So you want to save penalties like the German goalkeeper

As you all know, Germany eliminated Argentina from the World Cup through penalty shootout, with German goalkeeper Jens Lehmann saving two of the four Argentinian attempts.

How did he do it? We are told that Lehmann watched videos of all the penalties Argentina have taken in the last two years and prepared notes with the goalkeeping coach. During the shootout, the coach gave Lehmann a note before each kick, detailing where the kicker was likely to put it.

What we are not told is how exactly Lehmann made use of the information. For example, we know that Lehmann dived to his left and saved the kick from Cambiasso, who shot to the right side. But did the note actually say that from past experience, Cambiasso tended to kick to the right? Or did Cambiasso departed from his usual pattern, kicked to the right, only to be out-smarted by Lehmann?

But economists are experts on each and every thing. Ignacio Palacios-Huerta, an economist at Brown University, used game theory to analyse penalty kicks, examined the pattern of 42 kickers and goalies, and checked whether those professionals played minimax, as prescribed by game theory. The research paper is certainly too technical to be understood by many, even this Slate article about the paper is still to vague to be understood by most. Try these paragraphs:

Game theory, applied to the problem of penalties, says that if the striker and the keeper are behaving optimally, neither will have a predictable strategy. The striker might favor his stronger side, of course, but that does not mean that there will be a pattern to the bias.

The striker might shoot to the right two times out of three, but we cannot then conclude that it will have to be to the left next time.

Game theory also says that each choice of shot should be equally likely to succeed, weighing up the advantage of shooting to the stronger side against the disadvantage of being too predictable. If shots to the right score three-quarters of the time and shots to the left score half the time, you should be shooting to the right more often. But as you do, the goalkeeper will respond: Shots to the right will become less successful and those to the left more successful. It might sound strange that at this point any choice will do, but it is analogous to saying that if you are at the summit of the mountain, no direction is up.

But do trust us economists. We know, simpe as that. Every remaining team in the World Cup should have the service of an economist, sitting behind the goalie, advising him on how to triumph through a penalty shoot-out.


According to this latest coverage on Lehmann and the notes:

(1) the notes were prepared from a huge database of past penalty kicks;
(2) the Argentinians didn't deviate from their usual approach; and
(3) Lehmann followed what was suggested in the notes.

[Lehmann] had the benefit of the German FA's database ... and having collated the information about who takes Argentina's penalties and how they take them, Germany's goalkeeping coach Andreas Kopke wrote it on a piece of paper ripped from a hotel notepad. On it was written details such as "[Julio] Cruz - stand tall, don't move, dive right".

For Argentina's second penalty-taker, Roberto Ayala, it said: "Ayala - look at shooting foot, left low." Sure enough, Ayala placed the ball low to Lehmann's left and it was advantage Germany.

When Maxi Rodr?guez walked up to strike the third, Lehmann knew it would be "hard, right". He went the correct way and was unlucky not to make the save. But after Borowski had made it 4-2, Esteban Cambiasso had to score to keep Argentina in the tournament. Lehmann's notes said: "Wait, stand tall, left corner." He duly made an impressive stop to his left.

And so, it turned out that the Argentinian penalty shoots were largely predictable, and this predictability favoured the goalkeeper/goalkeeping coach who did their homework.

(photo credit: SI.com)