As far as the cops vs bad guys thing goes, bear in mind that the BG often starts the ball rolling, and the aggressor has a certain advantage. Also, cops don't generally shoot people from ambush, or just walk up and start shooting.
Police training is supposed to take into account handling aggressive people including those that start the aggression. Even if you don't consider ambush shootings, cops still have a rough time.
Even when the cops are the aggressors they don't always win despite that advantage and their training advantage.