Decision Making in 700 milliseconds: Penalty Kicks based on Behavioral Economics
Lewandoski lined up for the penalty, a chance to put Poland in front, and a beautiful save from Guillermo Ochoa! Mexico’s Ochoa was hailed as a World Cup legend after his penalty save against Poland. This year’s biggest international football tournament has officially commenced and a lot of anomalies have kept football fans on edge. Many were beyond entertained these past few days. Seeing Ochoa’s beautiful penalty save, many were curious on how he jumped to his left side before Lewandoski even kicked the ball. He correctly jumped to the kicker’s shot direction and stopped Poland from winning their World Cup opener.
In this moment of global euphoria for football fans, one of the cruelest facets of this game — the penalty kick — is put into the spotlight. A giant leap of hope, one kick, and in a blink of an eye the fate of a nation’s success in the biggest stage of football is decided. The 2020 Euros proved the significance of penalty shootouts when England failed to win their first international trophy since 1966 due to a misstep in decision making, which led them to lose against Italy in a penalty shootout.
Although it is thrilling to watch, how do keepers decide when to go right or left? How do kickers decide where to shoot? What is the best strategy for a penalty kick? It turns out that economics — particularly behavioral economics and game theory — have their own way of explaining this phenomenon.
Penalty: A Battle of Strategy or Luck? Game Theory Tells Us
A penalty kick is a one-on-one match between the kicker and the keeper, one of which must win or lose — no in betweens. Therefore, a penalty shootout is a “zero-sum game” in which one of them wins, the other one loses (Cornell University, 2016). The gameplay is rather simple: the kicker takes one shot at goal while it is only defended by the opposing team’s goalkeeper.
According to Michael Clegg, a Premier League sports performance coach, a ball kicked in a penalty travels at an average speed of about 70 mph. This gives the goalkeeper about 700 milliseconds to see the direction the ball is going, decide which direction to jump, and move his body and save the shot. However, all these actions take the keeper almost a second to do, requiring them to jump before the shot is taken. During the few minutes before the shot is kicked, the economic concept of game theory can help explain what goes through these players’ minds.
Economics is a study of how people make choices under different conditions. Choices are made in all aspects of human life, making economics relevant in almost any situation — including the world of football. This study of choice is intensified in game theory, the science of strategy and interacting choices, making it indispensable in showcasing the decision-making process regarding a penalty kick.
In the world of penalty kicks, both players have to pick one side — left or right — long before the ball is kicked. From the goalkeeper’s perspective, he ought to match sides, while the kicker tries to mismatch. In this case, the goalkeeper wants to dive right when the kicker shoots right, while the kicker wants to shoot right when the keeper dives left, and vice versa. This type of game is called matching pennies, a basic game theory example that demonstrates how rational decision-makers seek to maximize their payoffs. Assuming both the kicker and goalkeeper are top professionals, where the kicker will always score a goal if the keeper fails guessing and/or the keeper will always block the shot if he succeeds guessing, a simple solution represented by a payoff matrix can be attained, as seen from Table 1.
Fundamentally, both players are inherently inclined to maximize their utility by gathering their highest possible payoffs. When a goalkeeper successfully guesses where the ball is going, the keeper will obtain his highest payoff, gaining +1 for him and -1 for the kicker. For kickers to maximize his payoff, he needs to shoot the opposite side of wherever the keeper is diving, thus gaining +1 for him and -1 for the keeper. This game necessarily has a mixed strategy Nash equilibrium, due to the fact that every finite game has one (Massachusetts Institute of Technology, 2010).
The solution is for both players to choose each side with equal probability. If a kicker has a preference of kicking to the right side, the keeper will also take that into account and anticipate this choice. Therefore, to prevent being exploited by neither player, both players should behave arbitrarily. This economic theory establishes one thing — football is not just about how skillful players are, but how they perform unpredictable maneuvers to outsmart their opponents.
Behavioral economics has a say on it too
Behavioral Economics combines elements of economics and psychology to understand the decision-making processes of individuals and institutions (The Chicago School of Professional Psychology, 2018). What does psychology have to do with shooting a ball? Well, it might be shocking how big a portion psychology contributes to the factors that affect decision making during a penalty kick.
According to economist Michael Bar-Eli (2007), his research shows that goalkeepers are fundamentally inclined to dive far to the right or left when attempting to block the shot. In reality, however, it is proven by the same research that they are more likely to impede the course of the ball and save the shot when staying near to the center of the net. Taking a shot in the middle had the highest pay-off at 81% success rate compared to hitting it to the right or left (The Atlantic, 2010), as shown in Table 2.
Economist Steve Levitt once stated in his paper that players optimally choose strategies conditional on the opponent’s behavior, but the fact that shot-takers and keepers do not choose the middle path more frequently is perplexing. Despite giving both players a higher chance of success, players still choose to go right or left (Bar-Eli, 2007). This is due to Action Bias, a concept in behavioral economics that explains a phenomenon when people have an impulse to act in order to gain a sense of control over a situation and eliminate a problem (Patt & Zeckhauser, 2000). This completely explains situations where human beings prefer action to inaction. If the keeper stayed in the center and a goal was scored, it looks as if he did not do anything to stop the ball — while the norm is to do something or basically jump. This explains why keepers do what they do, and it turns out that psychology, with a touch of economics, does play a part.
Penalties: Closer than we thought to economics
Ultimately, economics is the study of choice. Choices range over every imaginable aspect of human experience, and so does economics. Economists have investigated the nature of virtually every aspect in people’s lives (University of Minnesota, 2016) — including decision making in sports. The thought process of a keeper deciding to jump to the right corner of the goal could be studied in economics due to the choices involved in it. The economic concepts of game theory and matching pennies really demonstrate the utilities each decision could bring to the players in a penalty. Behavioral economics also gave football fans a new perspective by introducing the phenomenon of action bias in the keeper’s thought process in an attempt to block the shot.
In conclusion, economic concepts can be applied to understand how decisions are made in a penalty kick. This analysis of penalty kicks based on behavioral economics tells us that — just like every other sport — luck is a factor we need to take into account. Even when succeeding to pick the right side, John Terry’s slip in the Champions League final match-deciding penalty shot against Manchester United in 2008 proved the importance of good luck — one which could’ve gotten him a major trophy. When shooting a penalty, ultimately it comes back to how much players have prepared mentally and technically in shooting from the spot. Now, it’s time for us to wait and see as the World Cup unfolds. Fingers crossed. Eu sou Brasileiro.
Michael Abimanyu Kaeng | Undergraduate Economics Student at the University of Indonesia | Trainee of Economic Studies Division at Kanopi FEB UI
Bar-Eli, M., Azar, O. H., Ritov, I., Keidar-Levin, Y., & Schein, G. (2007). Action bias among elite soccer goalkeepers: The case of penalty kicks. Journal of Economic Psychology, 28(5), 606–621. https://doi.org/10.1016/j.joep.2006.12.00
Chiappori, P., Levitt, S., & Groseclose, T. (2002). Testing mixed-strategy equilibria when players are heterogeneous: The case of penalty kicks in soccer. American Economic Review, 92(4), 1138–1151. https://doi.org/10.1257/00028280260344678
Experts corner: The science behind elite penalty kicks. (2022, November 18). NeuroTracker | #1 Cognitive Training System in the World. https://www.neurotrackerx.com/post/science-penalty-kicks
Patt, A., & Zeckhauser, R. J. (2001). Behavioral perceptions and policies toward the environment. Judgments, Decisions, and Public Policy, 265–302. https://doi.org/10.1017/cbo9780511584206.012
The game theory of soccer penalty kicks. (2015, May 28). William Spaniel. https://williamspaniel.com/2014/06/12/the-game-theory-of-soccer-penalty-kicks/
Thompson, D. (2010, June 10). The economics of penalty kicks in soccer. The Atlantic. https://www.theatlantic.com/business/archive/2010/06/the-economics-of-penalty-kicks-in-soccer/58001/
What is game theory? (2003, November 19). Investopedia. https://www.investopedia.com/terms/g/gametheory.asp