According to what I have read a deer can go from a standing start to 40 miles an hour for a short distance, now if hes looking at you and alert when you shootyou only have his reaction time for the arrow to get there.
According to my calculations hes moving 3.666 feet in that 16th of a second if he's at full speed which they reach a lot faster than most people would believe.
Now if hes looking the other way the speed of sound is a lot slower and he won't react as fast from a sound because he has to determine that it is not something normal;the distance the arrow has to travel makes a big differance; even at 300 ft a second it takes that arrow 1/4 of a second to go 25 yds.