Soccernomics (18 page)

To explain why penalties don’t change the pattern of match results, we need to consult Graham Taylor. The retired manager is now remem-T H E E C O N O M I S T ’ S F E A R O F T H E P E N A LT Y K I C K

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bered as the “turnip” whose long-ball game cost England qualification for the World Cup of 1994. However, the long-ball game had previously served Taylor very well at Watford and Aston Villa. No wonder, because it rested on one crucial insight into soccer: you will score goals only if you get possession in the opposition’s final third of the field.

Much the same insight applies to penalties: in practice you will get them only if you have possession (or at least a decent chance of winning possession) in the opponent’s penalty area. A penalty is often wrongly given. But it is almost always a reward for deep territorial penetration.

That makes it, on average, a marker of the balance of power in the game. That’s why good teams get proportionately more penalties than bad teams, and why home teams get more than away teams. On average, a penalty is given with the grain of a game.

RIGHT, LEFT, OR LET VAN DER SAR DECIDE FOR YOU?

GAME THEORY IN BERLIN AND MOSCOW

The next question is how to take them. Economists may have no idea when housing prices will crash, but they do know something about this one.

A surprising number of economists have thought hard about the humble penalty kick. Even Steve Levitt, author of
Freakonomics
and winner of perhaps the most important prize in economics (the Clark Medal, which some insiders think outranks the Nobel), once cowrote a little-known paper on penalties. Probably only a trio of economists would have watched videos of 459 penalties taken in the French and Italian leagues. “Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer” is one of those you might have missed, but it always won Levitt handshakes from European economists. Here’s an American who
gets it
, they must have thought. Levitt, P.-A. Chiappori, and T. Groseclose explain that they wrote the paper because “testing game theory in the real world may provide unique insights.” Economists revere the penalty as a real-life example of game theory.

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Game theory was developed in the 1940s by the likes of John von Neumann, a brilliant mathematician who also helped create the archi-tecture of the modern computer. It is the study of what happens when people find themselves in situations exactly like a penalty taker facing a goalkeeper: when what I should do depends on what you do, and what you should do depends on what I do.

The American government used game theory extensively during the cold war to plan its interactions with the Soviet Union and to try to predict Soviet moves. (It is said that game-theoretic advice was given during the Cuban missile crisis to consider questions like, “If we bomb Cuba, then the Russians will seize West Berlin, and then we’ll have to attack Russian troops, and then they’ll use nuclear bombs, and then . . .”) Today economists use game theory all the time, particularly to plan government policies or analyze business strategy. Game theory even plays a big role in research on biology.

The key to game theory is the analysis of how the strategies of different actors interact. In a penalty kick, for instance, the kicker and the keeper must each choose a strategy: where to kick the ball and where to dive. But each person’s strategy depends on what he thinks the other person will do.

Sometimes in game theory, what’s best for the actors is if they both do the same thing—going to the same restaurant to meet for dinner, for instance. These kinds of situations are known as coordination or cooperative games. But the penalty kick is a noncooperative game: the actors succeed by achieving their objectives independently of others. In fact, the penalty is a “zero-sum game”: any gain for one player is exactly offset by the loss to the other side (plus one goal for me is minus one goal for you).

The issue of game theory behind the penalty was best put in “The Longest Penalty Ever,” a short story by the Argentine writer Osvaldo Soriano. A match in the Argentine provinces has to be abandoned seconds before time when a bent referee, who has just awarded a penalty, is knocked out by an irate player. The league court decides that the last twenty seconds of the game—the penalty kick, in effect—will be played the next Sunday. That gives everyone a week to prepare for the penalty.

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At dinner a few nights before the penalty, “Gato Díaz,” the keeper who has to stop it, muses about the kicker:

“Constante kicks to the right.”

“Always,” said the president of the club.

“But he knows that I know.”

“Then we’re fucked.”

“Yeah, but I know that he knows,” said el Gato.

“Then dive to the left and be ready,” said someone at the table.

“No. He knows that I know that he knows,” said Gato Díaz, and he got up to go to bed.

Game theorists try to work out strategies for players in different types of games, and try to predict which strategy each player will pursue. Sometimes the prediction is easy. Consider the game in which each player has only two choices: either “Develop a nuclear bomb” or

“Don’t develop a nuclear bomb.” To make a prediction, you have to know what the payoff is to each player depending on the game’s outcome. Imagine the players are India and Pakistan (but it could be Israel and Iran, or any other pair of hostile nations). Initially, Pakistan does not know if India will or won’t develop a bomb, so it figures: If India has no bomb:

(a) We don’t get a bomb: we can live alongside each other, but there will always be incidents.

(b) We get a bomb: India will have to treat us with respect.

If India has a bomb:

(c) We don’t get a bomb: we can’t resist anything India does.

(d) We get a bomb: India will have to treat us with respect.

Plainly, if you are Pakistan, you will end up developing the bomb, whether India has the bomb or not. Likewise, India will choose the same strategy, and will develop the bomb whether Pakistan does or 122

doesn’t. So the
equilibrium
of this game is for both nations to acquire a bomb. This is the gloomy logic of an arms race. The logic of a soccer match is much the same, and there are many examples of arms races in soccer, from inflation of players’ wages to illegal doping.

PIECES OF PAPER IN

STUTTGART, MUNICH, BERLIN, AND MOSCOW

The problem for experienced penalty takers and goalkeepers is that over time, they build up track records. People come to spot any habits they might have—always shooting left, or always diving right, for instance.

Levitt and his colleagues observed “one goalie in the sample who jumps left on all eight kicks that he faces (only two of eight kicks against him go to the left, suggesting that his proclivity for jumping left is not lost on the kickers).”

There have probably always been people in the game tracking the past behavior of kickers and keepers. Back in the 1970s, a Dutch manager named Jan Reker began to build up an archive of index cards on thousands of players. One thing he noted was where the player hit his penalties. The Dutch keeper Hans van Breukelen would often call Reker before an international match for a briefing.

Nobody paid much attention to this relationship until 1988. That May, Van Breukelen’s PSV reached the European Cup final against Benfica.

Before the match in Stuttgart, the keeper phoned Reker. Inevitably, the game went to a penalty shoot-out. At first Reker’s index cards didn’t seem to be helping much—Benfica’s first five penalties all went in—but Van Breukelen saved the sixth kick from Veloso, and PSV was the European champion. A month later, so was Holland. They were leading the USSR

2–0 in the final in Munich when a silly charge by Van Breukelen conceded a penalty. But using Reker’s database, he saved Igor Belanov’s weak kick.

In Berlin in 2006, the World Cup quarter-final of Germany-Argentina also went to penalties. Jens Lehmann, the German keeper, stood in goal with a crib sheet tucked into his sock. On a page of hotel notepaper (“Schlosshotel, Grunewald,” it said), the German keeper’s T H E E C O N O M I S T ’ S F E A R O F T H E P E N A LT Y K I C K

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trainer, Andreas Köpke, had jotted down the proclivities of some potential Argentine penalty takers:

1. Riquelme

left

2. Crespo

long run-up/right

short run-up/left

3. Heinze

left low

4. Ayala

2 [His shirt number, presumably given for fear that

Lehmann would not recognize him]

waits long time, long run-up right

5. Messi

left

6. Aimar

16, waits long time, left

7. Rodriquez 18, left

Apparently, the Germans had a database of thirteen thousand kicks.

The crib sheet might just have tipped the balance. Of the seven Argentines on the list, only Ayala and Rodriquez actually took penalties.

However, Ayala stuck exactly to Lehmann’s plan: he took a long run-up, the keeper waited a long time, and when Ayala dutifully shot to Lehmann’s right, the keeper saved. Rodriquez also did his best to oblige. He put the ball in Lehmann’s left-hand corner as predicted, but hit it so well that the keeper couldn’t reach.

By the time of Argentina’s fourth penalty, Germany was leading 4–2.

If Lehmann could save Esteban Cambiasso’s kick, the Germans would maintain their record of never losing a penalty shoot-out in a World Cup. Lehmann consulted his crib sheet. Sönke Wortmann, the German film director, who was following the German team for a fly-on-the-wall documentary, reports what happened next: “Lehmann could find no indication on his note of how Cambiasso would shoot. And yet the piece of paper did its job, because Lehmann stood looking at it for a long time.

Köpke had written it in pencil, the note was crumpled and the writing almost illegible.”

Wortmann says that as Cambiasso prepared to take his kick, he must have been thinking, “What do they know?” The Germans knew 124

nothing. But Cambiasso was psyched out nonetheless. Lehmann saved his shot, and afterward there was a massive brawl on the field.

Both Van Breukelen’s and Lehmann’s stories have been told before.

What is not publicly known is that Chelsea received an excellent crib sheet before the Champions League final in Moscow in 2008.

In 1995, the Basque economist Ignacio Palacios-Huerta, who was then a graduate student at the University of Chicago, began recording the way penalties were taken. His paper, “Professionals Play Minimax,”

was published in 2003.

One friend of Ignacio who knew about his research was a professor of economics and mathematics at an Israeli university. It so happened that this man was also a friend of Avram Grant. When Grant’s Chelsea reached the final in Moscow in 2008, the professor realized that Ignacio’s research might help Grant. He put the two men in touch. Ignacio then sent Grant a report that made four points about Manchester United and penalties:

1. Van der Sar tended to dive to the kicker’s “natural side” more often than most keepers did. This meant that when facing a right-footed kicker, Van der Sar would usually dive to his own right, and when facing a left-footed kicker, to his own left. So Chelsea right-footed penalty takers would have a better chance if they shot to their “unnatural side,” Van der Sar’s left.

2. Huerta emphasized in his report that “the vast majority of the penalties that Van der Sar stops are those kicked to a mid-height (say, between 1 and 1.5 meters), and hence that penalties against him should be kicked just on the ground or high up.”

3. Cristiano Ronaldo was another special case. Ignacio wrote in the report: “Ronaldo often stops in the run-up to the ball. If he stops, he is likely (85%) to kick to the right hand side of the goalkeeper.”

Ignacio added that Ronaldo seemed able to change his mind

about where to put the ball at the very last instant. That meant it was crucial for the opposing keeper not to move early. When a keeper moved early, Ronaldo
always
scored.

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4. The team that wins the toss before the shoot-out gets to choose whether to go first. But this is a no-brainer: it should always go first. Teams going first win 60 percent of the time, presumably because there is too much pressure on the team going second, which is always having to score to save the game.

Ignacio doesn’t know how his research was used, but watching the shoot-out on TV, he was certain it was. Indeed, once you know the content of Ignacio’s note, it’s fascinating to study the shoot-out on YouTube. The Chelsea players seem to have followed his advice almost to the letter—except for poor Anelka.

United’s captain, Rio Ferdinand, won the toss, and turned to the bench to ask what to do. Terry tried to influence him by offering to go first. Unsurprisingly, Ferdinand ignored him. United went first, meaning that they were now likely to win. Carlos Tevez scored from the first kick.

Michael Ballack hit Chelsea’s first penalty high into the net to Van der Sar’s left. Juliano Belletti scored low to Van der Sar’s left. Ignacio had recommended that Chelsea’s right-footed kickers choose that side. But at this early stage, he still couldn’t be sure that Chelsea was being guided by his report. He told us later, “Interestingly, my wife had been quite skeptical about the whole thing as I was preparing the report for Coach Grant, not even interested in looking at it. But then the game went into extra time, and then into a penalty shoot-out.

Well, still skeptical.”

At this point Cristiano Ronaldo stepped up to take his kick for United. Watching on TV, Ignacio told his wife the precise advice he had given Chelsea in his report: Chelsea’s keeper shouldn’t move early, and if Cristiano paused in his run-up, he would most probably hit the ball to the keeper’s right.

To Ignacio’s delight, Chelsea’s keeper, Petr Cech, stayed motionless—