Yes, exactly...the range is your edge. Where in that range you are on any particular day is what is helpful to my psyche to view as more random. (And as you work hard and improve, that range will trend downward)
Are you saying that each player has a gaussian distribution around their average score? Or that we only have a limited amount of control over our score. Sure there are days that breaks will be bad, execution will be off and the combination will results in avery high score while others execution will be poor but luck will be with you and it won't be as bad. But ultimately a player's skill and decisions set the range.