Left, Middle or Right? Game Theory of Soccer Penalty Kicks

After a long, exhausting, slow-played 90 minutes of soccer, the possibility of determining the result of a match by penalty kicks is perhaps the most exciting part of the game.  While other sports tend to have complicated strategies for trying to gain advantages in their games, soccer is relatively simple. It’s a one-on-one matchup between the goalie and kicker, each of which trying to read the other person’s mind.  It comes down to the goalie guessing to block left, middle or right, with the hopes to have the ball coming in his or her direction.

Here is the 3×3 playoff matrix between the kicker/goalie matchup: (I assume that both the kicker and goalie are good; a goalie will block a kick if he/she guesses correct and a kicker will score if the goalie guesses wrong.)

Goalie

 Kicker Left Middle Right Left 0,1 1,0 1,0 Middle 1,0 0,1 1,0 Right 1,0 1,0 0,1

**(1 is a win, 0 is a loss)

Even though most goalies use pure luck to guess which way to block the penalty kick, there have been some trends that offer insight to give goalies a better chance to predict which side the kicker will shoot.  For example, sometimes a kicker’s shot depends on which is his or her dominant foot. This gives a stronger and more accurate shot.  Likewise, goalies also have a dominant side in which they block a higher percentage of shots. A question arises as to which strategy should each person use, considering that each knows the other person’s dominant “side.”  If we look at a study economist Steve Levitt wrote (Table 3 and 4 below), both kickers and goalies go left more than right.  Additionally, kicking to the right had the lowest payoff and kicking middle had the highest payoff of either player’s decision.

After analyzing Levitt’s study and his data, we can assume that there is much more involved during a penalty kick than just athletic ability.  Players use mixed strategies to maximize their chance at scoring or blocking a goal.  So next time when are you playing a pick-up game of soccer with some of your friends, make sure you complete your networks homework first!