The Underdog Strategy

Suppose we can model a baseball game between two teams as follows:

1. The incumbent team and underdog team draw a random variable from the following distribution
   Incumbent: $Z_I \sim N ( \mu_I, \sigma_I )$
   Underdogs: $Z_U \sim N ( \mu_U, \sigma_U )$
2. It is known that $\mu_I > \mu_U$ , indicating that the incumbent team performs better than average
3. 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 $\sigma_U < \sigma_I$ ?