Army Research Lab – Sniper Weapon Fire Control Error Budget Analysis
Do you know what a standard deviation is? If not, start with the Wikipedia entry on that then come back. The document above is rife with terminology from statistics. If you don’t understand the really quite simple definitions though you’ll probably miss the point.
What the document above says in short is that, all else being equal, a cold-bore shot on an animate or static man sized target beyond 700 yards is more or less a pipe dream. In fact, a first round hit even by a highly qualified shooter beyond 400 yards on a man sized target starts to get to less than 99% certainty of impact of metal on meat.