Depending on how you breathe, your posture, how you sit, if you exercised consistently as a child, etc. your face can look completely different. The greatest example of this is how early humans had significantly larger jaws due to their diet and exercise, while humans today who have almost the exact same facial genes have much smaller jaws.
Identical twins having extremely similar faces isn’t exactly a great argument for determining facial characteristics via dna, as identical twins also shared the same environment during fetal growth. It’s entirely possible that genetics and developmental experience combined creates facial structure, and that dna alone is insufficient.
I guess you should compare to non-identical twins. Who I think look like siblings who happen to be the same age. But no doubt someone somewhere has tried to quantify this.
I think "deforming accident" is a lot easier than some might realize. I personally have had an injury that probably changed the shape of my face, and it wasn't super note-worthy. Especially if someone gets something like a broken jaw, you can look almost unrecognizable.
Identical twins have very similar, but distinguishable fingerprints.