THE World Cup is finally underway. At long last, soccer fans can put on their team colors, head down to the local pub — and begin collecting data to test economic theories.
Or at least, some of us will.
For instance, I’m interested in penalty kicks. In addition to being an exciting part of the game, penalty kicks present an opportunity to test an important idea in economics: the Nash equilibrium.
The economist John Forbes Nash Jr. analyzed how people should behave in strategic situations in which it is not optimal to repeatedly make the same move — like the children’s game rock, paper, scissors, in which selecting one move again and again (rock, rock, rock …) makes you easy to beat.
According to Mr. Nash’s theory, in a zero-sum game (i.e., where a win for one player entails a corresponding loss for the other) the best approach is to vary your moves unpredictably and in such proportions that your probability of winning is the same for each move. In rock, paper, scissors, for example, the optimal strategy is to mix your choices randomly among the three options.
To test this theory in the real world, we can study penalty kicks, which are zero-sum games in which it is not optimal to repeatedly choose the same move. (The goalie has an easier time stopping your shot if you always kick to the same side of the net.) Unlike complex real-world strategic situations involving firms, banks or countries, penalty kicks are relatively simple, and data about them are readily available.
I analyzed 9,017 penalty kicks taken in professional soccer games in a variety of countries from September 1995 to June 2012. I found, as Mr. Nash’s theory would predict, that players typically distributed their shots unpredictably and in just the right proportions. Specifically, roughly 60 percent of kicks were made to the right of the net, and 40 percent to the left.
The proportions were not 50-50 because players have unequal strengths in their legs and tend to shoot better to one side. Shooting 50-50, in other words, would not take full advantage of their better leg, while shooting any more often to the stronger side would have been too predictable.
In accordance with Mr. Nash’s theory, penalty kicks shot to the left were successful with the same frequency as kicks shot to the right — roughly 80 percent of the time.
Penalty kicks are just one example. Data from soccer can also illuminate one of the most prominent theories of the stock market: the efficient-market hypothesis. This theory posits that the market incorporates information so completely and so quickly that any relevant news is integrated into a stock’s price before anyone has a chance to act on it. This means that unless you have insider information, no stock is a better buy (i.e., undervalued) when compared with any other.
If this theory is correct, the price of an asset should jump up or down when news breaks and then remain perfectly flat until there is more news. But to test this in the real world is difficult. You would need to somehow stop the flow of news while letting trading continue. That seems impossible, since everything that happens in the real world, however boring or uneventful, counts as news.
This is where soccer is useful. In a study published earlier this year in The Economic Journal, the economists Karen Croxson and J. James Reade analyzed live soccer betting markets, looking at second-by-second betting activity around goals scored just seconds before halftime and betting activity during halftime. Their data, which concerned 1,206 Premier League soccer matches in England, contained 160 such “cusp” goals scored within seconds of the end of the first half.
The break in play at halftime provided a golden opportunity to study market efficiency because the playing clock stopped but the betting clock continued. Any drift in halftime betting values would have been evidence against market efficiency, since efficient prices should not drift when there is no news (or goals, in this case).
It turned out that when goals arrived within seconds of the end of the first half, betting continued heavily throughout halftime — but the betting values remained constant, a necessary condition to prove that those markets were indeed efficient.
Other research by me and others has shown that data from soccer can shed light on the economics of discrimination, fear, corruption and the dark side of incentives in organizations. In other words, aspects of the beautiful game that are less than beautiful from a fan’s perspective can still be illuminating for economists.
But perhaps most beautiful of all, for me, is that the core principles of my beloved professional discipline are exemplified by my beloved game.