Questions: What calibers? What Rate of Twist? What groove depth? Which Minie used? How much did the minie weigh? How wide was the skirt at that the back/bottom of the minie? How much was the powder charge used? How were the minie's sized to the barrels? At what distance were shooting all these minies back then?
Because of the nature of the minie, it was studied quite a lot when first used in the 19th century, and again in the mid-20th century when these kinds of guns and bullets were replicated for re-enacting prior wars. Today, you can still find fine made rifles, and molds for the minie, and sizing dies that marry the bullet to these rifles well enough to give very fine accuracy.
The only problem I have ever seen or heard talked about is the skirts breaking when powder charges exceed 60 grains of FFFg powder, and that relates to a particular cast bullet with a thin skirt.
In the last 50 years, that problem has been largely solved, with molds made to produce minies with thicker skirts. The problem is still discussed because there are now so many replicas in those calibers being dusted off as the guns are passed from father to son, or grandfathers to grandsons, and the younger generation does not know much about the guns or the bullets.
Just remember that Battle Tactics at the time the minie was first introduces to military firearms still followed the Napoleonic traditions of lines of troops facing each other at 50 yds, and firing volleys of shots at each other. ( Musket tactics) Because of the death tolls created by rifled guns shooting minies, and the increase in the severely wounded coming off these battlefields, The Army generals were forced to change their tactics, by having their men shoot from cover. The Generals still like those bayonet charges. What's the point of having that great looking sword on your belt if you can't lead a bayonet charge??? And that still had men running towards enemy ranks concealed and shooting at them with accurate rifles and heavy minies, so the death tolls took a while before they began to drop. More soldiers died of infections and diseases acquired in camps due to poor sanitation, during our Civil War than from battle wounds. But that fact is not because the Generals didn't try harder to kill more men in battles.
I have seen some rifles shooting some minies do some extra-ordinary shooting at long ranges. But I have also seen guns with other minies that could hardly put the ball on a 2 ft.square piece of paper at 50 yds.
I don't think there is anything more mythical about finding accuracy with a gun shooting minies than any other gun shooting any other kind of projectile. My Hodgdon Data Manual No.23, dating back to 1978, lists loads for a variety of "mini-balls", weighing from 315 grains up to 570 grains, and in two different diameters: .575", and .577".
If the barrel is in good condition, and you have the right bullet diameter, and powder charge, there is no reason to expect the gun NOT to shoot well. Now, whether the shooter can hit anything with that gun is another matter. :thumbsup: