The number of cards drawn this way might not be equal to the number of cards in your hand (for example, if you apply Necroplasm’s dredge ability instead of drawing one of those cards). The number of cards that you actually drew is what determines how many cards you discard.

The number of cards in your hand is counted only as Ancient Excavation resolves. Ancient Excavation is on the stack at this time, so it’s not counted.