This needs to be put in perspective. At 120 yard with a Cap and Ball or any pistol, its a lob shot. Its not a sharpshooter shot. Sharpshooters did not shoot their targets with pistols, they shot them with a rifled gun and depending on what era and whose side etc etc etc.
So, yes you can take a shot at a mile if you want, once in a millions tried you hit what you are shooting at (note I did not say aiming). 120 yards with a pistol there is no aiming, you angel it up and guess.
Its why snipers have spotters. They see where the shot hit the ground and tell the shooter his setup is off and by how much. Then a 2nd shot (may or may not hit).
A sharpshooter and a pistol shoot are pretty close to being oxymoronic. No one sharp shot with a pistol.
So, 2.5 inches is considered acceptable with a modern pistol and certainly some finely tune BP will exceed that. Post Civil War was there any such thing? At 100 yards you are 10 inches (hoping there is no wind). So being generous lets call it 13 inches at 120 yards.
So that is what we call a manure shoot. Not given I am being shot at be the guy has a pistol or a rifle, its worth a try though at best you are likely to distract him (I am going to assume a guy here).
Your best shooter is limited by the equipment (and the equipment is limited capability wise to the skill of the shooter).
Now does a sharpshooter translate to a good pistol shot? No. Is it possible? yea. But would someone practice to hit things at 120 yard with a pistol. Oh hell no. That is what a rifle is for.
30-30? There is a reason its called minute of deer. Its more an Eastern US thing where the cover is thick and the shots are under 75 yards. More like 50.
I got pretty good with a modern pistol. 1.5 inches at 25 yards. I shot 100s of rounds to get there. How many people old west had the time to practice? Yea a few did but it was not a routine thing.
There were two phenomenal shots by a Baker Rifle in the Peninsula War. both by the same guy. Range is unknown, 400 yards probably a minimum. Pure luck (they laid on their back and supported the rifle with their feet for those longer shots). Was it worth a whack at 200 yards? Sure (you had a buddy to cover you while you reloaded). Worst case you just missed and you might well hit an adjacent person.
Sharpshooter and pistol shooter are a misnomer. Amazing shots were pulled off, but like the Baker shoots, a why not but you sure aren't counting on it.
For a guy with a Sharps? Yea, easy shot but even that is not guaranteed. You need a gun that is sub 1 MOA and a person who can shoot sub 1 MOA (a 2.5 inch at 25 is 10 MOA).
Longest sniper shot ever was proceeded by 2 shots. His spotter walked him in and the guys being shot at (3 as I recall) just stood there. No one ever said which of the 3 he was shooting at so the kill shot may have hit the adjacent guy.
