I found this article in American Rifleman and it caught my attention. After the Revolutionary War, it was believed that one of the advantages of the Continental Army was that, on average, Americans were better shots than their British counterpart. That belief held until WWII when it began to come under fire (pun intended).
In recent years, the argument against American marksmanship has even taken on a political tone with pro- and anti-Second Amendment advocates trying to make their case. It should also be noted that the American Rifleman is the National Rifle Association’s magazine.
It is an accepted fact on both sides of the argument that the musket was an inaccurate weapon, at least compared to today’s weapons. Among the British, it was considered that anyone who could hit a three-foot-wide target from 100 yards one out of five or six shots was quite a marksman.
Now what needs to be remembered is that many Americans depended on their marksmanship skills to bring them a meal at night. Also, many of them were veterans of the French and Indian Wars. While not professional soldiers, American Colonists knew how to shoot.
Author Alex Rose writes, “Sergeant Roger Lamb of the Fusiliers judged that ‘the generality of the Americans were good marksmen; the whole of their previous military knowledge had been derived from hunting, and the ordinary amusements of sportsmen. The dexterity which by long habit they had acquired in hitting beasts, birds, and marks, was fatally applied’ during 1775.”
While items like this are fine anecdotally, Rose looks at the statistics of the shots fired at Bunker Hill and compares it against the statistics provided by European military experts at the time for their army’s accuracy. His comparison leads to the conclusion that Americans scored a hit with every one out of 50 shots while the British hits one out every 500 shots.  So the Americans were 10 times better shots than the British.
Rose even compared the European military stats with the stats of one of the biggest critics of American marksmanship and found that Americans were still twice as good a shot as the British.
Check out the article for yourself here.