Why were Greece able to defeat the Persians despite being outnumbered?

The combined strengths of the Greek city-states matched the Persian strength on both sea and land. The Persian strengths have been greatly overstated by historians who have used the overall Persian strength rather than the forces the employed on campaigns. The Persian army was about 180,000, but after their navy was defeated at Salamis they had to send half that army home as they could not supply them by sea, and the countryside was too poor to support them all. This meant the sides were about equal, the Greeks had the benefit of their infantry being armoured, and the operated in rough ground to avoid the superior Persian cavalry.