I think '.400' here is referring to a baseball/softball batting average. Where for every 10 at-bats the manager would be successful in reaching base 4 times. 4/10 >> .400. In terms of baseball/softball, a batting average of .400 is excellent and a rare accomplishment.

The verb is to bat so bats is the 3rd person singular and here it refers to a sporting score. The manager's skill level should be about .400 , a term referring to a score or points. Cricketers, baseball and softball players use bats in their sport. From the lack of context i'm not sure if it is a metaphor for a high achieving manager in a business or for a sports manager with that average score.

It is a baseball metaphor. In the context of everyday life, it would mean "four successes of out ten attempts" (or forty successes out of one hundred attempts, or two out of five, etc).