Quote Originally Posted by GoktimusPrime View Post
From in universe POV when a Time Lord regenerates the body is basically rolling a bunch of dice in a genetic lottery for their next appearance.
Gotta disagree.

Sixth Doctor stated that he chose his looks based on something he'd seen before (Colin Bakers previous appearance in the series) and if memory recalls, Capaldi's Doctor said something similar.

Plus The Curator (Tom Baker) said to 11 that he may find himself revisiting some old faces in the future.

So to me, that seems to indicate that they have SOME control. Just not when it comes to the ginger gene apparently.