Ever read or listen to a sports athlete say something after a remarkable performance something like, "the basket just looked huge" or "I could tell it was a curve ball up in the strike zone"?
While athletes practice as do police officers or the Secret Service, how often they practice and under what conditions has a bearing on how well they perform. Psychologists and others have conducted studies as to what happens when people undergo stress. As things like respiration rate, heart rate, breathing increases, certain senses are sharpened to a large extent because other senses are diminished in their relative importance to the task at hand.
Now, there is an optimum area, a zone of you will, where we perform best. If you're below this zone, you've got irrelevant senses clouding the issue. If you go above, you literally start to break down and make inadvertent bad decisions.
So the thing is when it comes to police is to have practice under simulated conditions so that they not be rattled such that their heart rate is in a range where they perform at their best. This sort of training doesn't come at a shooting range and needs to be done on a regular basis.