The manager (the head of a baseball team is the manager, not the coach, for whatever reason) is also responsible for putting on the shift, telling the batter to bunt, calling for stolen base attempts, and other strategic things along those lines.

This. I was never a huge baseball fan, but my sons got into it, and observing beyond the surface it is really impressive how many split-second intelligent decisions you have to make in baseball, with (again) quick ad hoc coordination.