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EXPECTED VALUES AND STRATEGY IN SPORTS HOMEWORK
In the final section of this chapter we used win probabilities to investigate whether going for it
on 4th down was a good strategy in the NFL. Earlier in the game, however, it makes sense to
use expected points to evaluate whether going for it on 4th down is a good strategy. Suppose
that a team is facing a 4th down with 3 yards to go on the 50 yard line. The conventional
strategy would be to punt. Using historical data, the team kicking the ball in this situation
would have -0.3 expected points (the other team would have 0.3 expected points). If a team in
this situation attempts to go for it on 4th down, they have a 58% chance of earning a first down
and 2.0 expected points. However, if they fail on 4th down, they give the other team the ball
back around the 50 yard line and have -1.8 expected points (the other team would have 1.8
expected points).
1) Interpret the value -0.3
2) Interpret the values 2.0 and -1.8
3) If
expected points, display the probability distribution of
for teams in this situation.
4) In this situation, is going for it on 4th down a good strategy? Justify.
5) Some teams may be more likely to convert a 4th down than others. What minimum
probability of success should teams have in order to make going for it in this situation a good
strategy, assuming the expected points scored remain the same? Justify.