Did America win the Revolution against Britain?

I have studied the American Revolution in detail so obviously I know that America did gain its freedom and due to several contributing factors. I just feel that although the Americans did put up a valiant effort against Britain, and did enjoy some military successes, they did not win their independence for themselves. In my personal opinion, the only reason they secured their independence was due to the fact that a change in politics in London garnered anti-war sentiments which forced Lord North out of office. With the entrance of France, Spain, and the Netherlands, Britain's forces and resources were stretched fighting a global war to preserve its colonial empire. I think the only reason they granted America its independence was because they could not afford to lose their other colonies in India and the Caribbean. By War's end in 1783, The british still had a large military force and the largest navy in the world. If they wanted to, in an alternate history, I do believe they could have persecuted the war for several more years and probably won it. So in essence do not think America WON its independence, rather Britain felt that it was not a critical issue worth pursuing further and relinquished it. It was foreign intervention and political strife in Parliament that brought about its end. This is purely my thought based on research I am only posting this to facilitate discussion. If anyone else has knowledge on the topic and thinks otherwise please I ask you to post your argument, I am curious what others think.