"Unless you're proposing that circumstances may change the shooter's mechanics, I don't get what you're saying."
You think circumstances don't change the shooter's mechanics?
Consider that if a basketball player had perfectly consistent shot mechanics, and always shot from the same point on the court, he would always score. Shooting a basketball is a fairly deterministic ballistics problem--no wind since it's indoors, large target, large projectile. Thankfully, basketball gives us exactly that situation: free throws. The very best free throw shooters in the game only make 90% of free throws: http://www.basketball-reference.com/leaders/ft_pct_career.ht...
A basketball player who makes 45% of three point shots isn't some sort of machine which has a 45% probability of sinking any given three-pointer, he's a human being who varies in terms of age, physical condition, fatigue, and even psychology. When betting on black loses at the roulette wheel 16 times in a row that's pure math--when a human being misses 16 straight three point shots, it's more likely he's mentally and physically tired and his mechanics are shot.