To the best of my knowledge, it was Col. Jeff Cooper who first advocated firing two shots to the vital zone of the attacker. The idea being that two shots multiplied the chances of stopping the attack as quickly as possible.
Today, it is generally taught that these shots should be delivered in one of two ways, either as a Controlled Pair or a Hammer. With the Controlled Pair, the shooter sees his sights twice, each time before he breaks the shot, and then a third time as he comes back on target to evaluate the results. In the case of the Hammer, both shots are fired from one sight picture, again reacquiring the sights to assess the situation. Obviously, the Hammer is most effective at close range and the individual shooter has to practice the technique to determine just what that range is.
Some armed citizens, however, don’t understand the principle involved. They argue that the best thing to do is to keep shooting as long as the bad guy is up and still a threat. So, let’s take the worst-case scenario; your attacker is wearing body armor and your two shots have not had the desired effect. What, exactly, is firing more shots at the same target going to accomplish? It would appear that the answer is, more hits to the body armor.
When we suggest that you fire two shots at the attacker, we are not suggesting that you are only going to fire two shots in this encounter. You certainly may need to fire more, and when we talk about assessing the situation it’s not like we’re suggesting that you take a coffee break. The assessment should be split-second thing.
It works like this: I fired two shots and am confident that they went where I wanted them to, but he is still up and fighting, so I need to quickly put more shots into a different location. I may deliver those to the head, which will stop things quickly but is a much smaller target. Or I may deliver shots to the pelvic girdle which will likely get him down but not necessarily out of the fight, but the head shot will now be easier to make. In your practice sessions you have made it a point to reacquire your sights and get back on target after a shot string which helps you make the reassessments quickly and accurately.
The only time that firing a pair of shots might not be a good idea is when the armed citizen is using a 5-shot revolver and dealing with multiple attackers. In that case, one shot per attacker makes much more sense.
In either case, it is a mistake to just keep throwing bullets at one aiming point when you are obviously not getting the results you need.