Well, i'm playing a game on VH/VH as United provinces. I haven't had any land battles yet, but i have had a naval battle that makes me suspect the AI are getting bonuses on very hard battle difficulty.

At the start of the campaign i had a single pirate ship raid my supply line in my American holding. I sent the navy there, a large twin-decked admirals ship, a smaller single deck, and two even smaller vessels to deal with them.

I sent the admirals ship and next largest to either side of the pirate ship, which was larger than anything i had, and had both of them unleash their right and left full volleys, to very little effect. The pirate ship put a single volley into the smaller of my two ships and sent it routing. My admirals ship and the pirate ship were exchanging volleys from quite a distance while i moved my two very small ships up. One of them routed without being hit or even firing a shot, the other routed after taking only around 15-25% damage.

My admiral and the pirate ship, which had taken next to no damage at this point despite several point blank range volleys, continued to exchange fire, although it was clear i was going to lose. I tried to target the sails of the pirate ship to stop the damn thing sailing around in circles, at two point blank volleys the pirate ships sails had taken no damage and it was sailing around as if nothing had happened.

That was when a volley sent my admirals ship routing after taking around 50% damage.

I don't care that the pirate ship was a monster battleship, my admirals ship was only 1 step below it in terms of quality and i had the pirate ship sandwiched between my admiral and the smaller vessel, put a full volley from each ship into it at point blank range and did barely any damage to the pirates, yet every single volley from them ripped through my ships like a demolition ball to a brick wall.