You're forgetting that not all arrow hits kill instantly. If you're hit by an arrow from a random salvo, chances are you'll only get slightly in the arm, or the arrow slides off the helmet, and you can still go on fighting. If you have even smallest shield, raising it against the shadow of arrows is already decent protection in most cases, depending on distance and power of the bowmen. etc. etc. The fighting army is not just a "crowd of people".