Probably good genetics.

Wouldn't think "growth hormones" would have any effect on the antlers after years in the wild. Look like the usual normal red stags, not like the "special" "canned trophy" heads often seen in international magazines etc.

Genetics has a lot to do with it too. If (when it used to be legal) you can put some good superior animals to breed in wild herds, you also see quality progeny.

If all you do is shoot out the best heads, what do you think you will end up with after several generations of breeding ...

However good quality feed also has a LOT to do with an animal growing a good head each year. Even with the same animal from year to year.