The chart below assumes an arrow speed of 500ft/sec, speed of sound approx. 1300 ft/sec and a normal target pace of 4.5 ft/sec. I used my normal walking pace as a reference since I don't really know how to quantify a deer's pace but I can measure my own. However, I think it's safe to say a deer walking at a normal pace would out distance me.
Regardless, the movement number gives some perceptible reference to the time. When printed on a chart, a reaction time of 0.11 seconds sounds like a really short interval. In reality there's a lot of motion that can take place in that time frame.
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Edit: This also doesn't take into account the "whistling" of the arrow as it flies. Once the target hears the sound of the bow release it will continue to hear the arrow whistling toward it until impact. The longer that whistle exists the more apt a deer might be to react to it. For example, a clank or thud might get its initial attention but the sound of a steadily approaching arrow might be the driving factor in its decision to move. The longer that whistle duration is the more incentive there is to move.