Beautiful Game Theory

Game Theory in the Penalty Box

In 1890, when Northern Irish businessman and soccer goalkeeper William McCrum first bounced around the idea of instituting a penalty kick, players, the press and the game’s administrators greeted it with fierce opposition and protest. The penalty kick as a punishment for foul play did not emerge until 1929, and the Fédération Internationale de Football Association (FIFA), soccer’s governing body, didn’t replace the tie-breaking coin toss with the penalty shoot-out until 1970.

A penalty kick is an example of a zero-sum game. In game theory, a zero-sum game is one in which one player’s upside is always exactly offset by the other player’s downside, and vice versa. In 1928, scientist John von Neumann proposed the “minimax” theorem, which says that each player in a two-person, zero-sum game follows a “mixed strategy” of diverse, probability-weighted options that represent that player’s best possible outcome. Players try to minimize their own maximum losses and to minimize their opposition’s maximum gains. In a zero-sum game, no one shares the spoils: The kicker wants to score, and the goalie wants to prevent a goal.

Testing game theories...