How to win a penalty shootout (with game theory)

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This is Planet Money from NPR.

**Jeff Guo** (0:22)
Last week, one of the best soccer players of all time did something kind of shocking.
Lionel Messi missed a penalty kick. The top World Cup scorer of all time is actually a slightly below average penalty kicker. He's in the running for missing the most penalties of any player in World Cup history. Somehow, Messi is worse at scoring when he's just 12 yards from the goal, with no one but the goalie between him and the back of the net. And that might be because there's another skill at play when it comes to penalty kicks. It's not just about how good you are at kicking the ball. It's about something we here at Planet Money love, game theory. Hello and welcome to Planet Money. I'm Jeff Guo.
The use of game theory in soccer penalties might be one of the most interesting applications of economic theory ever. Today on the show, we hear from the folks at the Soccernomics podcast about the art and strategy of the penalty kick in a World Cup year where there might be more games going to penalties than ever before. We're going to learn how game theory has changed the sport.

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**Jeff Guo** (2:19)
OK, so the whole point of game theory is to come up with and analyze winning strategies. And where it gets fun is that in any game, your opponent, of course, is trying to anticipate your strategy and vice versa. So your strategy depends on what you think they think you think they think you think they think they're gonna do, right? Like game theory is probably the best subject to study if you are an over-thinker. And nowhere are these mind games more cinematically laid out than on the soccer field when it's time for a penalty kick. Stefan Schmeinsky is one of the hosts of the podcast Soccernomics. He's a retired professor at the University of Michigan and an expert in the economics of sports. And he says if you watch elite penalty kickers, they are not always taking the shots that they are the best at.

**Stefan Szymanski** (3:10)
Everyone who takes a penalty has a good side and a bad side, almost everybody. And you might think that you'd always shoot to your best side, but if you do that, you're predictable.
And so what you have to do is sometimes, even though your chances of scoring are lower, you actually want to shoot to your worst side.
And what you have to do is do this in a way that's unpredictable, and that's what's called in game theory a mixed strategy. Now, picking a sequence of random numbers is quite a difficult thing to do, to choose at random left or right in the sequence. Left, right, right, right, left, right, left, so on. That's actually very hard to do. Most people aren't very good at it. And that's what you have to do with penalty taking. Sometimes you have to go one way, sometimes you have to go the other way, but you have to do so in a way that's completely unpredictable. And professional footballers turn out to be very good at picking those random sequences.

**Jeff Guo** (4:03)
Now, in this game, of course, it's not just the penalty kicker who's trying to be unpredictable. Another host of this Soccernomics podcast, G. Smalhotra, points out that the goalie is also thinking about how to be unpredictable.

**Ashish Malhotra** (4:15)
So it's two simultaneous people thinking about this in this way and also knowing, if I know that he knows what my tendencies are, then that's going to complicate it further.

**Stefan Szymanski** (4:28)
That's exactly right. What's happening here is that both sides are in a mirror image situation. The penalty taker is trying to choose whether to go left or right. And the goalkeeper, if the penalty is well taken, doesn't have time to react to the direction, has to choose before the ball is hit which way to dive. And they're then choosing what is their best strategy, dive left or dive right. And they have the same problem because goalkeepers are often better going one way or going the other.