They might just be the least important.
Anyone can learn or be helped in managing a bullpen, not anyone can handle the Boston media with the blunt honesty and patience that Terry Francona does, while never throwing any of his players under the bus and always helping them and supporting them. The media sees as a straightforward gamer who always has a solid explanation for his moves, and the players see him as a friend and father figure who always has their backs.
Those characteristics are invaluable.
If you don't believe it, ask Joe Girardi.