Edit: I can unequivicably say that perception has absolutely nothing to do with VATS % chance to hit. Neither does it increase max VATS engagement distance. There you have it.
That's just bizarre. I think it was the same in FO3, too, and it didn't make sense. PE was
huge in classic FO, and other than for a couple perks and the rare dialogue option, it's pretty much useless in this game. Hopefully this will be a fixed for FO4.