For those of us who love sport, the Euros followed by the Olympics have given us a vintage summer. For those of us who love geeking out over data, even more so — because sport, like life itself, is ever more quantified, a world in which metrics are thoroughly analysed in the hope of finding an edge.
But while high-performance sport is hoping to learn from the geeks, there is also the possibility that the geeks may learn from sport. Sport is far more constrained than life, which helps social scientists looking for clear, sharp answers to vexing questions about how individuals and teams behave.
The economist Ignacio Palacios-Huerta has been making this argument for many years, and recently published a working paper titled “The Beautiful Dataset”, surveying a wide landscape of economic topics that have been addressed using data from sport.
For example, professional golfers are less accurate when trying to make birdies and eagles (better than the par score) than when trying to avoid bogeys (worse than par). This is an example of “loss aversion”: golfers, like us, seem to hate losses more than they like gains. Another example is whether a free market tends to reduce unfair discrimination. It might, in theory: after all, refusing to hire good people on the basis of race or gender is not only repugnant, but an expensive vice. But in practice? Hard to say.
The history of baseball offers a clue: after 1947, major league teams were permitted to hire Black players. Many managers disdained that idea. Those who were more open-minded could hire good Black players cheaply, and gain an advantage in the league. Did they? The answer, according to a 1974 study: yes . . . but with outrageous slowness.
The penalty kick in football is a great example of the stark simplicity of some sporting situations. Most strikers will have a stronger side, but to favour it too much is to become predictable. The striker might aim for the weaker side instead. So should the striker aim left, or right? And since the keeper has to guess which way to dive, which way should they go?
The situation, argues Palacios-Huerta, is perfect for testing a foundation of game theory: the Minimax theorem, proved by the brilliant mathematician John von Neumann in 1928. After looking at hundreds, and then thousands, of penalty kicks, Palacios-Huerta concluded that both strikers and goalkeepers play in accordance with the optimal game theoretic strategy, perfectly balancing the advantage of unpredictability and the advantage of favouring the stronger side.
When I previously wrote about this research, I quipped that top football professionals were also “superb economists”, suggesting that players intuitively optimised their tactics. But there may be nothing intuitive about it; teams can — if they wish — easily analyse such questions and advise star players accordingly. (Recall the England goalkeeper Jordan Pickford, who faced a penalty shootout with Switzerland. He was armed with a water bottle listing every opposing player and the best guess for how to save their shots.) Teams who neglect their data lose out.
So while Palacios-Huerta is justified in his proud claim that “these findings represent the first time that both implications of von Neumann’s Minimax theorem are supported under natural conditions”, the word “natural” might raise an eyebrow. Players are making optimal choices, yes — when supported by backroom teams. One might wonder whether there is any broader lesson.
Indeed, there is a question mark over whether top football players really do optimise. A study by researchers including Michael Bar-Eli and Ilana Ritov found that goalkeepers, contrary to game theory, demonstrate a predictable bias in the way they respond to penalty kicks: the action bias.
To understand what that bias is, consider what I left out of my earlier analysis of whether a keeper or a striker should go right, or left. There is another alternative for each. The keeper could stand still, while the striker could cheekily chip the ball down the middle of the goal — the “Panenka” penalty named after the Czech Antonín Panenka, who won the Euro 1976 final with the audacious technique.
The problem is that, as a striker, if you try the Panenka and the keeper stays still, you’ll look like an idiot. The goalkeeper faces a similar dilemma. Bar-Eli, Ritov and their colleagues find that goalkeepers would do better if they stood still more often rather than diving for the sake of looking keen.
Even the starkest of situations, the football penalty, is more complex to model than it might seem. Is it better to assume that each player has two options, or three? Is their aim to win the game, or to avoid embarrassment?
Perhaps the lesson here is not that professional players optimise, or fail to, but that sport is less clear-cut than it appears. As the statistician George Box was fond of saying, all models are wrong, but some are useful. A game theorist might well be able to give good advice to a team preparing for a penalty shootout, but it is too much to expect them to analyse every detail of the situation on the pitch.
One of the many pleasures of professional sport is that it offers us much of what makes life interesting, but in a purer, more concentrated dose. That is its attraction to economists too. But let’s not fool ourselves. Sport may be simpler than life, but that’s not saying much.
Written for and first published in the Financial Times on 9 August 2024.
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