Penalty kick shootouts and the importance of shooting first

J. Apesteguia and I. Palacios-Huerta, “Psychological Pressure in Competitive Environments:
Evidence from a Randomized Natural Experiment”, American Economic Review 100 (December 2010): 2548-2564.

This economics paper focuses on the psychological issues involved in high-stakes competitive environments, using the penalty kick shootout as an illustration.  The major finding of the paper is that there is a structural advantage in the penalty kick shootout to the team that shoots first, which can be explained by psychological factors.


This is the second of the two papers that I was going to review during the holiday period, and the one that has generated more attention from the broader sports media.  The paper centers itself in the research area of behavioral economics, in which economic models are developed that account for psychological factors.  In a way, it attempts to account for the irrational within the rational and determine how applicable insights obtained in lab might be to real world conditions. (Some primers of the topic can be found here and here, and even more can be found via your preferred Internet search engine.)

It is the question of applicability that is the most difficult for behavioral economists to answer, and therefore that which has generated the greatest interest in the field. There exist very few real-world examples that closely mimic a laboratory problem, and vice-versa.  José Apesteguia, an economics professor at Universitat Pompeu Fabra in Barcelona, and Ignacio Palacios-Huerta, an economics professor at the London School of Economics, have identified one example of equal interest to economists and soccer fans: the penalty-kick shootout.

Palacios-Huerta should be familiar to those who read Soccernomics, as he was the professor who had researched game theory and penalty kicks in graduate school and later sent a letter to Chelsea manager Avram Grant about the penalty-kick practices of the Manchester United kickers and goalkeeper Edwin Van der Sar.  It appears that the scouting report was used during the 2008 Champions League final, as Szymanski and Kuper recount in that chapter on the final.

The penalty kick shootout is described as an example of a randomized natural experiment, an observational study in which the treatment and control groups are determined through random means.  In this particular study, the subjects are professionals carrying out one — and exactly one — task.  All of the relevant variables are observable, and the outcome of the task is known immediately and definitively.  Moreover, all subjects are highly motivated to complete the task well.

Data were collected from 129 shootouts, which resulted in a total of over 1,300 kicks.  The data included not just the actions of the shooter and goalkeeper, but also the particulars of the match and the teams.  Data were presented with respect to the team which shot first in the penalty kick shootout, and in some cases the outcome of the coin toss was collected. This was most relevant after 2003, when changes to the FIFA Laws of the Game presented team captains with the option instead of the obligation to kick first upon winning the pre-shootout coin toss.

One might expect that both sides would have an equal chance to win the penalty shootout.  However, the data indicate that the team that shoots first has a 60% chance of winning the penalty shootout, which in this study is significant at less than a 2% level. Even more interesting is the finding that the team shooting second has a consistently lower shooting percentage and consistently longer odds of leading the shootout after each round.

So there exists a significant and persistent advantage to the team the shoots first in a penalty kick shootout.  But are the players and managers aware of that?  The authors sent questionnaires to players and managers of professional and amateur soccer clubs in Spain, from the Primera Liga to the regional amateur leagues.  The result was that across managers and players at all levels of the game, over 90% of those polled preferred to shoot first.  When given the opportunity to state the reason for shooting first, almost all of the respondents said that they wanted to place pressure on the kickers of the opposing team.  It appears that the players and managers are definitely aware of the psychological factors surrounding the penalty kick shootout.  Now Apesteguia and Palacios-Huerta seek to quantify them.

There were two types of regression tests made in this study.  The first one utilized a probit/logit model and determined the influence of certain regressors (team rankings, league positions, home team, shootout experience, team shooting first) on the win probability.  The only regressor with a significant regression coefficient (at a 1% level) was the one associated with the team shooting first.  This result tends to indicate that the penalty kick shootout really is a crapshoot in that all of the factors that would give an advantage to one side no longer apply.

The second type of test involved a panel data model, which was used to determine the mechanism of the scoring rates during the penalty shootout.  Panel data analysis appears to be an econometrics tool that is used by economists and social scientists to study the characteristics of groups (panels) over time.  For the penalty kick analysis it would be useful in understanding how scoring rates change as a function of the interim score in the competition.  What Apesteguia and Palacios-Huerta found was not very surprising: as a team lags in the interim score, their penalty kick performance degrades, and as it leads in the interim score, their performance improves especially in the later rounds.  Because in the current shootout format the team that loses the toss always shoots second, that team will almost always have a level of psychological pressure that the team shooting first does not have.  (Upon understanding that finding, Gianluigi Buffon’s decision after winning the coin toss to have Spain kick first in the Euro 2008 quarterfinal was one of the biggest unforced errors in international football.)

Finally, the authors analyzed data in which they had information on the shot outcome — was it missed by the kicker, or saved by the goalkeeper?  — and found that the save rate was approximately the same between the two teams in the shootout.  The difference in scoring rates in the shootout is correlated very strongly with the miss rate of the kicker.  Therefore the burden of success in the shootout rests not with the goalkeeper but with the kickers selected.

So in conclusion, the penalty kick shootout as it currently exists is biased toward the team that wins the toss, only becomes unbiased if the shootout reaches sudden-death (more than five rounds), and is less a battle between goalkeeper and striker and more one between the striker and the mass between the striker’s ears.  So how do these results explain Germany’s near perfect record in penalty shootouts, or England’s abysmal record in shootouts?  There are some goalkeepers who were exceptionally good in penalty kick shootouts; what about them?  What the authors are saying is that in the mean, the penalty kick shootout really depends on one event, which makes the aforementioned events so exceptional.  There are some policy implications for competitive environments where the interim result is known to all parties, but specific to football FIFA will be asked how they can make the shootout fairer to both teams.  I am intrigued by the use of a tennis tiebreaker system (ABBAABB…), but I would like to know if there is an advantage to the player who serves first in the tiebreaker (I’ve seen a couple of papers related to the topic, but they were what I was looking for specifically).  This paper will provoke a lot of debate about the use of penalty kicks to break ties, with which very few people seem fully satisfied until they seriously consider the alternatives.