[ElspethB]

I'd say that one of the later battles was unbelievable, except that I suspect that Mr O'Brian could point me to a report of a very similar action that really did take place.

Apparently Jack's character and many of his adventures are modeled in part upon those of Lord Thomas Cochrane (1775-1860).

Spoiler:

If you were referring to the defeat of the Cacafeugo, that indeed based on Cochrane's capture of the Spanish xebec El Gamo while in command of much smaller vessel. Also, point of interest: "Cacafuego" is a rather a rather colorful term in Spanish.