How to win a penalty shootout (with game theory)

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0:21Anthony Dembek: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.

1:01Anthony Dembek: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, like, 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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2:28Anthony Dembek:Okay, 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 going to do, right? Like, game theory is probably the best subject to study if you're an overthinker. 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.

3:07Anthony Dembek: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.

3:19Simon Kuper: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 a sequence. Left, right, right, right, left, right, left.

3:54Simon Kuper: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 footballers turn out, professional footballers turn out to be very good at picking those random sequences.

4:13Anthony Dembek:Now, in this game, of course, it's not just the penalty kicker who's trying to be unpredictable. Another host of this economics podcast, Ashish Malhotra, points out that the goalie is also thinking about how to be unpredictable.

4:24Simon Kuper:So it's two simultaneous people sort of thinking about this in this way and also sort of knowing, you know, If I know that he knows, you know, what my tendencies are, then that's going to complicate it further. 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, that 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.

5:00Simon Kuper:And they have the same problem because goalkeepers are often better going one way or going the other. And so what it turns out is the goalkeepers are also good at constructing these sequences as well.

5:11Anthony Dembek:By the way, in economics, these random mixed strategies, they actually used to be fairly controversial. There were economists who didn't think that people used mixed strategies in real life, partly because most people are just really, really bad at being truly random.

5:27Simon Kuper:People tested this in laboratories with very simple experiments offering students a few dollars to try and choose between alternatives to see if they could construct these random sequences of choices. And they couldn't. They weren't very good at it. So people started to say, oh, this mixed strategy theory is not up to much. And then what happened was a few economists came up, including Ignacio Clasio-Swebdo, who we're going to talk about a lot, actually studied penalty shooting and found out that the choices of penalty takers in practice almost exactly match the theory. So this was the sort of a breakthrough in game theory to be able to demonstrate that this concept of the mixed strategy, which many academics have been quite skeptical about as a practical strategy, that kind of showed that this really did work and that people could do it if it was important enough.

6:20Simon Kuper:And of course, in professional football, penalty take is pretty important.

6:24Anthony Dembek:Now, just as an aside, for those of us who aren't elite soccer players, this research into mixed strategies is still really important. They show up in everyday life. This could help you win your next game of rock, paper, scissors. You see, according to game theory, the best possible strategy in rock, paper, scissors is a mixed strategy. You want to be perfectly random so your opponent can't predict whether you're going to go rock or paper or scissors. But in real life, people are never perfectly random, right? Say you go rock like three times in a row. There's this big psychological temptation to go scissors or paper next time.

7:02Anthony Dembek:And your opponent knows that. This is where the mind games come in. There's actually an entire world of competitive rock, paper, scissors players. Back in 2007, they even aired the championships on ESPN. And the entire basis of this competition is that at the elite level, you're trying to exploit your opponent's tiny little deviations from that perfect random strategy. Now, in professional soccer, once people started to realize that there was this optimal mixed strategy for penalty kicks, you started to see teams collecting data on their opponents to see who was good at being unpredictable and who wasn't.

7:41Anthony Dembek:Simon Cooper is another one of the hosts of the Soccernomics podcast. He's a journalist and a soccer commentator, and he explains how one economist led a kind of data revolution in penalty shootouts.

7:52Simon Kuper:Well, for a long time, almost nobody is tracking how people take penalties. And of course, there isn't much TV footage in the 80s and 90s and many leagues. So it's hard to know, you know, what the guy, what penalties have been. Really, until into the 2000s, almost no teams are using records of how people have taken penalties. But the one guy who has this is an economist, a friend of ours, Ignacio Palacio Suerta. And he, from the 90s, is mapping, he's collecting this database of thousands of penalties. His wife and his mother are sending him videos of penalties from Spain and elsewhere. And he is creating the best database in the world of how footballers are taking penalties.

8:35Simon Kuper:And so you've got this weird situation that this guy who's a graduate student at Chicago, he knows more about the habits of penalty takers than any club, even though he doesn't need the knowledge and they desperately do. So when does this come to the fore? 2008 Champions League final, Chelsea-Manchester United.

8:55Anthony Dembek:So dramatic. The Champions League. This tournament features the top club teams in Europe. And ahead of the 2008 championship match, the manager of one of the teams in the final, Chelsea, had heard about Ignacio's database and asked him for his help.

9:12Simon Kuper:So Ignacio ends up writing a penalty report on Manchester United for Chelsea. And then, of course, the game goes to a penalty shootout. I'm in the stands in Moscow. It's about one in the morning when the shootout starts because it has to be prime time in Western Europe. And what does Ignacio's crib sheet say? It has some amazing advice. So, for example, Ronaldo, the young Cristiano Ronaldo, when he pauses in his run-up, the keeper should never move because Ronaldo watches what the keeper does. And when he pauses in his run-up, he usually shoots right. If you watch the penalty shoot out, knowing Ignacio's advice is absolutely thrilling.

9:50Simon Kuper:Cristiano Ronaldo. The world is watching. So Peter Cech, the Chelsea goalkeeper, follows this advice. Big, big step. And he waits and he looks and Cech stands big. And Cech dives right, stops Ronaldo's penalty. And Cech has saved from Ronaldo of all people.

10:07Anthony Dembek:Yeah, it seems like the Chelsea goalie is following the economist's advice to a tee. But the most important advice that Ignacio has for the team might involve what Chelsea's penalty kickers should do. How they can outsmart the opposing goalkeeper, Manchester United's Edwin van der Sar.

10:23Simon Kuper:And Ignacio says van der Sar, the United keeper, doesn't really follow a mixed strategy of randomizing. He dives too often to his right. And so clearly the Chelsea players got the note.

10:35Anthony Dembek:Yeah, there are clips of this all over the internet. We'll link to one of them in our show notes, where you can see player after player shoot to the Manchester United keepers left.

10:44Simon Kuper:He's taken some pressure penalties before Ansens and scored. And he drills this one in.

10:50Anthony Dembek:Chelsea's second penalty kick also goes in. And the third. The fourth sneaks in too, just barely.

10:58Simon Kuper:Oh, it got in just, just.

11:01Anthony Dembek:Then comes Chelsea's fifth penalty kicker, John Terry. He slips because it's raining, so he misses his goal, and now it is tied for all. This whole time, the teams have been going back and forth, and now they go to a sixth round, and then a seventh. Manchester United's kicker goes first, he scores, and that's when the Chelsea player, Nicholas Anelka, steps up to the penalty spot to face off against the Manchester United goalie, Edwin Van de Sar. And Anelka has to get this one in.

11:29Simon Kuper:And just when Anelka is about to kick, Van de Sar has figured it out. He's worked out they're all kicking to his left. And I was in the stadium. Nobody noticed, I think, this gesture in the stadium. It wasn't in newspaper reports afterwards. I didn't see it. I didn't write about it. But watching the penalty shootout on YouTube, you see very clearly Van der Sarre standing on his goal line like this, massive figure. And before Arnelka runs up, Van der Sarre points left to his left. And he's saying to Arnelka, I know what you guys are doing. You're all going left. And Anelka probably meant to go left like all the other Chelsea kickers.

12:07Simon Kuper:But now he knows that Van der Sarra knows that he knows that Van der Sarra dives door from right. So what does he do? Van der Sarra said, I think you're going to kick it left. Anelka is probably very shaken. He didn't look happy coming forward, Anelka. And he kicks exactly the kick. Ignacio said never take against Van der Sarra. He said against Van der Sarra, either go over the ground or high in the top corner, but do not hit it mid-height. So Anelka hits the ball mid-height to Van der Sar's right. And he's not happy now because it's red in Russia. Van der Sar saves it quite easily. Next night in Europe is Manchester United's night.

12:45Simon Kuper:United win the Champions League. So this brilliant data penalty report for Chelsea ends up backfiring.

12:52Anthony Dembek:OK, OK. I don't know if backfiring is the right word. Like, yeah, Ignacio's report didn't end up working for Chelsea. But I would say that game theory still prevailed, right? Because even though United's keeper was too predictable, in the end, so was Chelsea. They did the most obvious thing. They shot to the keeper's left every single time. So Chelsea themselves didn't quite employ that unpredictable mixed strategy. And that, and maybe the wet field, is what ultimately cost them the victory. After the break, we're going to learn a couple more tips about how game theory has changed the game of soccer.

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14:58Anthony Dembek:Since 2008, a lot of teams have used Ignacio's data strategy to prepare for penalty shootouts. Ignacio has worked with the English national team. He's worked for Athletic Bilbao in the Spanish league. And goalies now often even have their crib sheets taped onto their water bottles. And the opposing pickers know that the goalies have these crib sheets taped onto their water bottles. So how do things change now that everyone is trying to play their optimal strategy, which is based on what they think their opponent's optimal strategy is?

15:30Simon Kuper:There is a bit of a debate going on in the football world about whether really the better approach is the psychological approach or the sort of pure statistical approach. So I think the interesting thing is this. said. But what Ignacio did is he brought data and quantification to penalty taking. And that's just about the analysis of numbers. But the world doesn't quite fit perfectly with the theory, in the sense that the theory is based on there are two choices, left or right. Well, there aren't really two choices. There's obviously up top left, top bottom right. And so there are different options.

16:10Simon Kuper:And so I think the issue is how far does pure number crunching get you? And then how much is additionally, you know, psychology? And then what's interesting about Ignacio is he's clearly good at both. He does all the numbers, but then he sort of sits back and says, well, you know, what can we surmise from what we know? He sort of develops a feel for it.

16:33Anthony Dembek:So over the past two decades, between the research into game theory and the research into soccer psychology, most teams have started to treat penalty kicks in a totally different way.