Im kind or surprised nobody has said this but, in my opinion, a proper recoil pad installation usually requires hollowing out the stock so it balances right. Then again some people put lead in the butt...
Anyway, might as well make it balance right if you're going to the trouble of installing a pad.
Then, there are guns which were shipped from the factory with a recoil pad, but no longer have it because of deterioration or because some previous owner just didn't like a recoil pad and removed it. I have a AE Fox 16 ga. that letters as having been shipped with a Silvers pad. It no longer has it, and is way too short with the plain "hard rubber" buttplate it now wears. It doesn't feel right either, with it's 30" barrels and 13 +" LOP. It will soon be wearing an original Silvers pad as it should. It will again be in "spec", and I will like it much better.
SRH
