The guns of the sailing navy had nowhere near the range and accuracy of today’s naval rifles, although they were just about the most powerful weapons in their own time. (Indeed, the establishment of the “three-mile limit” as the boundary of territorial waters in international law was based on the extreme range of just such guns.)
The basic cannon was a model called a “long gun,” for it had a long barrel. In a ship like our famous old frigate Constitution (“Old Ironsides”), the 24-pounders were considered accurate to a range of about 1,200 yards, although a cannon ball fired from one might go three or four times that far. A carronade, on the other hand, although it might be able to fire a heavier shot from a lighter weapon, was largely ineffective beyond 400 yards. Thus, it can be seen that, at the longer range one fires a gun, the less the chance of scoring a hit on a target. In naval parlance, this was a “long shot.”
“Long shot” has come ashore strictly as a measure of the likelihood of something happening, and is most often heard today among bettors at a horse track.