This may have been a contributing factor, but the reason the American frigates were successful in the War of 1812 was because they were significantly larger and more powerful ships, with more powerful cannons. They had material advantages in size (100% heavier), crew (50% more numerous), and firepower (30-50% more weight of shot). The crews were well trained (and included many former British navy able seamen, pressed from American merchantmen) but it was the material advantages that swayed these combats.

It was curious how effectively the American naval establishment gamed the European 'honor' system of naval warfare - they knew that if they kept these warships technically rated as 'frigates' (even though they were the largest and most powerful frigates ever built, similar in size to smaller ships of the line), the British would still try to fight them one on one with their frigates.