When the ball goes in
The quintessential instance … occurs in basketball, where certain players suddenly and inexplicably acquire the ability to nail three-point baskets one after another (in basketball you get three points for any basket scored from a distance of over 23'9", a formidably difficult feat which means even the best players miss more often than they score).
With the start of the NBA season last week, I’ve been thinking about it again (actually, I think about this stuff pretty much year round, but the season is a good excuse to talk about it). As David wrote in his piece, statisticians will tell you there’s no such thing as a hot streak. If you look at the data, the shot that follows three straight makes is no more likely to go in than the shot that follows three straight misses. Tenured professors, with other things to do, actually studied the shooting patterns of the Cornell basketball team and compared it to the outcomes you get from flipping a coin.
In 1985 they published a paper about it, and after that the deep human need to believe counterintuitive ideas as a way of distinguishing yourself intellectually from other people kicked in. Most nerds subscribed as an article of faith. The paper argued that hot hands are a cognitive illusion: our brains want to see patterns in a world determined by randomness. We see a couple of our shots go in and feel as if, in this mood, we have some kind of control. Until a few years ago it was hard to find a mathematician who believed in shooting streaks, and it was impossible to find anyone who had actually played basketball who didn’t.
In other words, the professors argued that all those things you feel when you play sport, that you’re in some kind of zone or flow, in a heightened state of harmony with the universe, which is why you play sport in the first place – these feelings, the data tell us, are not real. They’re delusions produced by the mind’s inability to accept the role of chance.
Lately, the maths has moved on; a recent paper in Scientific American argued that the Cornell guys ignored selection bias. For most of this stuff, I’d need a software update to understand it, but what interests me here is the way the whole conversation became a test case for the way we deal with conflicts between academic expertise and first-hand experience.
Because the real problem with the Cornell paper was that it made a category mistake. It’s as if your dad bought you a silver dollar for your ninth birthday and started teaching you how to flip it. The first fifty times you tried, it landed heads only four or five times. But you loved your dad and wanted to please him. As you got older and stronger, you kept practising and soon learned to flip that silver dollar so that heads came up a quarter of the time, and then a third. Later, at college, you made the coin-flipping team and practised your technique with flipping instructors, who taught you the correct position of the thumb and the ideal amount of projectile force to apply. It got to the point where in practice you could flip that coin so it landed heads eight or nine times out of ten – a success rate that dropped, in the pressure and heat of the moment, during actual games, to something like 50 per cent.
Sometimes, though, in the heat of certain moments, in the pressure of actual games, you find a kind of calm or still centre that allows you to reproduce the fluency and control you feel in practice in the quiet of an empty gym, and flip that coin, against fierce and relentless opposition, so that three, four, five times in a row it comes up heads. And the statisticians and mathematical psychologists want to say that those are delusions, those feelings of fluency and control. The whole thing is random, like flipping a coin. What they leave out is the fact that when the ball goes in, the reason you feel ‘hot’ is because you did something right.