How often does firing an NFL coach make things better?

[SolidSnake84]

This may seem like a stupid question but watching TV this morning they were talking about Rex Ryan and how he is most likely going to get fired even though he is well respected and for the last two games the Jets have been playing their hearts out...

How much through NFL history has it been proven that firing a coach, the team was better off? In my life I've seen it make no difference in places like Oakland, St. Louis, Jacksonville, and our own Redskins are probably one of the best examples.

I realize that the Head Coach is ultimately responsible for everything that happens with the football team, and when the teams starts sucking, and on a losing streak - he ultimately pays the price. But do you think that is fair? For the sake of argument lets look at the Redskins:

Coach after coach and we basically are no better. This year we already have a lost season. But is it really Jay Gruden's fault that we have problems at QB, Defense, Special teams? I mean he isn't the one making plays, or throwing the interceptions, or letting the other team run the kickoff back..

I guess i'm just looking for examples where firing the coach was absolutely the right move for the franchise and it resulted in wins, playoffs, etc....