In books written by Patrick O'Brian and CS Forester captains of different ships often speak of having less than their complement of seamen. Which is the reason for my question. According to the same books, seamen were alloted a standard 14 inches to sling their hammocks below decks. Was the crews complement a simple mathemathical equation of the amount of men that could be fit on a given ship with this 14 inches of hammock space per person?
Or was it perhaps decided by some other metric like the rating of the ship or the amount of cannons? If not, was there a system in place where the admirality decided the complement on a ship by ship basis?
Each rating of ship was given an allowed complement of men for whom the admiralty would pay and feed. The main requirement for men on a man of war was the guns but there were also officers, idlers and men to work aloft required to make up a full complement. For example, a first rate ship of 100 guns had a complement of 880 while a third rate of 74 guns had a complement of 600-700. The actual numbers would fluctuate depending on the captain, where the ship was, how long it had been at sea and what its assignment was.
All the numbers that you see quoted are just an ideal situation that often could not be achieved. All ships were slightly different, even if built to the same plan, so it might be that a ship simply couldn't fit the required number of men. Recruitment was something that the Royal Navy consistently struggled with in this period so ships often were forced to set sail without the proper numbers even in times of war when press gangs were sent out to find sailors and force them to join. On top of this, men died at sea on a regular basis meaning that ships would end up being below complement by the end of a journey.
It's worth being careful with the 14-inch rule as well. There were plenty of ships that did not conform to that standard, particularly ships captured as prizes. The men posted on those ships were not scared to complain however such as this petition from the men of the Flamborough's Prize:
... we are almost devoured with vermin by stowing two in a hammock and so close, not having more room for two than is allowed for a single man ...
N.A.M Rodgers book "The Wooden World" is really good for understanding what life was like for sailors in the Royal Navy in the Georgian period. He includes a table at the back that goes into detail of how many men were authorised for each job on all the various ratings of ship. I would highly recommend picking it up.
This link to another question has a great answer from u/airchallenged that discusses the role of everyone on the ship.