It’s very well-established that a large fraction of shots fired by police fail to hit the intended target.This is true even at close range and it is true even for may officers who, at the range, are expert marksmen.
The human body under stress dumps adrenaline into the system which causes tunnel vision (loss of peripheral vision) and degrades fine muscle control. This is the fight-or-flight response, and is exactly why police training needs to emphasize correct procedures that, to the extent possible, prevent officers from ever getting into situations where the decision to apply or not apply lethal force must be made. At that point, the situation is effectively out of control.
It also puts the lie to the myth of the heroic Armed Citizen, who is even less likely to be able to control his or her weapon under comparable circumstances.