How to win a penalty shootout (with game theory)

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Last week, one of the best soccer players of all time did something kind of shocking. Leonardo Messi missed a penalty kick. The top World Cup score 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 Quow.”

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 Soccer Nomics 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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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 the strategy and vice versa. So your strategy depends on what you think they 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 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. Steffen Schminski is one of the hosts of the podcast's soccer nomics.

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. Everyone who takes a penalty has a good side and a bad side, almost everybody. Anyway, I think they always shoot to your best side, but if you do that, you're predictable. And so what do you have to do sometimes, even though your chance is scoring a lower, you actually want to shoot to your worst side.

And what do 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 a quite a difficult thing to do to choose it random left or right in a sequence left, right, right, left, right, left, right, left. So that's actually very hard to do, most people are 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 a 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. 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, she's my whole trip, went out that the goalie is also

thinking about how to be unpredictable. So it's two simultaneous people sort of thinking about this in this way and also sort of knowing if I know that he knows what my tendencies are, then that's going to complicated further. That's exactly right.

What's happening here is that both sides are in the mirror image situation. The penalty take 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, and they

have the same problem, because goalkeepers are often better going one way or going the other.

as well.

“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. People tested this in the baratries with very simple experiments, offering students a few dollars to try and choose between alternatives, 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 Placio Swater, who were going to talk about a lot, actually studied penalty choosing, and found out that the choices of penalty takers in practice almost exactly matched the theory.

So this was sort of a breakthrough in gain theory to be able to demonstrate that this concept

to 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, and of course, in professional football penalty takers pretty important. 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, like 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, 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. Simon Cooper is another one of the hosts of the Socceronomics podcast. He's a journalist and a soccer commentator. He explains how one economist led a kind of data revolution in penalty shootouts. 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 or many leagues. So it's hard to know what the guy's penalty's have been. Ready 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, the friend of ours, Ignacio Palacios Huerta,

and he from the 90s is mapping, he's collecting this database of thousands of penalties, his wife and his mother are sending in videos of penalties from Spain and elsewhere, and he is creating the best database in the world of how football is taking penalties. And so you've got this weird situation that this guy who's a graduate student of Chicago, he knows more about the habit of penalty take, is that any club, even though he doesn't

need the knowledge and they desperately do. So when does this come to the fall? 2008 Champions League final, Chelsea Manchester United. 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. 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 want the penalty shootout, knowing Ignacio's advice is absolutely thrilling. Cristiano Ronaldo, the world is watching. So pitch a check in Chelsea goalkeeper, follows the surprise, and checks stands big. And checks, dice right stops with all those penalty.

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 Vandesar. And Ignacio says, from the start, the Unitedkeeper doesn't really follow a mixed strategy of randomizing. He dives too often through his rights.

And so clearly, the Chelsea players got the notes. Yeah, their clips of this all over the internet will link to one of them in our show notes, where you can see player after player shoot to the Manchester United keepers left. He's taken some pressure penalties before Ancids and scored, and he drills this one in.

Chelsea's second penalty kick also goes in, and the third. The fourth sneaks into, just barely. 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 Enelka steps up to the penalty spot. Two face off against the Manchester United goalie Edwin Vandesar, and Enelka has to get this one in.

And just when Enelka is about to kick, Fondesar 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 the Manchester in the stadium, it wasn't in the newspaper reports afterwards,”

I didn't see it and rice about it. But watching the penalty shoots out on YouTube, you see very clearly, Fondesar is standing on his goal line like this, massive figure, and before Enelka runs up, Fondesar points left to his left. And he's saying to Enelka, "I know what you guys are doing, you're all going left."

And Enelka probably meant to go left like all the other Chelsea kickers, but now he knows that Fondesar knows that he knows that Fondesar dies off from right, so what does he do? Fondesar has said, "I think you're in a kick at left." Enelka's probably very shaken.

"You didn't look happy coming forward Enelka."

And he kicks exactly in a kick, Ignacio said, "Never take against Fondesar."

He said, "I guess Fondesar either go over the ground or high in the top corner, but do not hit it mid-hides." And Enelka hits the ball, mid-hides to Fondesar's right.

“"I think not happy now, because it's red in Russia."”

Fondesar says it quite easily. "Night in Europe is Manchester United tonight." You nice it win the Champions League, so this brilliant day to a penalty report for Chelsea ends up backfiring. Okay, okay, 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 costs 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. Every episode of it's been a minute, NPR's What's Happening in Culture Podcast starts by asking three questions, "Who?

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and why. Since 2008, a lot of teams have used ignosos data strategy to prepare for penalty shootouts. Nosos worked with the English national team, he's worked for athletic bill bow and 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.

Now that everyone is trying to play their optimal strategy, which is based on what they

think their opponents are optimal strategy is. There is a bit of a debate going on in the football world about whether really there's the better approach is the psychological approach or the sort of pure statistical approach. So I think the interesting is it. So what it now is new did is he bought data and quantification to penalty taking.

And you know, that's just about the analysis of numbers. But the world doesn't quite fit perfectly with the theory. In this sense, 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.

“And so I think the issue is how far does pure number crunching get you?”

And then how much is additionally, you know, the psychology.

And that's what's interesting about McNapsio 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, he surmise from from what we know, he sort of develops a feel for it. So over the past two decades between the research and two game theory and the research and two soccer psychology, most teams have started to treat penalty kicks in a totally

different way. I mean, there are some findings from broader penalty research about things that are good to do. So, for example, take your time before your shot, take a few seconds. England players, Jamie Carrant, 2006 playing this example, we're often watching shoots, which is a bad way of doing it.

And then you want to practice under kind of shootout conditions. So I think they pipe in noise of the crowd, even in training sessions, and you actually recreate the shootout in a training session. You make everybody practice, there's even a strategy for the order in which you want to take your penalty kicks.

“You should always shoot first, because the team shooting second is often in the psychological”

position of having to score just to stay in the game.

So there's higher stress on the team shooting second, which probably explains why certainly

in the past in the era before penalty reports, the chances of winning if the shot first was 60%. I've said going first is lost some of its value now that pretty much every top team has penalty reports now, every top team will go into a game with a report for the shootout. And that makes it a slightly more skill-based and less about psychological pressure, I guess,

so on the team going second. Yeah, the game is changing. We've even seen studies that say the advantage of going first might not even exist anymore. Now that penalty reports have become so common. It used to be that team's treated penalty kicks as basically a lottery, a game of chance,

something you couldn't really prepare for. But nowadays you see a lot of teams commissioning these strategy reports. They take time to practice penalty kicking, piping in, you know, that fake crowd noise, so that players can learn how to perform unpredictability under pressure. And we might see the product of all that over the next couple weeks at the World Cup.

The 32 teams moved on to the knockout rounds, which means there could be more penalty shootouts than ever before. So we'll get to see how this data analysis and psychology works out on the world's biggest stage. I need your help for an upcoming episode.

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Also, if plant money were a flavor, what flavor would we be? I think maybe salty. Send us your ideas, record a voice memo, email us [email protected]. Also, we loved seeing all of you plant money plus subscribers at our virtual live event. You had awesome, awesome questions and we want to do more of these events in person and

virtually. So let us know what you're interested in, email us again at [email protected]. This episode of Planet Money was produced by M.A. Peasley with help from James Sneed, who's edited by Jess Zhang, back checked by Sarah Huarez, and engineered by On Lee Huang. Al Skullmark is our executive producer.

The soccer nomic episode was originally hosted by Ashish, Simon, and Stefan, and it's sound designed by Alex Wolden. They have great episodes about the world cup, including one on whether soccer managers actually make a difference. Their podcast is based on Simon and Stefan's book, also called Soccer Nomics, and if you

want to learn more about soccer and game theory specifically, Ignacio's Placios Huarez has also written a book that's called "Beautiful Game Theory". How soccer can help, I'm Jeff Woe, this is NPR, thanks for listening.

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