I do want to note just for the point of historical accuracy: Britain did not possess by any means the strongest army in the world. Britain was primarily a naval power, and they concentrated most of their recruitment efforts into supporting that navy, which left their army short on manpower. When it came to land warfare on the continent, they tended to rely a lot on their alliances. Nevertheless I agree with your overall appraisal: when the American Revolution began, I think it would have looked like a complete mismatch.

Even so, the colonists did have some advantages. For one thing, the British were orchestrating the war from an ocean away. On a related note, the colonists knew the land much better than the British did, and they exploited this advantage quite successfully in their conflict with the British. In addition, they received assistance from European advisors such as Baron von Steuben, whose influence brought colonial forces closer in line with European military standards.

Finally, there was the impact the Battle of Saratoga, the Revolution's first decisive victory over the British, had in Europe. Keep in mind, Britain had a lot of enemies (perhaps most notably France), and this victory gave those European rivals enough confidence in the American cause to justify intervening themselves. In essence, the American Revolution was not just a war between the revolutionaries and Britain—it also drew in France (and later Spain), which provided a counter to British naval and military superiority.

The American victory in the Revolutionary War was nothing short of amazing. Nobody would have predicted an American victory. Even Britain’s rivals, France and Spain, waited some time before actively helping us.

There are reasons why the colonists won this war. One factor was the colonists had several reasons for which to fight. The colonists were fighting for their freedom and the right to govern themselves. Some colonists were also fighting for their life. It is likely some of the colonial leaders would have been tried for treason. If they were found guilty, they could have been executed. The British, on the other hand, hired some of their soldiers to fight. They were fighting for pay, not for a cause in which they deeply believed.

Another factor helping the colonists was the brilliant military leadership of George Washington. Washington was a great leader who understood how to develop and follow military plans. He knew how to lead troops. Compare his leadership to the British generals, and it is easy to see why we had an advantage in this area. Some British generals got their command because of whom they knew, not how good of a leader they were. General Howe didn’t follow the plan to move his army to Albany. Instead, he went the other direction and went to Philadelphia. General Burgoyne carried so many luxury items with him, his troops could only move very slowly. This gave the colonists time to regroup and block the path of Burgoyne’s army. The military leadership was one of the colonial advantages.

Finally, we were fighting on land that we knew well. The British had to defend the whole empire. While they were good at defending the coastal regions, they weren’t good at defending the land away from the coast. We knew the land better than the British did. This gave us an advantage when fighting some of the land battles. Our victory, while very unexpected, had some logical explanations for its success.