Ya know what? I'm not sure ATM. I'll have to read the description again when I play tonight. I took Trigger Discipline and never use VATS. Hope I didn't waste a perk.
If I can see it, I can hit it. To put it another way, if it's close enough for the game to render it, I can hit it. It doesn't appear there are any physics for the bullets, damage is the same and it travels in a perfectly straight line with no travel time. This is with a gun score of 40 or less and
without Trigger Discipline. Does not appear to me that any aspect of your character affects accuracy outside of VATS.
As for your experience with the Cowboy Repeater, the iron sights on that aren't very conducive to sniping. I can snipe easier with a 9mm than with that thing. The ideal sniper gun for the beginning of the game is the Varmint Rifle with Varmint Night Scope. Gives you a nice zoom and a cross hair. Crouch on a rock and you can one hit kill everything in sight even on Very Hard, just aim for the head.