What I wanted to point out (I dont know if anybody already mentioned this, cause I havent read the whole thread) is that I think its just the free throw skills which influences free throws. If a mediocre shooter gets 23-27 and a strong 27-43, it could just be pure coincidence. I think theres a percentage for every throw you take (E.g. a mediocre shooter has 62% chance to hit and a strong 73%). So it could be that the mediocre shooter was quite lucky and the strong shooter had bad luck. If you really wanted to proof this you should compare higher numbers (for example 10000 tries), so the result gets (in a mathematical point of view) more precise.