-Suppose that a football team is down by 5 points and faces a 4th down with 1 yard to go and 1 second left on the clock. The offense can either run or pass the ball. The defense can either defend against the run or the pass. Refer to Figure 6.2 summarizes the probabilities of each team winning the game. The optimal mixing rule for the defense is:
A) Randomly defend against the pass 1 out of 8 times.
B) Randomly defend against the pass 7 out of 8 times.
C) Randomly defend against the pass 2 out of 8 times.
D) Randomly defend against the run 6 out of 8 times.
E) Randomly defend against the run 7 out of 9 times.

Question

-Suppose that a football team is down by 5 points and faces a 4th down with 1 yard to go and 1 second left on the clock. The offense can either run or pass the ball. The defense can either defend against the run or the pass. Refer to Figure 6.2 summarizes the probabilities of each team winning the game. The optimal mixing rule for the defense is:
A) Randomly defend against the pass 1 out of 8 times. 
B) Randomly defend against the pass 7 out of 8 times. 
C) Randomly defend against the pass 2 out of 8 times. 
D) Randomly defend against the run 6 out of 8 times. 
E) Randomly defend against the run 7 out of 9 times.

Quizplus · Accepted Answer

The optimal mixing rule for the defense to make the offense indifferent between running and passing must balance the probabilities such that the expected outcomes of both options are equal. Choice A suggests a strategy that could potentially achieve this balance by varying the defense's focus between run and pass plays.

-Suppose That a Football Team Is Down by 5 Points