I have little doubt Blucher's arrival saved the day, so to speak; at one point even Wellington believed he was defeated. After the battle he admitted it was a "near run thing."

A great American general, George S. Patton used the axiom, "Hold 'em by the nose and kick 'em in the seat of the pants."

One could say that Wellington and his allied army held "Boney" by the nose, buying time so Blucher could come up and kick him in the pants. Hammer and anvil. A very risky strategy and one that required complete trust between Blucher and Wellington but one that ultimately paid off for a variety of reasons - many of which already discussed here.