From what I recall, Cashman and Girardi fell out because of Joe's unwillingness to become more of a saber-metric oriented manager. I understand the need for metric stats in certain situations but none of those stats reflect what is happening in a game/inning at that particular moment when a decision is being formulated. Saber metric stats are a useful tool but they need to be used in conjunction with what has already taken place in the game.
For example, I've long been of the belief that if ANY pitcher is dominating a team for 6 innings or so, and is still well under what is consider a pitch count limit, leave him in !
I don't care how many times he's been through the line up or how many days the relievers have not pitched, leave the starter who has already shown that he's on his game that night and let him pitch until there are some real warning signs to warrant taking him out of the game....how many times have we seen a starter removed prematurely only to watch as some "reliever" stinks up the place and blows the game? The simple fact is that teams are blowing games in the later innings at the same rate as they were 50 years ago.
Again, "if it ain't broke, don't fix it" !