I doubt that was the case as I doubt British statistics and call it for what it is which is bollocks , Do you really think after every battle somebody went round and counted the exact wounds on every causality and then counted every round spent , I very much doubt it.
Their are too many variables involved in battle to get an exact ratio of hits to shots what we do know is that in the ACW some volleys could be horrific and others fly over the heads , We know that soldiers well entrenched or in cover perform vastly better than their attacking counterparts.
The reason why some units performed better than others is not down to firearms training but unit cohesion and the abilities of some officers to take the initiative.
To simply state that dodgy statistics prove that the British soldiers were better shots than their American counterparts is absurd at best no offence , This fixation you have with statistics obscures you vision and and defeats common sense.
I would have thought that the Boer War and the debacle at Isandlwana would be a good indication that it does not matter how well your trained a band of farmers and natives armed with spears can still kick the **** out of you
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As Saph says, we known how many rounds were issued before the battle, and how many were accounted for after the battle. The difference approximates those fired.
At Inkerman, the British expended 199,820 rounds of small arms ammunition (176,670 Minie balls and 23,150 smoothbore balls), and 2,066 artillery rounds, and inflicted the best part of 11,959 casualties* (from which those inflicted by the French 7e Legere and their 2 engaged batteries should be deducted), i.e. 1 hit per 16.7 small arms rounds expended. Of those wounded, it was found that 91% had been hit by Minie balls.
* NB: Russian casualty reports exclude minor wounds. This presents a challenge when comparing to British casualty reports which include bruises, twisted ankles, burnt thumbs from continuous firing etc. in the wounded category.
Rosecrans made an estimate of rounds expended per hit at Stone's River, and estimated 20,000 artillery rounds round 728 rebels, and 2 million small arms rounds hit 13,852. To conflate them, it took 137 rounds of small arms ammunition per hit. In fact, Rosecrans overestimated the damage, and only around 9,243 rebels were actually hit, or 216 small arms rounds expended per hit.
In other words, British musketry at Inkerman was roughly 13 times more effective than Federal musketry at Stone's River.
At Gettysburg, it is recorded that Federal artillery ammunition expenditure was 32,815 rounds, and small arms expenditure may have been as low as 1.33 million rounds (by one reckoning, possibly as high as 2.67 m by another). 17,401 rebels were hit, so the range of effectiveness is 1 in 75 - 1 in 150 rounds per hit. The Federals used 16 times the ammunition as the British at Inkerman, but perhaps only 6.67 times the small arms ammunition. This shifts Federal fire effectiveness to being less effective.
As to the British at Isandlwana - after the battle it was lamented that "An assegai has been thrust into the belly of the nation". British fire effectiveness was so great that the 580 British riflemen, supported by some poorly armed NNC and militia cavalry inflicted around 4,500 killed and wounded on the charging Zulus. Ammunition expenditure is unknown, but archeology has found lines of groups of 35 cases where the British formed their skirmish line (i.e. 35 rds/man expended). Estimates are not more than 40,000 rounds were actually expended, perhaps down to 30,000. So hit rates were above 1 in 10. In all probability, had there been a full brigade at Isandlwana rather than a single understrength battalion, the Zulus would have been annihilated by fire alone. Had the British formed a solid line, rather than a dispersed skirmish line, the result would probably have been annihilation of the Zulus. The tactical lesson learnt by the British was the need to form close order squares against the Zulus etc., which were then extremely effective in African warfare.
The Boer war was of course a completely different conflict, fought with smokeless powder against an enemy who concealed themselves and dug in. The primary determinant of hitting the enemy was finding them. After the war, competitions showed that the British shot much better than the Boers, but of course the Boers fought from concealment. That's hardly a factor in 1862 or so.