I think a good manager's impact shows up in overall athletic performance and execution by players on the field. To me, a great manager instills a certain philosophy in the team. It is like a general guideline that emphasizes execution, effort, and consistency. I don't know if I would describe this as fire, but more as maximizing potential of athletic performance. Each player's strengths should be brought out as best they can and weaknesses should be minimized.
For example, the Hanley outfield experiment was an example of poor management. Once his deficiencies there were observed, the plan should have been immediately scrapped. Now it can be argued this was not all the fault of just Farrell, as his hand was forced somewhat. But it is still a management issue in the broadest sense.
Management is always a team effort with key players being the GM and the field manager. The more closely they work in sync, the better job they can do. A GM should work with the field manger to address needs on the field and try to find players to address those needs. Much of the field manager's success hinges on the talent he has to work with. It is then up to him to maximize the potential of that talent. So winning is not really the true measure of a successful manager. It is rather a subjective evaluation of whether or not he has brought out the best in his team and they are performing near enough to their best potential. That is really all a manger can do. He can't win games by being smarter but he can get the best out of the players he has. How to judge that is subjective because it depends on your view of the talent he has and how good you think they should be performing.