Suppose we can model a baseball game between two teams as follows:
- The incumbent team and underdog team draw a random variable from the following distribution
Incumbent: \( Z_I \sim N ( \mu_I, \sigma_I ) \)
Underdogs: \( Z_U \sim N ( \mu_U, \sigma_U ) \)
- It is known that \( \mu_I > \mu_U \), indicating that the incumbent team performs better than average
- The team that wins, is the team with a higher \( Z \) score.
As the underdog team, to maximize your probability of winning, do you want to be risky (\( \sigma_U > \sigma_I\)) or conservative \( \sigma_U < \sigma_I \)?