Sure, the players do the hitting and pitching, but managers really do impact a team's success. Talented players, like the Red Sox have, and a good manager can be the difference between a winning team and a below .500 team.
First of all, there are at least 1,000 signs flashed during a baseball game between the two teams. Most are generated by the managers, if not directly at least by the managers' designs.
The pitchers and catchers sign at least once per pitch and usually more. The pitch strategy has been pre-determined by the manager and staff before the first pitch is even thrown. The manager and his staff have to determine how batters will be pitched to.
Infielders have to know where to be positioned and who will cover the bag on a throw. If the wrong infielder leaves position to cover the bag, he will leave a hole for the batter. It is not always a left or right handed thing. The inside or outside pitch has to be called and the positioning has to be coordinated.
The outfield needs to know where to position themselves, and not just by the batter, but also by the pitches being thrown.
The offense has to be designed around strengths of the individuals. Whitey Herzog was an excellent example of a manager who would take advantage of personel. When he had only Jack Clark with any power, he ran the bases. He made sure Clark got fastballs to pound by sending runners. His offense put pressure on the defense and manufactured runs.
Pitchers and bullpen might be the hardest part of managing. When does the manager replace a pitcher? It can affect several games if the manager gets the relief pitcher up too early. It can lose a game if he waits too long.
The manager has to be a clubhouse leader. A manager can't simply say, "It will be my way." He has to earn that respect and act in a way that inspires athletes who earn millions of dollars.
Managing large egos and knowing the important nuances of baseball are not easy. I hope the Red Sox find the right guy. In my opinion, Bobby Valentine is not the guy.