I'm not looking for an accurate string of shots. I'm looking to poke my assailant in the gut and blow his heart out.
Frank Ettin's post above covers the explanation of the presentation as taught by those who follow "The Modern Technique of the Pistol" as propounded by Jeff Cooper and memorialized in the book of the same title by Gregory B. Morrison.
Consider that if you do everything right and first to incapacitate a deadly threat, you might still have a fighting threat attacking you for several or many seconds. Even humans with non-functional hearts have fought for several seconds. Several seconds can equal many aimed shots.
In competition with timers and with shooters punching paper targets a few hundredths of a second can make a difference between first place and second. However, I submit that in a self-defense shooting one one hundredth (1/100th) of a second is irrelevant. Competition is good to simulate stress as far as it goes.
You must not expect two shots to center of mass to instantaneously
incapacitate the threat. It might do so, but do not stand there in disbelief that it did not.
In addition to your other practice, add practice for moving to cover. Practice follow-up shots.
Unfortunately, many ranges prohibit movement as it is impractical and/or not possible to do with safety concerns and range designs. So if you can not actually practice it, at least put it in your mental expectations.
NRA Life Member - Orange Gunsite Member - NRA Certified Pistol Instructor
"When plunder becomes a way of life for a group of men living together in society,
they create for themselves in the course of time a legal system that authorizes it and a moral code that justifies it." Frederic Bastiat