When the ball goes in

Benjamin Markovits

On the LRB podcast a few weeks ago, David Runciman and I got into a discussion about the ‘hot hand’ phenomenon. He wrote about it in the London Review in 2006, in a piece on José Mourinho:

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.


  • 31 December 2020 at 5:54pm
    Sebastien Neilson says:
    I feel this ‘ the deep human need to believe counterintuitive ideas as a way of distinguishing yourself intellectually from other people...’ lies behind the success of books like freakonomics.

    The case you make with basketball is a good one, throwing a three pointer is a mechanical act born of practice. Successfully sinking one gives you a very tangible recent experience of executing and so it would be surprising if it didn’t influence the outcome of the next shot (ie the probability of each ‘event’ is not independent of the outcome of the previous.).

    We are not robots after all and even the most impressively drilled and stoic athlete must benefit from the very clear confirmation that their ‘action’ is correct.

    I play golf more than basketball now and if any sport makes this point clear in my experience it is golf - success begets success, until it suddenly doesn’t and you go back to square one!

    Thinking of a model to check this could you take a number of players average success rate accross the season, then group all attempts a)after a miss, b) a single success c) two in a row... etc and simply check relative success rates?

    Deeper analysis with hyp testing could be done but the above (if clear) would suffice no?

  • 31 December 2020 at 6:34pm
    Sebastien Neilson says:
    Looking at this I may be talking nonsense:

  • 31 December 2020 at 11:25pm
    Marmaduke Jinks says:
    Or, as Gary Player discovered “the more I practise the luckier I get”.

  • 4 January 2021 at 10:17pm
    Harvey Greenberg says:
    Over decades of poker, new players emerge who are widely hailed for their skills, ascend quickly to the top of the punter firmament, only to drop from sight within another year or so. Granted psychological factors inter alia can tip it the Daedalus
    for these brief-candled stars. But an overlooked factor is that he or she has been on an exceptional roll. Cards, liked flipped coins, have no memory. Over a lifetime of play, everyone gets

  • 4 January 2021 at 10:20pm
    Harvey Greenberg says:
    Chop out my last sentence which ended in mid air

    Harvey Greenberg

  • 7 January 2021 at 2:51pm
    John Jones says:
    Very funny that the original paper about how the punters get this wrong seems to have got the maths wrong itself - egg on their face!

    I think though there's something deeper going on with the popularity (among certain groups) of this kind of scorn for intuition. The original Cornell paper was part of the "Heuristics and Biases" research programme founded by Daniel Kahneman and Amos Tversky, which aimed to show that far from being the uber-rational utitility-optimising machines of neoclassical economic theory, human beings are biased, inconsistent, and reliant on rather stupid rules of thumb. The corollary of this is that markets (and much else) won't behave themselves, because the people that make them up aren't rational in the relevant sense.

    So how would you fix this? It's a pretty small leap from there to saying that what we really need to do is to vest as much power as possible in technocrats who have the expertise to escape these popular follies. The appeal of this to certain types of academics and radical centrist politicians is obvious!

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