The Saintes

Background

The American Revolution was effectively over by April 1782. It was certain as anything can be that the rebellious North American colonies would get and keep their independence, while Canada would stay subject to the Crown. What was less certain was the future in the Caribbean.
On the mainland, effective military assistance from the French on the one hand, and indifference and political opposition at home, as well as less than competent command on land and at sea (compare the US experience in Vietnam), had settled the issue. The Caribbean situation was different: here the British thought there was an important issue at stake (the West Indian colonies were a source of wealth, not a drain on it), here the warfare was virtually all at sea, and here there was a competent commander, Admiral Sir George Brydges Rodney, victor in the Moonlight Battle two years before.
The French admiral, de Grasse, had landed the French troops that ensured Cornwallis' defeat in Virginia, and then defeated the British at the Battle of the Capes to stop British naval power coming to their rescue. Now he would sail to the Caribbean to see what he could do for France.
He took one island after another until by the beginning of 1782 only four islands remained under British control - Jamaica, St. Lucia, Antigua and Barbados. Jamaica, where Rodney had just arrived to take command of a total force of 36 ships of the line, was the next target. De Grasse left Martinique with 33 of the line on April 8 to make rendezvous with a Spanish fleet of another twelve, and 15,000 troops.
Informed of this by scouting frigates, Rodney left harbour and gave chase. He came up with the French on April 12, off the Iles des Saintes, close to Martinique, before they could meet the Spaniards.

The battle

The initial engagement was in line of battle, with the two fleets sailing on opposite courses at close range. As the leading French ships reached the rear of the British line, de Grasse gave the order to reverse course, to continue the battle with the other broadside.
Unfortunately, for whatever reason - a shift in the wind, incompetent sail-handling - the order was not carried out smoothly, and three gaps opened up in the French line. Rodney saw the same opportunity that Nelson and Duncan were to see in more famous battles twenty years later and ordered his ships to turn 90 degrees and make for the gaps.
The situation was even more favourable for Rodney than for his successors, in that the lines were much closer together, so that the approaching British ships were not subject to the lengthy bombardment from the French that they suffered at Trafalgar. Once the gaps were reached, the British could use both broadsides to rake the French, virtually without counter-fire.
De Grasse's 130-gun flagship Ville de Paris was the seventh ship to strike, with 400 killed and 700 wounded. As the day wore on, the rest of the fleet was either sunk or surrendered.

Aftermath

The overwhelming victory at the Saintes restored Britain's faith in itself and its navy, and earned Rodney a peerage and a statue in Kingston, Jamaica. It had no effect on the fate of the mainland colonies, but ensured that in the peace that followed Britain would keep her Caribbean ones - and the revenue that flowed from them.