It's interesting to think about how much coaches actually affect wins/losses. I think at the lower levels, including college, where the coaches are still doing a lot of actual teaching and thereby impacting the development of their players, you could reasonably say that a coach dramatically impacts whether or not his/her team wins. When you get to the professional leagues, those players are by and large fully developed talent-wise and aren't as impacted by coaching. Of course, some aspects of coaching will always matter, like game preparation or in-game strategy, but generally speaking, I think a team wins or loses based on the performance of the players on the field. At least at the pro level, I think coaches/managers generally get too much credit when a team wins and too much blame when it loses.
It's impossible to know one way or the other, but it is interesting how many "genius", or HOF-level, coaches in the various pro leagues achieved their genius status when they coached a team with one, or even a series of, transcendent talents. Would Belichick be considered such a great coach without Brady? Would Torre be considered a great coach without Jeter/Rivera, etc.? Sometimes it's the opposite, like with Calipari and his army of NBA-ready players -- people fall over themselves trying to knock his ability as a coach. Of course, that's more because he's just so damn shady...
It would be great to actually know the true impact of a coach, like if we got to witness some alternate, bizarro 90's with Phil Jackson coaching the Mavs, or in the 2000s, the Clippers. Then we'd know for sure if he was a genius with an amazing offensive system, or perhaps just competent and in the right place at the right time. I'm tempted to think it's the latter.