When he 1st arrived in NY he had 19,000 with mmore troops coming in until the battle.
They were certainly not all high caliber
The English had 20,000 on Long Island but Washington had made the glaring mistake of splitting his forces and only had about 6,000 to face the entire British & Hessian force there
Seems to me the mighty British made quite a few glaring mistakes themselves throughout the battles in the New York area. They failed to finish Wash off on several occasions, allowing him to escape to fight another day. The first time was at Brooklyn Heights where they had him pinned against the East River. They assumed he would surrender. The second time was in Manhattan when the battle moved there. Again they had him trapped. Another major screw-up was when Brit general Johnny Burgoyne and Brit Admiral Howe failed to meet up along the Hudson when they sought to take control of it. Howe apparently never got the message, or thought otherwise and never bothered to move his forces up from the southern end of the river to meet up with Burgoyne who had started from the northern end. Gaining control of the Hudson may well have sealed a victory for England. There were some other serious blunders made by the British high command but these are the only ones I can recall at the moment.