The other thing that pops up related to police training is the nuget of conventional wisdom that 'A man with a knife can kill you faster than you can use a gun'. This is sometimes stated as 'within 25' a knife is faster than a gun'.
Like most such bromides there is a grain of truth. In a situation where the knife man can use concealment a highly trained or talented person with a knife, a cross between a ninja and 'Mack the knife', can cover ground so fast, and inflict so much damage, that they might, conceivably, get the drop on an inattentive person carrying a gun and kill them before they can shoot.
In training, this is actually known as the Tueller Drill. Interestingly though, it doesn't assume the person is concealing the knife, is a 'Ninja', or is getting the drop on an unaware person. Quite the contrary, when the drill was first developed, it was tested using both recruits from the Salt Lake City PD and people attending Gunsite training courses (which were comprised of civilians, LEO, and Military of varying levels of experience, age, and physical fitness).
They would typically start with the 'knife' in hand and try to tag the person before he/she could draw and shoot his dart gun with relative accuracy, more or less being a test of reaction time. It was found that most people could reliably cover a 7yd distance in about 1.5 seconds. This is where the whole "21 foot rule" came into play. Though, Tueller never called it that, as he felt calling it a rule implied it was always true....whereas, in actually, there is a bit more variability. Some officers can draw faster or slower, some assailants can cover 7 yards faster or slower.
Either way, it became generally accepted that a potential attacker "under 21 feet" was considered to be in the person's danger zone. As they were able to grab/touch the officer before most could shoot. At the time, this was exacerbated by the fact that most officers were trained not to draw their weapon unless absolutely necessary and not to move once they drew their weapon, as it was thought to be unsafe to walk with gun in hand. Nowadays, better training will focus on properly and safely moving both backwards and forwards, as necessary, with a firearm in hand. (Of course, that doesn't guarantee anything in the way a person will react.)
One of the other results it had, with regard to training, was a fundamental shift in thoughts on "when" to draw a firearm. It's why you now often see officers drawing their gun from their holster long before an apparent escalation of force. Tueller found that already having one's firearm in hand significantly reduced reaction time.
All in all, it's a pretty interesting thing to read up on. Dennis Tueller is still training officers and is well regarded in the field. He'll often speak at a variety of conventions and such, which are quite interesting to listen to.
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