I have no idea how far coaches can bring players vs.what percentage is on them.
This is a good question. Maybe CoachOrange can respond.
Becoming a better player is most definitely a mix of both player and coach responsibility. it would be stupid to assign a percentage, but let's do it anyway. Let's say it is 65% on the player, and 35% on the coach. The ascension of an Etan Thomas, or an AO, or a Rick Jackson, is probably more about them than it is about Boeheim or Fine.
It's probably not much different than learning how to read. The kid has to want it. The teacher has to know how to teach it. To become elite, the kid has to have a foundation, an aptitude, a drive, and an environment in which to succeed. The teacher needs to know what they are doing, be organized, help the kid identify and set milestones.
Becoming a better team is on both as well. However, I'd inverse the percentages. It's 45% on the individuals and 55% on the coach. The coach sets the tone. He/she recruits the individuals. The individuals in turn have to respond, and accept the team concept. Average emotional leaders, like a Shumpert, cannot overcome the distractions caused by a Me-shaun. However, when you have competitors like GMac, Melo, and Kueth, and willing role players like Forth, Pace, and to a lesser extent Edelin, you have a perfect storm of success.
My experience is limited to being coached in HS, and briefly in DIII, then coaching about 4 of my kid's teams. I'll say this, great players make you look like a better coach. Average players make you look like an average coach. Bad eggs are incredibly, incredibly hard to manage, and can drag the whole team down. Selfish players can drag the whole team down. Not having a plan, not being organized, not sticking to your plan or philosophy, not being adaptive, essentially not knowing what you are doing and where you are going, will limit development. Skimping on your long term plan for short term success lengthens the time it takes to reach your long term goals. You have to know what you are doing. Some kids already need to know what they are doing, so they can lead by example. The others have to accept being part of a team, a diminished role in some cases, and do what you ask to get better.
It's dynamic and complex. Which is what makes the year-after-year, in-season & post-season successes of a Pitino, Donovan, Izzo, and K so incredible. Their teams always seem to buy into that team concept, play with incredible intensity, and gel as the season progresses. Some of those guys can select whatever recruit they want. However, others are in no better a situation than JB. I think there is something about the system, work ethic, focal points, that these guys teach, that is superior, IMO, than what Boeheim teaches.
I don't agree with some of the JB knocking that is going on in this thread. His success speaks for itself. It would be cheap to over-state his superlatives in his defense. Bottom line, IMO, emphasis on opinion, his players do not play with the same consistent intensity that the players of the guys mentioned above do. It's hard to watch. But to say he is a bad coach is over the line. I may disagree with finer points of his philosophy and approach, but he is one of the all time best at something that I've already stated is really hard to even be average at. He does it a different way, and in the post-season, it occasionally works well. Maybe not K or Izzo or Pitino well, but it works.