Why goalies in soccer shouldn’t dive for penalty kicks
During my study of game theory in business school, the professor gave an example of a game in which the equilibrium should produce independent, randomized choices by all players: penalty kicks in soccer. Strikers should kick the ball to a random location in the goal and goalies should dive in a random direction.
If you simplify the game, you could say that there are three locations in the goal—left, center, and right—and each player should choose them with equal probabilities of one third. However, while strikers do this, goalies don’t. Goalies are more likely to dive right or left than to stay put in the middle. Call it the negative consequences of having a bias to action, or think of it like playing rock-paper-scissors and always picking rock.
