The paper “Action Bias among Elite Soccer Goalkeepers: The Case of Penalty Kicks” (Journal of Economic Psychology [2007]: 606– 621) presents an interesting analysis of 286 penalty kicks in televised championship soccer games from around the world. In a penalty kick, the only players involved are the kicker and the goalkeeper from the opposing team. The kicker tries to kick a ball into the goal from a point located 11 meters away. The goalkeeper tries to block the ball from entering the goal. For each penalty kick analyzed, the researchers recorded the direction that the goalkeeper moved (jumped to the left, stayed in the center, or jumped to the right) and whether or not the penalty kick was successfully blocked. Consider the following events:
L = the event that the goalkeeper jumps to the left
C = the event that the goalkeeper stays in the center
R = the event that the goalkeeper jumps to the right
B = the event that the penalty kick is blocked Based on their analysis of the penalty kicks, the authors of the paper gave the following probability estimates:
P(L) = 0.493 P(C) = 0.063 P(R) = 0.444
P(B| L) = 0.142 P(B| C) = 0.333 P(B| R) = 0.126
a. For each of the given probabilities, write a sentence giving an interpretation of the probability in the context of this problem.
b. Use the given probabilities to construct a “hypothetical 1000” table with columns corresponding to whether or not a penalty kick was blocked and rows corresponding to whether the goalkeeper jumped left, stayed in the center, or jumped right.
c. Use the table to compute the probability that a penalty kick is blocked.
d. Based on the given probabilities and the probability computed in Part (c), what would you recommend to a goalkeeper as the best strategy when trying to defend against a penalty kick? How does this compare to what goalkeepers actually do when defending against a penalty kick?