Playing odds on penalty kicks
On July 17, 1994, a glaring sun beat down on the Rose Bowl as two of the world's soccer powerhouses duked it out in the final match of the World Cup. After two hours of soccer, neither Brazil nor Italy had scored. The inevitable coda ensued: penalty kicks.
The principle of penalties is simple. The ball is put on a spot 12 yards from the goal line. The kicker has to shoot the ball directly from the spot, and the goalkeeper has to try to stop it without leaving his line before the ball is struck. Because the ball travels so fast, the goalkeeper may guess which way to dive before the kicker touches the ball.
That July day offered a nail-biting finale. Each side had five chances to score. Italy's fate was sealed only when Roberto Baggio, the team's offensive star, sailed his kick over the crossbar and into everlasting infamy.
Obviously, statistics could not have helped Baggio strike the ball on target. But they might have helped Daniele Massaro, the previous kicker, whose effort was saved by Brazil's goalkeeper, Claudio Taffarel.
Penalty kicks have attracted quite a bit of academic interest because they provide an ideal situation for checking some of the predictions of game theory. You have two players choosing their moves simultaneously with only two possible outcomes: score or no score. The 18-yard box in front of a soccer goal may as well be an economics laboratory.
Clearly, a kicker or goalkeeper who always plays to the same side will not be worth too much to his team; each type of player needs to mix things up. What interests economists is whether players mix things up in the best possible way. When players of similar ability are using their optimal strategies, the chances of scoring should be the same whether they play left, right or center. In other words, a player should not be able to improve his success rate by changing the mix.
Pierre-André Chiappori of Columbia University, Steven Levitt of the University of Chicago and Timothy Groseclose of UCLA analyzed all the penalty kicks taken in the top French league from 1997 through 1999 and in the top Italian league from 1997 through 2000. Kickers scored 77 percent of the time when they went to their natural side (right foot kicking to left side, for example), 70 percent of the time on the opposite side and 81 percent of the time in the middle - pretty similar success rates, or at least within a statistical margin of error.
Goalkeepers are even closer in their success rates. When they guessed center or the opposite side, kickers failed to score 27 percent of the time. When they guessed the kicker's natural side, there was no goal 24 percent of the time.
The players were not all the same, though, so the researchers looked at the scoring records of individual penalty takers. Again, they could not reject the hypothesis that the chances of scoring were the same no matter which way the penalty takers - and the goalies they faced - chose to play.
Ignacio Palacios-Huerta, a professor of economics at Brown University, extended the research with data on more than 1,400 penalty kicks in European leagues from 1995 through 2000. The players - kickers and goalkeepers alike - seemed to be doing the best they could. No matter how often they shot left, right or center, their chances of scoring were always statistically indistinguishable. The same went for the goalkeepers' choices.
But Palacios-Huerta went further, by analyzing the records of individual players who struck or faced at least 30 penalties each.
He wanted to find out whether the kickers and goalkeepers followed any predictable sequences. And indeed, at the moment of each individual kick, the decision looked random, as in an optimal strategy.
So, on average, the players are close to the best possible at what they do - a comforting thought for people who buy expensive soccer tickets. But another part of Palacios-Huerta's paper may be of more interest to World Cup coaches in Germany. A few of the kickers and goalkeepers he tracked are actually playing with their national sides right now.
If Raymond Domenech, the coach of the French squad, is looking for a penalty taker, he might want to pass on his captain, Zinédine Zidane. He ranked 21st out of the 22 kickers who took at least 30 penalties, with a 75 percent success rate.
By contrast, Marcello Lippi, who is coaching Italy, should probably trust Alessandro Del Piero to improve on his countrymen's performance from 1994; Del Piero, who plays for Juventus, ranked second, scoring 91 percent of the time. Lippi may also want to swap his starting goalkeeper, Gianluigi Buffon, before a game goes to penalties. Kickers scored on him 83 percent of the time, leaving him 16th out of the 20 keepers who faced 30 or more penalties.
If the Italian team finds itself in another shootout on a sunny July day, a few statistics may go a long way.
By Daniel Altman
The New York Times
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Very interesting record for Alex
