AI Summary
5 min readIn the 2008 Champions League final, Chelsea’s goalkeeper followed an economist’s advice to stop a penalty from Cristiano Ronaldo. The economist, Ignacio Palacios-Huerta, had spent years building a database of thousands of penalty kicks. His report for Chelsea correctly predicted Ronaldo’s habit: when he pauses in his run-up, he shoots right. The goalkeeper waited, did not move, and saved the shot. It was a triumph of data and game theory. But Chelsea still lost the shootout. The reason why reveals something subtle about how game theory works in practice—and how it can backfire when only one side uses it well.
The mixed strategy at the heart of penalty kicks
The central insight from game theory is that penalty takers and goalkeepers face the same problem. Both have a stronger side and a weaker side. If a kicker always shoots to his strong side, he becomes predictable. The goalkeeper will dive that way and save more shots. So the optimal strategy is to sometimes shoot to the weaker side, in proportions that make it impossible for the opponent to guess. This is called a mixed strategy: you randomize your choices so that no pattern emerges.
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What you'll learn
- 1 (00:22) **Introduction: Messi's Penalty Problem** - The episode opens with Lionel Messi, one of the greatest soccer players, missing a penalty kick, setting up the puzzle of why even elite players struggle from 12 yards.
- 2 (01:04) **Game Theory Basics: The Mixed Strategy** - Stefan Szymanski (Soccernomics podcast) explains the core game theory concept behind penalty kicks: the mixed strategy.
- 3 (04:19) **The Goalkeeper's Mirror Problem** - Shemuel Hotra (Soccernomics) explains that the goalkeeper faces the same game theory dilemma.
- 4 (05:19) **Mixed Strategy Theory Validated by Penalty Data** - Economists were skeptical that mixed strategies worked in real life because lab subjects were bad at being random.
- 5 (06:26) **Everyday Application: Rock Paper Scissors** - The mixed strategy concept applies to everyday games like rock-paper-scissors.
- 6 (07:34) **The Data Revolution: Ignacio Palacios-Huerta's Database** - Economist Ignacio Palacios-Huerta built a massive database of thousands of penalties starting in the 1990s.
- 7 (08:47) **The 2008 Champions League Final: Theory Meets Reality** - Ignacio's database was used by Chelsea to prepare for the 2008 Champions League final against Manchester United.
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Show Notes
According to game theory, there’s an optimal strategy for taking penalty kicks. This strategy involves an idea that was once somewhat controversial in economics — that is, until economists started studying soccer players in real life.
On today's show, we kick it over to the hosts of the Soccernomics podcast to explain how game theory has changed soccer, and how soccer has changed game theory.
Watch the penalty shootout between Manchester United and Chelsea in the Champions League final in 2008.
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This episode of Planet Money was produced by Emma Peaslee with help from James Sneed. It was edited by Jess Jiang. It was fact checked by Sierra Juarez and engineered by Annlie Huang. Alex Goldmark is our executive producer.
The Soccernomics episode was originally hosted by Ashish Malhotra, Simon Kuper and Stefan Szymanski and sound designed by Alex Roldan.
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