It depends on the arrowhead and bow type potjteh. There are known events where archers killed lots of knights despite them wearing armor. And full plate only started being used very late, roughly at the same time as firearms, it's a common misconception to think it was a medieval thing. The point is that there is a constant arms race where there is a counter for every weapon and armor. Dying should have been very easy.
Before all that roman and medieval lethality I recall reading about battle wounds in ancient greece. The report concluded armors did work and were not penetrated by the weapons of that time, and that people died by wounds on uncovered areas like arms, thighs and neck, or by being trampled at combat - no wounds to head, chest, or legs.