The World Cup starts this weekend, and many of the matches will be determined by the cruelest facet of the beautiful game: the penalty kick. A hopeful kick, a simultaneous leap, and 0.2 seconds later, you have a goal or a goat.

Freakonomics economist Steve Levitt co-wrote a paper on penalty kick strategy, and it's pretty cool. Conventional wisdom says kickers are best at pulling with their strong leg, so you'd expect most kickers to be right-footed and aim left (the goalie's right). Goalies know that, so you'd expect most keepers to guess the kicker's left. But about 75% of all shots are scores. So what strategies are working?

Levitt and his co-authors made some surprising finds. First, check out these two charts of shots taken and goals scored as percentage of shots taken in French and Italian leagues.

kicking 2.png
kicking.png
What do we learn?

(1) Both goalies and kickers go left more than right (left-left is the most common observation).

(2) Kicking to the right had the lowest payoff of any decision, of either goalie or kicker.

(3) Kicking middle had the highest pay-off of any decision, of either goalie or kicker.

The paper's economic conclusion is interesting, but it won't be satisfying for fans who derive morbid pleasure from screaming at their goalie or penalty kicker for being irrational. The authors write: "We cannot reject that players optimally choose strategies, conditional on the opponent's behavior." Good penalty kickers and goalies are also good at randomization of strategy.

*Update: It's also notable that the success probabilities of Left, Middle, and Right for goalies are practically identical.

[via Freakonomics blog]

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