Morgan had his men set up in a spot where the only option the British had was to go directly into them. They were surrounded by very wet terrain that made it very hard for the British carryall to go through. This caused the British to basically have to march right into the American solders. Another huge factor in the battle was the weapons used. The first line of the American troops were armed with rifles while the British solders were armed with muskets. The rifles fired with more accuracy and distance then the muskets. This allowed American solders to pick off British officials before they were even in range to fire back.
Taking out a lot of officials and even Calvary really softened the blow of the British solders This was a massive advantage for the American solders. Also, even though General Morgan only reported 800 men, there is a very good chance he had many more than that. Almost 800 solders that said they fought in the Battle of Cowpony applied for pension about 50 years after the war ended. Considering the fact that many of the solders that fought at Cowpony would die in later battles and it is unlikely that every solider would apply for pension there could have been close to 2000 American solders fighting in this battle.
This would make the British the underdog and not the American solders like has been previously thought. One other factor that probably played a role in the defeat of the British is the conditions they had to go through. They had been perusing General Morgan men for over two weeks. On the morning of the battle they got up at am to march 12 miles to get to the site of the battle. Also, it was January and had rained the night before. The British had to be freezing cold, red and hungry which could have played a role in how well they performed in the battle.