From what the Doctor himself has said, it seems to be random:
- "That's the trouble with regeneration. You never quite know what you're going to get." (Fifth Doctor in "Castrovalva")
- "But it's a bit dodgy, this process. You never know what you're going to end up with." (Ninth Doctor in "The Parting of the Ways")
In addition, in "The Night of the Doctor", Ohila says the change is random (though the Sisterhood of Karn has the ability to direct regeneration), and in "The Day of the Doctor", the Tenth Doctor refers to regeneration as a lottery.