As a former range officer for a couple different departments, I can assure you the average recreational shooter is generally more competant than the average cop with their weapons, especially handguns. Some of my officers would come to me for practice time at the range a month before qualification, because they knew their skills were um, "deficient". And quite often, it took a month to get them up to snuff! Good thing they weren't involved in any shootings the week before they came in, eh?
The most recent stats I've seen for officer-involved shootings put the usual range at between 5 and twenty feet, and officers miss about 70% of the time. Between the lack of training and the adrenaline dump, most just start blazing away, as the previous post suggests.
I left LE six years ago, but took most lessons with me. I still work armed, and for that reason alone I try to practice with my sidearm twice a week. Most of my practice is rapid fire at close range, as I suspect if I ever have to shoot on the job it will be at Halitosis Range. I also practice with my speedloaders, in case that "70%" figure applies to me that day. The one thing I repeatedly tell myself when practicing is what to focus on, my mantra as the gun comes up is, "Front sight.......press!" when the shot looks right. Bowling pin shooting is a great training aid, I did 350 rounds on pins yesterday, and still missed more than I should. I think often of Ross Seyfried's advise on shooting under stress, when he said, "You can't MISS fast enough to catch up!" It also applies to Serious Social Situations.
Papajohn the Practicing Pin Pounder