Potential helps a lot, I remember Elias training at the very begining; up until skill 10, during the first season he played, he poped up nearly every week when training only 1 position.
Actually, unless I am mistaken, it doesn't change training at all up until you get to the limit of the player's potential.
Meaning that in most cases, unless it's really low, you won't see the effects of potential until 4 or 5 seasons from when he was drafted.
I'm guessing height had more to do with it.