After reading laram say that all great coaches have great players I wonder how much is just being in the right place at the right time and that even the best coaches can't make chicken salad out of chicken ya know.
Maybe not luck per se, but timing in terms of walking into an organization that is solid behind center or about to become so.
Belichick has had great QB play more or less all his time in NE, but he didn't have it in Cleveland and whereas he did fairly well, he still only went to the play offs once in 5 years and had an overall losing record - and even then he had Kosar.
It's difficult to name a truly elite coach who didn't also have an elite QB at some stage.
If BB had been wallowing with the QB's that The Bills, Jets or Dolphins have had for all his tenure do you really think it's possible he'd be being viewed as one of the greatest of all time?
Aside from the newer ones who will still don't know about, all the highly ranked coaches in the NFL have either great or solid quarterbacks.
There have been occasions in top-level soccer where great coaches have elevated average players, but it's a lot rarer now than it used to be 40+ years ago because now you can buy success if you have the cash.
There is nothing either good or bad, but thinking makes it so.