due" for heads and bet that way, while others might conclude that it was on a "tails" streak and bet that way. (For what it's worth, I flipped a quarter ten times and that's exactly the way they came out.)

This has major implications for how we watch and remember sporting events. Maybe the most obvious example of this is the so-called "hot hand" in basketball: the idea that a shooter is "in the zone," and more likely than normal to hit any given shot. Various studies have looked for and failed to find evidence for the hot hand. It's entirely possible that the hot hand is wholly illusory, that it's just the clustering illusion in play. However, as Carl Sagan was wont to say, absence of evidence is not evidence of absence. Except for free throws, in which shot selection and defense have no play, shooting accuracy is highly contextual. Some shots are wide open, while others are tightly contested. They are shot from all over the field. Some are shot on the run, others are shot on the step back, while still others are spot up shots. What's more, players are intensely aware that they're hot, and as a result may shoot any hot hand they have in the foot (as it were). All these factors conspire to make the hot hand difficult indeed to discern. (For free throws, there is apparently a moderate hot hand; see this paper (or at least its abstract) by Jeremy Arkes.)

But a more basic example is in how we all remember and talk about the game afterward. We talk about the shooting struggles of such and such a player, and how (if our team won) he overcame that adversity and pushed through to get the win. We look back in our memory and find events that, although they seemed minor at the time, turned out to have momentous impact on the outcome of the game. Consider this account of Game 7 of the 2010 NBA Finals:
With 8:24 left in the third quarter, Celtics point guard Rajon Rondo picked up a loose rebound off Paul Pierce's miss from 19 feet, and pushed it back in to put the Celtics up 49-36. And through 28 minutes of play, Kobe Bryant had had an abysmally poor night on the offensive end. He had shot three of 17 from the field and one of three from the free throw line for seven points and a true shooting percentage of only 19 percent. Largely as a result of his terrible performance, the Lakers found themselves down by 13. To be sure, Bryant had eight rebounds (four of them on the offensive end), but that hardly put a dent in his overall play.

On the play, however, Pierce injured his shoulder and had to sit out for a spell. Bryant thought he saw something that he could exploit as a result, and went to work. On the very next play, he drove into the lane and drew a shooting foul on forward Rasheed Wallace. He only made one of his two free throws, but from then on his performance surged abruptly upward. Starting with that play and for the rest of the game, Bryant gathered seven more rebounds and shot three of seven from the field and 10 of 12 from the free throw line for 16 points and a true shooting percentage of 65 percent, leading his team to a 83-79 win for the title.
Sounds pretty interesting, doesn't it? Makes you wonder what it was that Kobe saw that he could take advantage of. I would wonder, too, except that I just now made it up. Everything else is true, but the sentence in bold is conjured out of whole cloth. Actually, Kobe simply tossed his hands in frustration for a second before taking the inbounds pass and dribbling it upcourt. In trying this narrative out on a couple of folks, though, I found that it was compelling because once people see the remarkable contrast between Kobe's play before that moment and his play after it, they assume that something equally remarkable must have happened to precipitate it. We will latch onto any little thing as an explanation, even if it had no more to do in fact with the game than any other little thing. Right place, right time.

As far as I can tell, though, there was nothing in that game that happened to Kobe. Aside from a trio of truly horrible shots that he took with the shot clock running down, his shot selection was not noticeably worse while the Lakers were falling behind than it was during their comeback. Sometimes, you know, a cigar really is just a cigar.


  1. Human performance is such a mystery, though -- surely there is statistical evidence for having an "off" day? I can understand limited evidence for the "hot hand", but presumably people have good and bad games, and there is evidence in the statistics that breaks down the better and worse performance, right?

    I'm reluctant to trust my intuition, based on cycling and other sports (and programming?), and I do presume that professional sports provides better evidence for this kind of thing because of both consistent motivation and elaborate stats keeping.

  2. @K: Yes, people do have good games and bad games, and yes, there are lots of statistics that examine such things. The problem is to figure out when such variation is due to just random chance, and when it's due to something else. It's a very difficult task.

    For what it's worth, I do think there is such a thing as a hot hand. However, it's a difficult thing to substantiate beyond a sort of plausibility argument: Shooting a basketball accurately requires lots of body parts to be in proper working order, so any injury detracts from that. It requires a smooth shooting motion (for the most part), so that any uncertainty or hesitation, again, detracts from that.

    Given that health and confidence do swing up and down, it would be surprising if there weren't SOMETHING like a hot hand. But of course that doesn't prove that there is.

    Likewise, though, it's difficult to prove that there ISN'T such a thing as a hot hand. Some people think it has been proven, but what they've really proven is that there isn't the specific kind of hot hand they've been looking for. There are kinds of hot hands--as a statistician, I would say "models"--that do not lend themselves to being identified by the kinds of tests that people have done so far.

    For instance, suppose that Ray Allen had the following kind of hot hand: Each game, there is a probability p that he will hit any three-pointer he takes. Some games, p is high, and some games, p is low, but for any single game, p is constant throughout.

    If p varies like a bell curve (that is, most of the times, p is near, let's say, 40 percent, but occasionally it's closer to 30 percent, or closer to 50 percent), it would be very difficult indeed to discern that kind of hot hand. It would not be possible to do, using the kinds of tests that people have done to date (that I'm aware of). And yet it would, in some platonic sense, be entirely distinct from a simple model in which Allen simply makes any three-pointer with probability 40 percent.

    Even if you chose a specific model, shooting is so contextual (intensity of defense, shot selection, exhaustion) that determining what it is you've actually detected is still tremendously difficult, using the statistics we have right now. Someday, when basketball is better instrumented, perhaps...but not yet.

    Thanks for the keen comment.