-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 6.3 summarizes the probabilities of each team winning the game. The optimal mixing rule for the offense is:
A) Randomly pass 5 out of 9 times.
B) Randomly run 4 out of 9 times.
C) Randomly pass 2 out of 7 times.
D) Randomly run 5 out of 7 times.
E) Both c and d are correct.

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 6.3 summarizes the probabilities of each team winning the game. The optimal mixing rule for the offense is:
A) Randomly pass 5 out of 9 times. 
B) Randomly run 4 out of 9 times. 
C) Randomly pass 2 out of 7 times. 
D) Randomly run 5 out of 7 times. 
E) Both c and d are correct.

Quizplus · Accepted Answer

The optimal mixing rule ensures that the offense's strategy makes the defense indifferent to defending against the run or the pass. Choices C and D together suggest a mixed strategy where the offense passes 2 out of 7 times and runs 5 out of 7 times, making it unpredictable and optimally balanced.

-Suppose That a Football Team Is Down by 5 Points