The kind of accuracy described by examination of the British fatalities at King's Mountain also suggests that many among the American forces were quite proficient and comfortable with shots at and beyond 200 yards... which requires much experience with one's weapon and how it handles at such ranges.
Again with respect, this is only partially true, but that is not a criticism of the Overmountain Men at King's Mountain or other American Riflemen.
Since King's Mountain was so heavily covered in tree's, the Overmountain Men fought "NA Style" taking cover behind trees while firing and advancing and doing quite a few tactical retreats before the battle was over. Original accounts talk of them getting within 80 to at most 60 yards of the British, but having been turned back a number of times by British Loyalist (smoothbore) firing until the Overmountain Men finally killed Major Ferguson (the ONLY British Regular in the battle) and took the place.
As to firing at and hitting British Soldiers fairly often at 200 yards, this was possible by aiming at the hats of British Soldiers and with the drop of the bullets at that distance, the ball would strike the enemy in the abdomen or groin, as long as the Riflemen estimated wind corrections correctly. If not, then the balls would go wide of the enemy soldier being aimed at pretty regularly.
Bullet drop at longer distances made hitting the enemy much less certain UNLESS they had time to "range their shots" as they did only one time I'm aware of and that was during the fighting around New York. In one area, they were shooting from a rest and across a river at the British. They were in those positions for 2-3 days, so they had plenty of time to range their shots. It is documented the American Riflemen hit a small portion of British Soldiers there out to around 325 yards, BUT again, this is the furthest documented source where they did so. (In this case it was documented by measuring the distance after the fighting.)
There was an EXTREMELY unusual case recorded by then British Lt. Col. and later General Banastre Tarleton, where an American Rifleman shot at him and his XO at 400 yards. However and even though they watched the Rifleman lay down and take careful aim at them on a day that offered PERFECT environmental shooting conditions, the only thing he hit was the "Bugle Man's Horse."
Further, there was another case in Carolina where around 25 riflemen shooting from inside a cabin and others using the split rail fences as support at a distance of around 150 yards when they began shooting. ALL fired at least once and many fired twice at a "Rather Portly British Major" while he crossed a river on horseback coming towards them. Now the target was moving, but not that quickly, as the horse was swimming for a good part of that crossing. Not ONE of their at least 30 shots fired hit the British Major.
After this, Light Horse Harry Lee who was a STRONG supporter of and VERY knowledgeable on American Riflemen, ordered that henceforth they were ordered to no longer shoot at anything beyond 150 yards.
About 6 years ago on this forum we had a great discussion on the Accuracy of 18th Riflemen and much of the information is from that thread.
Gus