ESPN examined continuity. "The New England Patriots' 31 NFL rivals have combined to employ nearly 300 general managers, head coaches, offensive coordinators and defensive coordinators from 2012 through this offseason. Three men have filled those roles for the Patriots over the same period."
Players matter. What predicts success? "The only variables that predicted NBA success were youth, college performance, and college quality. These variables predicted NBA performance better than draft order."
The coaching carousel is seldom kind to revolving door management. Constant changes in management means change in philosophy, system, teaching, and communication. The Freakonomics blog reviewed studies and showed that coaching changes of poor and middling teams generally produced mediocre results. "These authors find that if you are a bad team, changing your coach didn’t make a difference. And if you are “not bad,” a new coach makes it worse."
Analysis of NBA results by coaching tenure concluded that longer-tenured coaches did win more and attributed this to three factors:
On average, first-year coaches have a small negative effect...which improves with time. They also found that longer-tenured coaches produced improved player, team, and coach performance.
In other words, process - and all that encompasses - matters. The quality of the players and the coaches probably limit the extent of the differences in professional sports. I believe that with more heterogeneity at lower levels (both players and coaches), that coaching can have its greatest impact at lower levels.