Question about +stat buffs on familiars

OK, I've gotten a few now and I'm wondering this; does the summon rank increase the buff amount? I just got a Phantom Watch (common) and it states that it gives a "large amount of INT", so I summoned it and it gives...3INT. Basically, I'm asking, does a unique/legend/whatever summon give that same ratio or does it work sort of like potential, ramping up based on tier?