The thing to remember is that handguns are fantastically inaccurate beyond 20 yards or so. And no, I don't mean the accuratized competition models. That is why cops never try for a head shot - they go for body shots - a larger target.
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I am a retired police chief and I am also a retired soldier. This statement is incorrect.
Many pistol competitions involve shooting at "long" range up to 100 yards. Police are trained to shoot for body mass because
almost all cops are NOTORIOUSLY bad shots. The average cop shoots his weapon twice a year for qualification.
Any current service pistol or revolver(a pistol is an automatic, a revolver has a rotating cylinder) firing 9mm 40 S&W or 45 aacp is more than capable of hitting targets at 100 yards if the shooter is well trained and practiced.
I hunt deer with an S&W Model 686 six inch barrel in 357 magnum that i also used to carry on duty.
I am a graduate of several police firearm instructor schools and the US Army Small Arms Instructor School at Fort Bening, GA.
There is a well document recent case where a USAF Air Police Officer interdicted an active shooter at McCord Air Force Base in Washington and shot the AK-47 armed offender at a measured 77 yards with a an M9 (Beretta Model 92 FS) 9mm pistol. This was not a lucky shot. The AP fired four times and hit the offender three times including the final shot which was a head shot.
As far as militart police go, the US Department of Defense just bought another 400,000 M9 pistols from Beretta. The contracrt runs through 2016 and the weapons are expected to have a twenty year service life. A military police officer armed with a handgun through the next two decades would have an M9 9mm pistol. As stated, the 9mm is more than adequate at ranges up to 100 yards by a well trained individual. The current 9mm round is a full metal jacket bullet weighing 124 grains.
Sorry for the correction, but I speak from experience and education.