Brown Bess (Long Land Pattern Musket - various versions 1722 to 1860) had a 0.75" bore and used 0.69" balls in paper rolled cartridges. They were more interested in continued fast & easy loading in a fouled bore than accuracy. Both sides used them in the Revolutionary War and the War of 1812; thought by the latter most American troopss were using 0.65" balls in 0.690" bore Committee of Safety Muskets.
The 0.50" ball could be for a .52 caliber rifle. Or, more likely, it's a deformed 0.53" for a .54 caliber rifle (popular in the early US and Colonies,- I still hunt with one)