A college football team is trailing 14–0 late in the game. The team just made a touchdown. If they can, hold the opponent and score one more time, they can tie or win the game. The coach is wondering whether to go for an extra-point kick or a two-point conversion now and what to do if they can score again.
a. Develop a decision tree for the coach’s decision.
b. Estimate probabilities for successful kicks or two-point conversions and a last minute score. (You might want to do this by doing some group brainstorming or by calling on experts, such as your school’s coach or a sports journalist.) Using the probabilities from part (a), determine the optimal strategy.
c. Why would utility theory be a better approach than using the points for making a decision? Propose a utility function and compare your results.