People often use the example of Cus Amato and Mike Tyson to illustrate the case of where someone might be a great teacher yet was never a high level practitioner himself. I'd say that makes Amato a great boxing coach, but not a great boxer, nor would I call him a 'master' in my own personal parlance.
So to your way of thinking, mastery requires both physical and intellectual excellence. Would you say true mastery is weighted more towards one or the other? Or does it require the highest levels of skill at both performance and teaching?