The angles most battles happened at would mean the shot would have to go through water to hit the keel, and water is VERY good at stopping high velocity impacts. Also in the age of sail, you usualy wanted to capture the ship and take it home, either as your own ship or for a “salvage” prize from the government. Basically the government would buy the spoils of war.
The goal wasn’t to sink the ship, but rather to incapacitate it and demoralize the crew so that they would give up, allowing you to capture the ship and any cargo. Also, it was much more common for the crew to simply give up and change sides if they weren’t officers, so if you could get them feeling hopeless and beaten, they might just join you and voila, new, experienced sailors!
Very few ships were sunk in battle in the age of wooden warships (a few – as at the Battle of the Nile – blew up when a shot triggered a chain of explosions that led to a magazine). Water stopped balls aimed below the waterline, and hitting ‘between wind and water’ was hard. Also, ships of the line had galleries at the waterline patrolled by carpenters with plugs and shores, to control this kind of damage. The best way to disable a ship was to kill the gun-crews, either by superior weight or speed of fire or by firing along the decks, through the less protected stern or bow (a raking fire). The Shannon, a crack gunnery frigate, walked a cone of concentrated fire along the gun-deck of the Chesapeake, killing crews and dismounting guns, then boarded and captured the demoralised remnants. Capture was so common that one historian remarked that the British regarded the French navy as a sort of floating reserve (eg Trafalgar – 21 ships taken)
Smooth-bore cannons, accuracy was crap. Aim at the centre of the target and some of your broadside will inflict damage. Aim at the waterline and most will be stopped by the water.
In the US Civil War, Fort Pulaski was bombarded by them-thar new-fangled rifled cannons. They could reliably hit the same point every time. The walls were breached in 30 hours and the fort surrendered. Fortified strong-points became redundant overnight.
Cannonballs actually have shitty (relatively) penetrating power due to their shape (a ball instead of a conical bullet) so just a bit of water would make it much less effective at damaging the ship.
Plus as other said – you would want to capture the ship if possible, even if just to plunder it for goods instead of sinking it.
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