It’s a shame Andy Murray didn’t win, it really is. I quite like the gangly lad, with his bad media training and his wildly disproportionate adam’s apple, and it would be nice to see a Briton win something. But I want to take this opportunity to say something about the myth of momentum in sport.
Roger Federer got bogged down in a five-setter against Julien Benneteau earlier on in his run to the final, but then played beautifully to beat Novak Djokovic in four in the semi, and the talk was all about how this would give him momentum going into the final. It’s a staple of sports commentary: “he’s coming into form at the right time”; “they’re really building up a head of steam with that win”; “they’ve got great momentum coming into the final games of the season”. It’s also implicit in the idioms of sport: they’re on a winning streak, he’s got the hot hand (in basketball), he’s got his shooting boots on today. When a striker is struggling for goals, the old hands in the commentary box will nod sagely and say “He just needs one to go in off his backside, and he’ll go on a scoring run.”
It makes intuitive sense to us: the idea that winning is a habit; that confidence is important in sports; that the more you win, the more you will continue to win. But it is, largely, a product of humanity’s inability to detect randomness – or, more accurately, our overeagerness to detect patterns.
Assume a player has won three games in a row. Is he more or less likely to win the fourth? Almost every commentator and sportsman – and probably most fans – would say that he is. He has the momentum. But we can rephrase the question like this: “Is the sequence WWWW more or less likely than the sequence WWWL?” And it turns out it isn’t.
In 1985, a psychologist called Thomas Gilovich showed that it isn’t, at least for the so-called “hot hand” in basketball.The implication of the “hot hand” is that someone who has hit a basket with their last shot is more likely to hit with their next one: Gilovich reported that 91 per cent of fans agreed that a player has “a better chance of making a shot after having just made his last two or three shots than he does after having just missed his last two or three shots”. However, he found that it was not true. Examining the results of shooters with the Philadelphia 76ers for a season, he found that players who had hit their last one, two or three shots were no more likely to hit their next than players who had missed their last one, two or three. In fact, they were slightly less likely (weighted average of 51 per cent hits after a hit, compared to 54 per cent after a miss). Similar results have been found for winning and losing streaks, by eg Vergin in 2000.
(Note: this isn’t to say that all players and teams are equally likely to win or lose. But a good team, say one that wins 60 per cent of its matches, still has a 60 per cent chance of winning its next match, all else being equal, regardless of its last result.)
So what is going on? Why are we so keen to attribute “hot-handedness” to explain random sequences?
At heart, it’s because humans are incredibly keen to detect patterns, in almost all forms. This is for a very simple reason: in general, a false positive is far less dangerous than a false negative. If our visual system detects a tiger’s face in the bushes, or an enemy holding a club in the shadows, which on closer inspection turns out to be a flower or a hatstand, that is far less of a problem than not spotting a real tiger or enemy. With number patterns, you can imagine something similar: if you see three cases of a disease in a local area, it might be a statistical fluke, or it might be a pattern of contagion. If you see a pattern and you’re wrong, it’s not as dangerous as not seeing a pattern and being wrong. Two mathematical psychologists, Amos Tversky and Daniel Kahneman, described this in terms of the “belief in the law of small numbers” – the idea that even small samples of a large set of numbers should show the patterns of the whole set, despite what the laws of probability actually tell us.
Regardless of the reasons, though, it seems that there is no such thing as “momentum” in sport. If your chosen team or player is going through a dry patch, take heart from the fact that they’re just as likely to win, even in their darkest time, as they are when on a nine-game winning streak. Remember it also, when the pundit on Match of the Day, after confidently predicting a sixth win on the bounce for Manchester City and watching them lose unexpectedly to Swansea City, says “Well, they were due a defeat”. No, they weren’t. It’s a weighted random number generator, the throw of a loaded dice: sometimes it’ll come up six, sometimes it won’t. Don’t try to build any more of a narrative around it than that.