Game Theory has been a prominent topic throughout the course and I chose this article because it uses them to analyze one of my passions, soccer. In this weekend’s Champions League final between Real Madrid and Atletico Madrid, the game was a draw after regulation and came down to a penalty shootout. In a shootout, players alternate taking one-on-one shots against the goalie. Due to the short distance between the two players, (12 yards) “guessing” where the ball will be kicked is vital for the goalie. Game Theory attempts to predict someone’s optimal decision and can be used to model penalty kicks.
Although it is a complex coordination game, I modeled it using four simple choices of where to kick/defend:As you can see, the only combinations for the goalie to win is choosing the same location as the kicker. This simple graphic shows that if a penalty kicker and goalie were to make their decision randomly (with each option having a probability of .25), the likelihood of a goal is 12/16, which equates to 75%. Interestingly enough, in professional soccer, the percentage of penalty kicks made is 73%. So is it truly a guessing game?
Ignacio Estefanell, the author of the article, believes that both teams chose their kick locations prior to the game and had strategies in place. All five Real Madrid kickers shot to the keeper’s left, and all four Atletico kickers shot to the keeper’s right. For as long as soccer is played, economists will attempt to figure out the tendencies of a team but, at the end of the day, there’s always a level of unpredictability in human choice.