World Cup Edition

Freakonomics Radio

World Cup Edition: Steve Levitt on why the center cannot hold in penalty kicks, why a running track hurts home-field advantage, and why the World Cup is an economist’s dream.

Listen Now

We’ve got a new Freakonomics Radio podcast for you. (Download/subscribe at iTunes here, get the RSS feed here, or listen live via the link at right.)

This is a short, sweet, and simple episode — a conversation with Steve Levitt (hey, you could do worse) about World Cup 2010, which begins tomorrow in South Africa and in the coming weeks will consume tens of billions of hours of global mindshare. The latest odds leaders: Spain (4-1), Brazil (9-2), Argentina (13-2), England (9-1), and Germany (12-1). The U.S. is listed (generously?) at 80-1; remember, despite the conventional wisdom, bookies do not necessarily seek to “balance” their books and live off the vig, but rather take advantage of bettor sentiment. (Here’s an article we wrote on the topic; here’s a related research paper of Levitt’s.)

The podcast covers two topics in particular: home-field advantage and penalty kicks.

The home-field advantage stuff is based on clever research by Thomas J. Dohmen (“In Support of the Supporters? Do Social Forces Shape Decisions of the Impartial?”; press summary here).

DESCRIPTIONPhoto: Bill Ward’s Brickpile A San Jose Earthquakes player prepares to take a penalty kick.

The penalty-kick findings are based on research by Levitt, Pierre-André Chiappori, and Tim Groseclose; their paper’s very sexy title is “Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer.” I will not give away its most surprising finding here, but I will give a hint, courtesy of Yeats: the center cannot hold.

If you are the kind of person who can’t get enough empirical analysis about soccer, you should definitely read Soccernomics, by Simon Kuper and Stefan Szymanski, parts of which I found to be very good.

Spain celebrates its World Cup 2010 win. (Photo Pedro Ugarte/AFP/Getty Images)

I was in Madrid last month and saw Real Madrid beat Athletic Bilbao in a game that was very important when it began but became less so since Barcelona was beating Sevilla at the same hour, essentially clinching La Liga title. Even so, seeing Kaka, Cristiano Ronaldo, and Iker Casillas in person, surrounded by thousands of Spanish fans who watch the match as carefully and reverently as if it were the national theater, has made me more excited about this World Cup than any in the past. I cannot wait for tomorrow morning.


Audio Transcript

[Female Voice] This is Freakonomics Radio, here’s your host Stephen Dubner.


Stephen J. DUBNER:  So, Steve Levitt, it is World Cup time, World Cup Soccer, every four years, it’s here in South Africa.  What can the World Cup teach us about economics or even about human behavior?


Steven LEVITTSo I think there’s a lot to learn from soccer maybe surprising about economics and human behavior.  Now, one of the most interesting studies that’s been done looked at the home field advantage and in soccer as in almost every sport there’s an enormous home field advantage and it’s puzzling, why is it across all these different sports that the team at home always does better?  Does it have to do with sleeping in your own bed, is the referees, is it knowing the quirks of your own field or your own court, well, in soccer there’s a little hint as to what the source of the advantage is and that comes from two different kinds of stadiums.  Some soccer fields are build in stadiums that are especially made for soccer and in those stadiums people can be very close to the field.  There are other soccer stadiums which are also used for other things, for instance, for track and field events.  In that case there is a big track that circles around the field.  In this study they were able to divide teams into two groups, one of which had a much bigger home field advantage than the other.  The only difference that they could (1:56) between these two groups was something small and insignificant that you never would really associate with home field advantage but it turned out indeed to be quite important.  In the one group that had the big home field advantage they played in stadiums that were built exclusively for soccer, the other set of teams which had a much smaller home field advantage, they played in stadiums that were multiuse, not only was it used for soccer but they would have a track there where they held track and field events.  So I would think well, yeah, you can see how there might be a relationship but how does having a team that plays on a field, on a pitch that was built just for soccer and this stadium used for nothing else, how does that translate into being better?  Does that make you a better team at home than the others, how could that work?  Well, what they conjecture is that in the stadiums that have no track the fans are much closer to the pitch, they’re right on top of the players and more important than the players the referees, the officials, and what they conjecture is that it is this presence of the fans so close, this intimidating presence of the fans that bullies the officials into making decisions that benefit the home team and they can actually measure this so one of the easiest ways to measure the effect of the officials is to look at the extra time that is added on because of injuries and delays and it turns out that in these stadiums where the fans are right on top of the stadium, there’s no track in between, that when the home team is behind, the referees add on a lot of extra minutes.  When the home team is ahead they add on very few minutes relative to the stadiums where the track is in between so it seems that the intimidating presence of the fans has the effect of influencing the number of minutes that the referees add onto the game in order the benefit the home team.


DUBNER:  So Levitt, what do you know about penalty kicks in soccer matches? 


LEVITTPenalty kicks in soccer turn out to be an economists dream and that’s because there is an enormous body of research in something called game theory and game theory is about this strategic interaction between small numbers of competitors.  The beauty of the penalty kick is that it matches almost perfectly with the theoretical requirements of a two person simultaneous move game.  So the idea is that the soccer ball gets kicked so hard that if the goalie doesn’t jump really before he knows where the ball is going, he’s got no chance of stopping it and the kicker kicks the ball, they move at the same time and it’s a very simple strategy, the kicker can either kick it to the right, he can kick it to the left or he can kick it in the middle, three choices.  The goalie either stands there and doesn’t move or he jumps to the left or he jumps to the right.  So game theory, when you write down the math actually makes surprising predictions about how penalty kicks will work.  A fact of life is that a right footed kicker has an easier time kicking it to the left side of the goal than the right side of the goal because of the curvature of the ball when he kicks it.  So you might think that being the case that a right footed kicker would always want to kick it to the left, that’s where he’s better at kicking it.  Of course the goalie knows that the right footed kicker is better at kicking it left, that means the goalie has a very strong incentive to jump to the kickers left or the goalies right to try to block those kicks.  When you write down the math it turns out surprisingly that in order to make everything work out you might have thought that the kicker and the goalie would both jump to the right at the same percentage of the time but in fact it’s got to be the case.  The goalie will jump to the kickers left more often than the kicker will actually kick it to the kickers left.  That’s a strong prediction that comes out of game theory but it’s something that intuitively you would never really expect to see.  The striking fact is that these players play almost perfectly in line what they predict so indeed as we expect, the goalies jump much more to the kickers left than the kickers actually to the left and indeed every single prediction we make except for one is validated in the data and the one that doesn’t occur in the data is actually extremely interesting.  It turns out that there’s one kind of strategy that kickers don’t employ nearly as much as they probably should and that’s just to kick the ball right down the center.  So in our data, if you’re a kicker, the single best way to score is to just kick it right down the middle because it turns out the goalie is almost never there because in some sense I think it’s too embarrassing for the goalie to stand in the middle and just let you kick it and not even try.  The press will berate the goalie if he doesn’t seem to be trying to stop it and because the goalie has these strong incentives not to stay in the middle, the kicker should just kick in the middle but the problem is I think that when we write down our theory we’re assuming that the goal of the penalty kick is to score.  I think that’s wrong.  It’s not just to goal a score, the goal is also not to look foolish and indeed, the way you look most foolish in a penalty kick if you kick it right down the middle and it gets stopped.  So in the end what we conclude is, while game theory is very predictive in many dimensions with respect to trying to understand penalty kicks, by focusing only on whether a goal is scored, we really get it wrong because there’s other private incentives, the idea of not being the goat of the century, the guy who’s remembered.  Renaldo kicked one out of the goal right over the center, will never be forgiven for having made that mistake in the World Cup so there are private incentives that players not just want to score but they don’t want to look foolish when they don’t score and consequently they don’t do what’s best for the country or for the team, they shade their strategies just enough so that they’re doing the thing that’s safe even though it won’t result in as many goals. 


DUBNER:  So if I kick left and the goalie jumps to his right, to my left, and the goalie stops it makes a great save, I failed but heroically. 


LEVITTYeah, you made a good kick, the goalie made an even better play and people won’t be happy but that won’t be what you’re remembered for, it won’t be on your gravestone that you’re the guy who kicked it to the left and the goalie stopped it.


DUBNER:  And if I kick to my right and the goalie goes to his left and saves it, the same thing, but, if I kick to the center and goalie happens to kind of hang out there and stop it then I’m seen as a total fool.


LEVITTThat’s the end of your endorsements for the rest of your career most likely.


DUBNER:  Alright, so let’s say you, Steve Levitt, are playing for the United States of America in this World Cup and you’ve got a penalty kick and you know this, you know that your odds of making a kick are much better if you kick straight down the center but your odds of being considered personally a fool or much higher if you kick down the center and fail, what do you do? 


LEVITTI’m an economist, I’m only worried about myself, I kick to the left because that’s where it’s easiest for me to kick.     

Leave A Comment

Comments are moderated and generally will be posted if they are on-topic and not abusive.



View All Comments »
  1. Richard, Uk says:

    It’ll be interesting to see how the US gets on, I wish you the best of luck after Saturday!

    Thumb up 0 Thumb down 0
  2. frankenduf says:

    how does one account for bettor sentiment in an international event?- are the odds stratified for different markets (maybe by popularity of betting sites?)- or are they tilted towards the wealthy country teams, where people have more $ and computer access?
    ps- i love the british press summation of england’s draw:

    Thumb up 0 Thumb down 0
  3. Skip says:

    “Spanish fans who watch the match as carefully and reverently as if it were the national theater”

    Dude, it IS the national theater!

    Thumb up 0 Thumb down 0
  4. Bill says:

    Absolutely brilliant! I love football, and have come to love game theory.

    Thumb up 0 Thumb down 0
  5. Pramod says:

    Kickers have a “natural side”. How come goalies have equal capability to make a save in either direction?

    Thumb up 0 Thumb down 0
  6. Bruce says:

    I don’t think keepers have equal capability in both directions, or at least not all of them do. My guess is that at least one in a while, there’s word amongst players that a goalie has a weak side for stopping penalty kicks.

    Thumb up 0 Thumb down 0
  7. oneNil says:

    Big takeaways from the “Soccernomics” chapter on penalty kicks:

    – never confuse “change” with “randomness”
    – “the plural of anecdote is data” – Tunde
    – the penalty “creates an enormous disproportion between the foul and the reward”
    – Left? Right? Strong side? ABSOLUTE CHANCE!

    If you’re into exploring World Cup historical data, do check out the new Spotfire app:

    Thumb up 0 Thumb down 0
  8. Luke says:

    Looks like people have been studying the goalie / penalty-kicker dynamic for some time now. This article describes research that led to a conclusion opposite from Levitt’s – that it’s actually better for the goalie to “stay at home” and not dive to either side:

    Ironically, the author of this article and Levitt both use the same reasoning (actually speculation) to explain why goalies dive more often than they stay in the middle (“do something rather than nothing”)…even though the studies they cite seem to disagree on whether this strategy is effective in the first place.

    Given the numbers used by this other study, I’m inclined to think there’s another reason penalty-kickers don’t kick down the middle more often. Since they kicked to the center 30% of the time in the study and were unsuccessful 66% of the time, it appears that it’s just not a good strategy for the kicker. Therefore, one might assume that kickers would aim to either side, where their odds would be better (which is what they’re doing – 70% of the time). If 70% of the kicks are going to the sides and not the center, doesn’t that explain why goalies don’t stay in the center more often? That’s not where the ball is most likely to be kicked.

    Another aspect of this is that, even if one were to assume that the strategy of kicking down the middle IS effective, the advantage of this tactic would lessen over time as the goalie caught on.

    Thumb up 0 Thumb down 0