How's that?
You release the arrow and send it flying.. the sound wave travels at around ~760mph, the arrow flys at around 170mph (a conservative number).. Once the sound wave gets to the animal, its ears have to conduct the signal to the brain (a very short distance), the brain has to make a decision to move, then the brain has to conduct the signal to the rear legs..
Nerve conduction velocity run at around 220 mph which is not a whole lot faster than an arrow in flight.. (although the distance is much shorter).
Once the muscles get the signal to move, they then have to execute that order and then they have to actually move the proper distance out of the way of the flight path of the projectile.
Do the math..
When a deer ducks an arrow, it is usually a combination of the animal already being spooked and an "off shot" that combined to let it get lucky. Either that, or the hunter has taken some crazy unethical long shot out at 50+ yards and the flight time is so long and the flight path so off that the animal barely even needs to move.
When I shoot an animal, they arrow impacts long before they have a chance to react.
If you want to see an example of how relatively slow nerves are, do the money drop test.. Have someone hold their thumb and forefinger about an inch apart.. Dangle a 100 dollar bill vertically by holding the top edge.. position the bill so it is between their thumb and finger where the presidents head is.. tell them if they can catch it when you drop it, they can have it.
Their fingers only have to move 1/2 of an inch to close and grab the bill but the time it takes for the bill to slide through their fingers is faster than the time it takes for the signal to get from eyes, to brain, to fingers. Its a cool trick..
Here you go:
http://www.youtube.com/watch?v=eaZ9Gdj93kg
It works every time... No different with an animal.