Deer are tough, but everything eats them. They respond in certain ways, one of which is to run like heck. They also dodge and run from the noise of the bow and the arrow in flight.
I believe that if you put an arrow through the deer's chest, with very little bone impact, the deer will often kick, look around and go on with what it was doing.
With some bone impact (ribs), it may run away, then stop and look back to see what it was and if it is chasing (which is why it is important for you to NOT move or jump up and down yelling how you Smoked the deer etc).
With major bone impact, shoulder, spine, hip, leg, the deer knows it is under attack and runs all out to get away.
Many folks have been shot or in some manner became skewered by a broadhead tipped arrow. In all the interviews I ever read, they all stated that they felt pressure, but it didn't hurt.
CHuckC