For those of us who love sport, the Euros, followed by the Olympics, were a summer of excellence. For those of us who love data, this is even more true – because sport, like life itself, is becoming increasingly quantified, a world where metrics are thoroughly analyzed in the hope of finding an edge.

But while elite sport hopes to learn from geeks, there’s also a chance that geeks will learn from sport. Sport is far more constrained than life, which helps social scientists find clear and precise answers to difficult questions about individual and team behavior.

Economist Ignacio Palacios-Huerta has been making this argument for many years and recently published a working paper entitled “The Beautiful Dataset,” in which he examines a wide range of economic issues addressed using data from sports.

For example, professional golfers are less accurate when trying to make birdies and eagles (better than par scores) 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 the question of whether a free market tends to reduce unfair discrimination. In theory, it might: after all, not hiring good people based on race or gender is not only repugnant, it is also a costly vice. But in practice? Hard to say.

The history of baseball provides a clue: after 1947, major league teams were allowed to hire black players. Many managers despised the idea. Those who were more open-minded could hire good black players cheaply and thus gain an advantage in the league. Did they? The answer, according to a 1974 study: yes… but with unheard of slowness.

The penalty in football is a great example of the stark simplicity of some sporting situations. Most strikers have a stronger side, but if you favor it too much you become predictable. The striker might aim for the weaker side instead. So should the striker aim left or right? And since the goalkeeper has to guess which way to jump, which way should he go?

The situation, Palacios-Huerta argues, is perfect for testing a foundation of game theory: the minimax theorem, proved by the brilliant mathematician John von Neumann in 1928. After studying hundreds and then thousands of penalty kicks, Palacios-Huerta concluded that both strikers and goalkeepers play according to the optimal game-theoretic strategy, perfectly balancing the advantage of unpredictability and the advantage of favoring the stronger side.

When I previously wrote about this researchI joked that top football players are also “excellent economists,” meaning that players optimize their tactics intuitively. But that may not be intuitive; teams can easily analyze such questions if they want to and give their stars advice accordingly. (Think of England goalkeeper Jordan Pickford, who had to play in a penalty shootout against Switzerland, armed with a water bottle on which he listed all the opposing players and made his best guess as to how he could save their shots.) Teams that neglect their data lose.

While Palacios-Huerta is justified in proudly claiming that “these results confirm for the first time both implications of the Neumann minimax theorem under natural conditions,” the word “natural” might be surprising. Players do make optimal decisions, yes – when they are assisted by backroom teams. One might wonder if there is a broader lesson here.

In fact, it is questionable whether top soccer players really optimize. A study by researchers such as Michael Bar-Eli and Ilana Ritov found that, contrary to game theory, goalkeepers show a predictable tendency in the way they react to penalties: the action bias.

To understand this bias, we need to consider what I left out in my earlier analysis of whether a goalkeeper or a striker should go right or left. There is another alternative for both. The goalkeeper could stand still while the striker could cheekily kick the ball into the middle of the goal – the “Panenka” penalty, named after the Czech Antonín Panenka, who won the 1976 European Championship final with this audacious technique.

The problem is that as a striker, you look like an idiot if you attempt a Panenka and the goalkeeper stands still. The goalkeeper faces a similar dilemma. Bar-Eli, Ritov and their colleagues have found that goalkeepers would be better off if they stood still more often, rather than diving just to look good.

Even the most extreme situation, such as a penalty in football, is more complex to model than it seems. Is it better to assume that each player has two or three options? Is he trying to win the game or avoid embarrassment?

Perhaps the lesson here is not that professional players optimize their performance or fail to do so, but that the sport is less straightforward than it seems. As the statistician George Box liked to say, all models are wrong, but some are useful. A game theorist may be able to give good advice to a team preparing for a penalty shootout, but it is too much to ask that they analyze every detail of the situation on the field.

One of the many advantages of professional sport is that it offers us much of what makes life interesting, but in a purer, more concentrated dose. This is also what makes it so attractive to economists. But let’s not kid ourselves. Sport may be easier than life, but that’s not saying much.

Tim Harford’s children’s book “The Truth Detective” (Wren & Rook) is now available

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