Firstly, the Americans received a great deal of international assistance, as another user pointed out. The British and French were historical antagonists and the French had lost great swaths of territory in North America during the Seven Years War (also known as the French and Indian War). As a result they were greatly interested in seeing the British receive a dose of their own medicine and provided both economic and military support to the Americans. Further, European military advisors like the Marquis de Lafayette, Philippe Tronson de Coudray, Baron von Steuben, chevalier de Laumoy, Thaddeus Kosciusko, Baron de Woedtke, Louis Duportail, and Johann de Kalb helped mold the Continental Army from a ragtag force into a military in the European sense.
It's also important to note that most of the American's military successes in the war, especially early on, came as a result of guerilla and irregular warfare epitomized by generals like Francis "Swamp Fox" Marion. These sort of attacks taxed British supply lines as any reinforcements and resupply had to be shipped across the Atlantic Ocean from Britain. Further, most British trops were fighting on unfamiliar terrain and, unless they were in port cities or Loyalist territory, they had no local sources of manpower or food. Also, all communications for the British forces had to be sent across the Atlantic as well, meaning it was often outdated.
Another thing going against the British was that there wasn't any center of gravity in the Colonies - after major cities like Charleston, New York, Boston, or Philadelphia were captured, the War kept on since the Americans were not centralized at that time. The size of the colonies played a role in the British defeat as well, as the British had to simultaneously fight a war and occupy the colonies to suppress the rebellion. They could easily fight the war, but not garrison troops, as doing so meant that those trops could not be readily sent into combat without allowing revolutionary sentiment to creep back into a previously occupied area. The British couldn't conduct suppression operations the same way they did in places like Ireland and Scotland, because doing so would mean that the British would lose the support of the Loyalists that they so desparately needed to maintain to ensure that they had any chance at all of winning the War, thus they were limited in how brutal they could be and whether they could employ slaves and American Indians to fight with them (keep in mind the greatest concentration of Loyalists existed in the American South) - especially after the hiring of Hessian mercenaries proved as controversial as it did.
In the end the combination of American tactics, European aid/intervention, and the limitations imposed on the British by fighting a war from across the ocean were the major reasons why the Colonies won their war for independence
It's also important to note that most of the American's military successes in the war, especially early on, came as a result of guerilla and irregular warfare epitomized by generals like Francis "Swamp Fox" Marion. These sort of attacks taxed British supply lines as any reinforcements and resupply had to be shipped across the Atlantic Ocean from Britain. Further, most British trops were fighting on unfamiliar terrain and, unless they were in port cities or Loyalist territory, they had no local sources of manpower or food. Also, all communications for the British forces had to be sent across the Atlantic as well, meaning it was often outdated.
Another thing going against the British was that there wasn't any center of gravity in the Colonies - after major cities like Charleston, New York, Boston, or Philadelphia were captured, the War kept on since the Americans were not centralized at that time. The size of the colonies played a role in the British defeat as well, as the British had to simultaneously fight a war and occupy the colonies to suppress the rebellion. They could easily fight the war, but not garrison troops, as doing so meant that those trops could not be readily sent into combat without allowing revolutionary sentiment to creep back into a previously occupied area. The British couldn't conduct suppression operations the same way they did in places like Ireland and Scotland, because doing so would mean that the British would lose the support of the Loyalists that they so desparately needed to maintain to ensure that they had any chance at all of winning the War, thus they were limited in how brutal they could be and whether they could employ slaves and American Indians to fight with them (keep in mind the greatest concentration of Loyalists existed in the American South) - especially after the hiring of Hessian mercenaries proved as controversial as it did.
In the end the combination of American tactics, European aid/intervention, and the limitations imposed on the British by fighting a war from across the ocean were the major reasons why the Colonies won their war for independence
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