Hilf posted some results from an accuracy test he did on the energy/chem pistol thread (
http://underrail.com/forums/index.php?topic=2008.15):
6 perception, 125(146) guns = 78% chance to hit
11 perception, 125(199) guns = 79% chance to hit
My target was Plasma Sentry. I did another test, same setup but with flare and result was again 1% point.
As I said in that thread, these results seem a bit strange, considering the effective skill difference is quite significant at 53 points. And because of that, I did a quick test of my own:
12 PER, 125 (210) Guns skill, Scoped Compensated 7.62 Hornet, character Focused, target is Praetorian Sniper right next to a light source, 13 tile/max sight distance = 66% chance to hit with normal attack, 33% with burst
Rapid Compensated 7.62 Jaguar, same conditions except distance is 9 tiles and less = 89% chance to hit at all distances with normal attack, burst precision increases as the distance decreases
15 PER, 125 (241) Guns skill, with the Hornet = 78% chance to hit with normal attack, 39% with burst
Jaguar = 90% chance to hit at all distances with normal attack, burst precision increases as the distance decreases
Assault Rifles (and very likely Crossbows as well, considering they have the same max range and only one tile less optimal range) seem to benefit considerably at maximum distance, but as soon as you move 2 or 3 tiles closer, chance to hit jumps to 95%, with both Perception values. Burst CTH is higher with 15 PER at all distances, although it caps at 92% with both 12 and 15 PER, the latter reaching it a tile or so sooner. Same thing with the Jaguar, although precision cap is lower than the Hornet's 92%. The Jaguar's normal attack is the weird one: it kinda seems to imply that the less range a weapon has, the less it benefits from extreme skill values.
I guess the builds that really want to max Perception for the accuracy gain are mainly burst-focused Riflemen, and crossbow users to a considerably lesser degree due to lacking burst fire. I'm fairly sure Sniper Rifles benefit even less, since they're always in optimal range.