How many hundred rounds of Brown Bess musket & rifle have you shot? Not many, I suspect. Anyone who has spent any time on the range with Revolutionary War era smoothbore muskets knows that there is no such thing as a perfectly aimed shot with one of those things. That is for the simple reason that they have no sights. You don't have to take my word for it, trained soldiers left a graphic record of how accurate muskets & rifles of the C.W. period were.
During tests carried out by the U.S. Ordinance Bureau in 1860, ten men fired 5 shots each at a 6'X6' target with .69 cal. muskets. At 100 yds only 37 of the shots scored hits that were scattered to every corner of the target; at 200 yards between 18 & 24 shots hit the 6'X6' target. These were trained soldiers that did the shooting. These & the results of 20 smoothbore & rifled musket tests are reproduced in The Rifled Musket by Claude Fuller.
Brown Bess, Charleville & other muskets of that era have no sights for the simple reason that in the tactics of the day, no sights were deemed necessary. (On the Brown Bess, the bayonet lug is on top of the barrel, which provides a sort of crude front sight, but without a rear sight that really isn't much of a help.) A major factor in the lack of accuracy even if there were sights is that when the ball leaves the muzzle at about 1,000 f.p.s. it begins to drop at 9.8 meters per second per second due to gravity. At 75 yards it will drop 10"; at 100 yards it will drop 18"; at 125 yds, it will drop 30". With no rear sight to adjust the angle of the barrel, there was no way anybody could accurately aim a musket of that era beyond roughly 50 yards where the bullet only dropped 4"'.
The drill for Brown Bess & Charleville infantry was to level their piece & fire. The sergeants carried pikes not as weapons, but to allow them to reach out & tap the muskets of their men level before firing. The ball would carry in a reasonably straight line for the short distances that these tactics dictated. A blast of .69 caliber lead balls from a line several ranks deep would have been murderous at 30 yards. That was when the real work of the infantryman began.
I am of course aware that the Brown Bess could not
in general be used accurately at long range (though I'm about to demonstrate that firing at area targets could actually be done) but the point is that out to 100 yards or so the difference in effectiveness between a smoothbore musket and a rifle is as much the provision of fixed sights for the rifle as anything - it's the aiming of the long arm at the target, not the tendency of the ball to go wild.
1) Your test numbers actually prove that the smoothbore musket had a reasonable utility against targets at 200 yards if aimed well. You yourself say that 18-24 shots out of fifty strike a 6 foot wide by 6 foot high target; a line of infantry is not the full 6 foot high, but it's more than 6 foot wide, so about 1/3 of shots could be said to hit at 200 yards.
I would say that a regiment of 1,000 infantrymen scoring 300+ hits on an enemy regiment of the same size at 200 yards would be extremely effective! Of course the problem is that men were never able to achieve theoretical performance in combat, not that the theoretical performance of the weapon at 200 yards was no good... but the point is that it doesn't really
matter if you hit the man to the left of where you were aiming, a hit is still a hit and that's why firing at area targets (dense lines of infantry, for example) was still done at longer range.
2) Firing on area targets could be done:
An unusual duel developed between their artillery and the muskets of the 1/43rd at a distance of 400 yards, far beyond the normal range of the Brown Bess. The 1/43rd had taken up a position in and around the church, a strong building constructed in the Basque fashion with two balconies above the nave. Windows lit all three levels. The wall surrounding the churchyard was lower than the nave, giving the 43rd four protected firing levels. Due to the conformation of the land in front, the French artillery, if it wished to fire on the church at all, had to expose itself on a crest 400 yards to the north. No infantryman could hope to hit a single opponent at such a range, but a target as large as a battery of artillery was a different matter. The 43rd, firing four-tiered volleys, caused the French gunners to fire inaccurately, and later abandon their pieces.
Weller, Jac. Wellington in the Peninsula (Napoleonic Library) . Pen and Sword. Kindle Edition.
3) Light infantrymen in the Napoleonic era tended to fire their weapons as individual aimed fire.
The ones who were trained at it and who had practice with their weapons would tend to have a sense of roughly where to aim, and the bullet drop isn't as much of an issue at 100 or 125 yards (aim at a man's head and the bullet drops 30 inches to strike him in the abdomen? No problem, it's still hit him). Weller in
Wellington at Waterloo states that the Brown Bess and other such smoothbore muskets would hit a man more often than they missed - in skilled hands - at 75 yards, which probably factors in some human error because at that range the ball's dispersal isn't enough to miss a torso and because he gives the same figure for the rifle (jager and Baker) as 150 yards (while in expert hands the Baker could hit reliably at ~500 yards).
4) For a weapon in soldiers' hands to be effective it is not necessary for it to be 100% reliable shots-fired-to-target-hit, or even 10% - 1% is quite manageable, though of course if you're facing an enemy with a
higher hit rate you have a significant disadvantage. The point is that there is a maximum performance (the theoretical capabilities of the firearm) and if a man is superbly trained he will approach that limit; a poorly trained man won't get even close.
As for the Brown Bess specifically, the British reserved their fire to unusually short range. This was because they wanted their best volley (the most psychologically damaging and effective one) to be as effective as possible at short range, and because British tactics of the time often involved a short bayonet charge on the heels of a damaging burst of fire - so the shorter the charge range the better. I suspect their usual method was to wait until an enemy column was just starting to deploy into line for combat, and then blast them at the moment of hesitation, as this would maximize the impact.