Washington didn't just wait for the enemy to come to him.
In Boston, he pressed an encirclement and caused the enemy to retreat.
New York did not go well, but it was Washington who pressed into the City for the fight.
The attack on Trenton was bold, and an important turning point.
To the extent that Saratoga can be credited to Washington's overall strategic plan: keep Howe facing him, to let Schuyler, then Gates, amass the militia and cut-off Burgoyne, although Washington didn't pass to the attack, he kept the enemy fascinated with him long enough to prevent the enemy from using the one wing of his army to rescue the other.
It is said that an NVA officer referenced Gen. Greene when a visiting American officer made the comment that the "NVA never defeated the US Army in battle." The reply was something like, "Do you not recall your own Gen. Greene?"