In any human engagement, there is always a psychological factor. So, even though the Americans were outnumbered and under-equipped, they were determined to break from the oppression of the British since most had originally come to American in order to flee that very thing, whether be it in another form such as convicts, indentured servants, or a persecuted religious sect.
Many of the militia were farmers, merchants, or artisans. But they had experience in guerilla warfare as they had fought many a battle with Indians. They ambushed their opponents just as they shot game; they wore hunting shirts and blended in with the environment and were undisciplined, unlike the British who wore red uniforms and fought in military formation.
The line "Don't shoot until you see the whites of their eyes" is famous, and it expresses the method of fighting that the Revolutionaries employed. This element of surprise became a major tool of the American army, and their Indian allies used it to its maximum advantage.