Well, that's what no less than Roosevelt and Black - a century and more apart - have said. It's what Bibbings has laid out in his excellent essay on Broke , "A Gunnery Zealot", showing in detail how Broke departed from his RN peers in emphasizing gunnery drill and training. And it's why in his "Standing Orders on the North American Station" Sir John Warren had to direct his captains to spend far more time and effort on gunnery drill. Your "data" is limited to weight of iron/broadside - show me "data" on shots fired, hits, and location of hits.
Broke did a lot of gunnery drill, but that was the norm. In all the other cases the RN showed very good gunnery too, but when a thick hulled 24 pdr armed ship goes up against a very thin hulled (especially
Guerriere and
Java, both of which were prizes) ship with 18 pdrs, the result is pretty inevitable.
Guerriere shredded
Constitution' s upperworks and masts with her extremely effective fire, getting 50% more hits per gun than the American ships. However, her 18 pdrs simply couldn't match the 24 pounders. Already rotten and in need of docking,
Guerriere was simply getting hit harder despite having far better gunners.
Java's gunners also completely outshot
Constitution, but despite Java getting a raking shot in at close range, the 18 pdrs simply didn't penetrate the hull. Hence
Constitution gaining the "Ironsides" moniker because the 18 pdrs didn't pierce. Again, the weight difference mattered,
Java's guns could not penetrate
Constitution's hull.
Constitution's guns easily penetrated
Java's hull.
The
Macedonian was the only British-built frigate lost . Hence she had a stronger hull (and it shows because unlike the
Guerriere and
Java, she was still seaworthy after the fight). Whilst this is the greatest firepower disparity was the highest of all the fights, the British captain made things worse for himself by holding the range open because he misidentified the enemy as the carronade armed
Essex. This was also the American Captains plan. The
United States' 24 pdrs were hence in effective range, but the
Macedonian's 18 pdrs were out of range. Hence again it was the weight of the guns that was decisive.
Then there are the two combats against 24 pdr armed RN frigates, both of which the US lost, despite in both cases having the larger, more heavily armed ships. Excuses of course are made, but I note no excuses are made for the rotten hull of the
Guerriere or other RN disadvantages.
By summer 1813 there was 11 24 pdr armed RN frigates on the American station. All US victories had been against much weaker ships, and now the US captains would have to face nearly equal ships. The gig was up.