Started a new rebels and patriots campaign with the gf, she the British I'm the Americans

The British were tasked with holding 2 fences, with the one in the north being a sunken road providing hard cover. The American force must capture the road in the north.

British forces were 3 light Infantry with the good shooter trait, plus one small militia unit(due to a trait of the British officer), a total of 42 men, which were deployed behind the fence in the south which provided light cover.
The Americans had 1 unit of regular line infantry, which the commander was part of, 3 large units of green line infantry and 4 large units of militia, a total of 138 men, and deployed in the forest to the south of the fence.

I thought the sheer number of troops would pour enough firepower into the British to break them, but even with the advantage of 1st fire, it turned out very early on that the numerically inferior British force had the shooting advantage.
The American troops were spread out and most had to score very high on the dice to even take an action.
In a blunder at the beginning of the game, the British commanders unit advanced forward into the open ground ahead of the fence, yet the American shots had no effect, most likely due to the light infantry counting open ground as cover.
The British infantry were able to focus fire and inflict severe casualties on the American commanders unit, causing him to be badly wounded, with the unit fleeing the field. This caused a chain rout among the militia units, but 2 of the green regular units escaped in good order, and the British were relentless in their fire, inflicting even more casualties in the rout. Despite the loss, the American commander was praised in the press for his "true grit", insisting to stay and fight as he lay wounded, he was forcefully carried off the field by his men.

The British suffer 10 casualties, with 4 being local militia, while the Americans suffer 20.