According to Len Pasquarelli in the first 10 games of the 20

According to Len Pasquarelli, in the first 10 games of the 2004 professional football season in the United States, two-point conversions were successful 51.2% of the time. We can compare this rate with the historical success rate of extra-point kicks of 94%.

a) Calculate the expected value of each strategy

b)over the long run, which strategy will maximize the number of points scored?

c) From this information, should a team always use only one startegy? Explain.

Solution

These are binomil distribution variables with p=0.512 and 0.94 respectively

a) Expected value of 2 point strategy = p = 0.512

Expected value of extra-point kicks = p = 0.94

b) Number of points in the 2 point conversion = 2*0.512 = 1.024

Number of points in the extra point kicks = 0.94*1=0.94

(Note: An assumption is that two point conversions score 2 points if successful and extra point kicks score one point if successful. If that is not the case, kindly change the w and the 1 above to the appropriate score and calculate that value)

c) No, as the expected values of the points obtained are close, a team should not always stick to one strategy. It may want to play safe with the extra point kicks for low returns, or can go for the two point conversion for higher returns