MLS’s Beautiful Game Theory

2014 was a huge year for US Soccer. We managed to escape the World Cup group-of-death at the expense of Portugal, with a squad of both veterans and bright young stars, a former World Cup winner in Jurgen Klinsmann at the helm, and without the talismanic if not a bit egomaniacal Landon Donovan anywhere near the USMNT setup.  The MLS playoffs featured some really high quality play, including, I’ll begrudgingly admit, that which ended the playoff run of my beloved DC United.

Then, on the last day of 2014, we learned the truth about Frank Lampard.

Long story short,the supposed marquee signing of a new MLS team, New York City FC turned out to actually be under contract by English Club Manchester City FC, owned by the same parent company. MLS, a league desperate to be taken seriously on the international stage, was treated as a plaything for a powerful European team.

Lampard was touted as the first signing of New York City Football Club, the new MLS that will begin playing in 2015.  NYCFC is owned by the same corporation as Premier League side Manchester City, and us fans were lead to believe that the 35 year old English veteran Lampard was loaned back to Manchester City by NYCFC for the start of the year. Well, a funny thing happened when Lampard started playing for City.  Beginning with a goal against the club Lampard had spent his entire career at, Chelsea FC, Lampard proved at his ripe old age that he still has plenty of ability and went on a run of scoring goals for fun.  Lampard proved to be an important player to City, so important that the Manchester club decided they would hang onto him for the remainder of the 2014-2015 season. We then learned that Lampard never really had a contract with the New York City expansion team, and was in fact signed to Manchester City on a permanent deal.  After NYCFC used Lampard’s image to promote the team and sell season tickets, it was revealed he was never their player at all.  Worse, since all MLS contracts are negotiated through the league and not the individual teams, MLS would likely have been aware of this situation, and may possibly have been content with an English Club treating their assets as a glorified farm system.


MLS commissioner Don Garber spoke on the issue on Sunday night in his typical uninformative fashion, claiming that NYCFC doesn’t operate as a farm team for Manchester City without providing any evidence to the contrary.

After this mess, US Soccer fans could use something to be positive about, and an empirical look at the state of the sport in the not-so-distant past gives us, in my opinion, plenty of reason to be positive.

In The Beautiful Game Theory, social scientist Ignacio Palacio-Huerta uses empirical data collected from soccer matches to discuss and test common social sciences and economic hypotheses.  One of his coolest insights relates to penalty shootouts, where he presents evidence showing that the best professional players in the world appear to use mixed-strategies in line with the “minimax theorem” when they decide where to kick the ball.

I’ll try to break it down in laymen’s terms: penalty shootouts work like what economists call a “zero-sum” game.  For each shot, either the shooter wins (by scoring) or the goalie wins (by stopping them from scoring).  Shooters usually have a strong side, where they can hit the ball with more power and accuracy, and a weaker side (the book discusses the possibility of shooting down the middle, but I’m not going to talk about it here for simplicity sake).

So say I’m a professional soccer player, and I’m right footed which means I can shoot better at the left side of the goal.  If I were to use a “pure strategy”, meaning I shoot at the left every time, the goalie would be able to guess which way I will shoot easily, and would therefore be able to save my shot pretty easily.  Instead, my optimal strategy would be to shoot left most of the time, but also shoot right pretty often, so that I play to my strengths without being predictable.  I also want each shot I take to be an “independent trial”, meaning I want to make the decision about where I shoot anew each time, without worrying about whether I shot to that side last time or not.

As a shooter, I want to pick a strategy where my probability of scoring is equal for both sides. An optimal strategy is one where I cannot improve on it by choosing to increase the frequency with which I shoot to one side. An optimal strategy – meaning the perfect breakdown of choosing left/right – is one where for the given strategy: p(R)=p(L) – the probability of scoring if I shoot left is the same as the probability of scoring if I shoot right. If this were not the case, if for instance, p(R)>p(L), this would not be an optimal mixed strategy, because it would make sense for me to shoot to the right more often.  This is called “equating payoffs.”

At least, that’s how economists would predict that a perfectly rational player would make this decision.  Economic models don’t always line up with the way living, breathing, human beings make these decisions in real life situations, but Palacios-Huerta used data from 9,017 penalty kicks taken from September 1995-June-2012 to test whether players actually act the way the perfectly rational hypothetical player would.  He found that the vast majority of players in the top leagues equated pay-offs, and that they passed the “runs test”, meaning they appeared to choose where to shoot independently each time.  In a rare victory for social scientists, theory matched up with real life behavior, because these top professionals chose optimal strategies when they stepped up to the spot.

More technical stuff

The study looked at whether the data could reject the null hypothesis that players would use a pure strategy. At the 95% confidence level, out of 40 players, they were able to reject the null hypothesis for only 2 players (interestingly, those 2 players were David Villa and Frank Lampard, the first two signings of New York City FC), meaning that the other 38 players chose strategies that were close enough to the theoretical predictions that, using the data, they could not conclude the other 38 players did not use pure strategies. I have some issues with the methodology, as Palacios-Huerta seems to treat the thing he’s trying to prove (that players use strategies in line with the minimax theorem) as his null hypothesis. The study also looked at the amount of “runs” that occurred for each player – where a player would shoot at the same spot multiple times in a row, and found that for almost all players, the amount of runs that occurred were consistent with the statistically likely outcome if players selected where to place their penalties independently.


What does this have to do with American soccer?  Well, researchers also did a similar test with 20 MLS players with data from the league.  Looking at the players in the top European Leagues, only 2 out of 40 players were shown not to use optimal mixed strategies when choosing where to shoot their penalty kicks (interestingly, one of these players was Lampard). With MLS, 10 out of 20 players,  half of the players that they looked at, used non-optimal strategies when they took penalties.  But that’s not even the worst of it, a 2009 survey asked MLS players where they like to place their PKs, and 44% of MLS players said that they would shoot the ball in the same spot EVERY TIME.  This is the equivalent of professional rock-paper-scissors players saying that their strategy is to “play scissors.”

The date of these studies isn’t specified, but they definitely date back to a bygone era in the history of MLS. This was before the arrival of former Premier League stars like Thierry Henry, Robbie Keane, Tim Cahill, and Obafemi Martins… before the return of Michael Bradley and Clint Dempsey to MLS… before players that graduated from MLS development programs like Perry Kitchen showed they can dominate experienced internationals like Rafa Marquez in midfield battle… before Deandre Yedlin shined against some of the best teams in the world and earned a dream move to Tottenham…before Jurgen Klinsmann instituted changes to the entire structure of youth soccer coaching in the US at all levels, similar to the reforms he pioneered years ago in Germany that may have been crucial to Die Mannschaft’s  2014 World Cup triumph.

Another study by Palacios-Huerta showed that players from the top leagues will pick optimal strategies even when playing a card game with the same payoffs as a penalty kick shootout (but with no direct resemblance to soccer), while players in lower leagues may not.  In other words, players in better leagues are better able to intuitively apply their understanding of the dynamics of penalty kicks, even in situations that look nothing like a penalty kick.

I would be willing to bet that if the preceding studies were conducted today, you’d find that players in MLS are much more competent at choosing where to place their penalty kicks, because the standard of play in the league, and consequently the “footballing brain” required to make it in MLS, has risen considerably.

The Lampard debacle has made it very difficult to take MLS seriously as a professional soccer league, but that shouldn’t overshadow the progress that the league has made.  The analysis of penalty kicks from the past shows that in some regards, the European elites were right to scoff at us.  In spite of setbacks like the Lampard situation and Garber’s tendency to kowtow to anyone with even a moderate amount of influence, things are getting better and its happening quickly.  The more prestigious leagues may be right to think of MLS as a joke for now, but I have a feeling that in a few years time when the gains of improved development structures have been realized, the European has-beens looking to MLS for a cushy retirement in a non-competitive league won’t find us so funny.