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Business News/ Opinion / Book review | Beautiful Game Theory: How Soccer can Help Economics
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Book review | Beautiful Game Theory: How Soccer can Help Economics

Can sports, football for example, shed some light on economics, a role reversal of sorts?

Photo: Sneha Srivastava/Mint Premium
Photo: Sneha Srivastava/Mint

Long after Major T.J. “King" Kong rode away on a nuclear bomb in Stanley Kubrick’s Dr Strangelove, the motivation for the idea that one can win in a nuclear war remained a mere theorem. The idea behind the beliefs that one could survive a nuclear war—the minimax theorem—is now being proven right, in a most unlikely arena, a football field.

Much has been written about the economics of sport—the huge salaries of football stars, the revenues garnered by big clubs and the “value" of individual sportstars in a variety of games. But can sport, football for example, shed some light on economics, a role reversal of sorts?

Beautiful Game Theory: How Soccer can Help Economics (Princeton University Press, 2014) by Ignacio Palacios-Huerta, a football enthusiast and a professor of management, economics and strategy at the London School of Economics, does just that. Using data from a large number of football matches, the professor has sought to explore a variety of economic behaviours—belief formation, discrimination and game theoretic concepts. The results are stunning.

One idea in particular has been explored in great detail: strategy formation in zero-sum games. Zero-sum games, as the name suggests, are winner-takes-all situations. What should a player do in a zero-sum game? One solution, suggested by mathematician John von Neumann in 1944 was simple: both players strategize to minimize their maximum possible loss and hence the name for the mathematical model that describes it, the minimax theorem.

The minimax theorem was written during the Cold War when nuclear war between the US and the Soviet Union was an ever present possibility. Kubrick’s film described what most “sane" persons felt at that time about the minimax theorem: it was pure madness. No one can possibly win in a nuclear war.

So how does football salvage this theorem? Penalty kicks are a natural domain to test what economists call pure and mixed strategies in a game. For example, consider a penalty shooter. He has three options: to kick the ball to the left, at the centre or to the right of a goal. The goalkeeper has the same options—move to the right as the ball hurtles towards him, remain in the centre or move to the left. Any mismatch, for example, the ball goes to the left while the keeper moves to the right, will almost certainly lead to a goal. Both the kicker and the goalie want to outdo each other. This setting forms a perfect zero-sum game. The ball goes in the goal net; the kicker wins; the goalie stops the ball, he wins. If the goalkeeper ends up coordinating his actions with those of the kicker, he wins. In contrast, for the kicker to win, he has to ensure that the goalkeeper is unable to predict the ball’s motion.

Palacios-Huerta analysed the results of 9,017 penalties and found that a goal is scored in 80.7% of all penalty kicks. The scoring rate is close to 100% when the goalkeeper’s choice does not coincide with the kickers, and it is over 60% when it coincides. The data shows the minmax theorem works. If a goalkeeper does not coordinate his actions, the possibility of a goal rises by a formidable 20 percentage points. (The details of the model, the data and the tests, described in chapter 1 of the book are eerily close to what the theorem predicts).

He does not, however, stop there. Given the speed and the times involved in a penalty kick and defence—barely 0.3 seconds elapse between a kick and its final end in or outside the goal net—it may be hard to believe that a goalkeeper and a kicker can evaluate complex probabilities and physically execute the winning strategy with a ball. Even the most supremely talented mathematician (barring, or course, the likes of von Neumann) cannot do that. Mathematicians are unlikely to play professional football and a footballer is unlikely to be a game theorist.

So what happens? In a scintillating chapter, the author details the results of a series of Magnetic Resonance Imaging (MRI) experiments in which these minimax strategies are mapped to the brain itself. Much like the empirical results seen on the football field, MRI experiments show that minimax play is virtually hardwired into our thinking processes. Economic theory is a highly mathematical area far removed from our daily experience. Without years of careful training, it is hard for anyone but specialists to think and compute strategies in a game theoretic situation. Yet here it is that talented footballers, with no exposure at all to math, end up playing exactly what a theorem predicted a long time ago. Math may after all not be so distant from real life.

Siddharth Singh is Editor (Views) at Mint.

Comment at views@livemint.com

Follow Mint Opinion on Twitter at https://twitter.com/Mint_Opinion

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Published: 24 Jul 2014, 07:12 PM IST
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