There doesn't appear to be a whole lot of science available in the matter of handgun cartridges stopping attackers. There are just lots of anecdotes. The only thing I've been able to come up with that makes the anecdotes fit together is that wounds inflicted by handgun cartridges rarely or never mechanically incapacitate anybody in less time than it takes to empty a magazine, reload, empty another magazine, whip out a Bowie knife, cross the room, inflict dozens of stab wounds, jump out the window, and run down the block. Consequently, I conclude that the mechanical effects of wounds inflicted by handgun cartridges do not often prevent dangerous attackers from causing as much damage as they want to cause before they bleed to death. And yet, there are lots of anecdotes and estimates about handguns stopping and preventing attacks. How to reconcile this? Not sure. But dangerous attackers are acting on some impulse or other. Murder is, I suspect, rarely a carefully reasoned act. I think that rational calculations about personal benefit rarely motivate the violent criminal. Criminal violence is symptomatic of some psychological pathology, some irrational, pathological impulse. From a psychological point of view, people are covered with buttons and they do things to some extent based on how their buttons are pushed. When some violent criminal gets into a state where he feels like harming you is going to make him king of the world and you whip out a handgun and put a JHP through his isles of langerhans, he might not be mechanically incapacitated, but you would have pushed some of his buttons which might alter his mood. The injury, the percieved increased difficulty of carrying out his attack, and the danger of additional injury may demoralize him.
If, on the other hand, your attacker is in a state where he can't be demoralized, then you're going to need a shot to the top third of his head and maybe more than one. Anything that penetrates the skull and gives good penetration will work about as well and anything else through the forehead.
That's my theory. Might not be right, but it's hard to disprove. Just like everybody else's theory.
The idea that anything that starts with a 4 is a great stopper, but anything smaller isn't might be true, but think about what that would imply. There would have to be a very significant nonlinearity in the response of attackers to the caliber of projectiles inflicting injuries. .22 through .355 won't do a lot; attackers eat those bullets like candy. Then a rather small increment in bullet diameter from .355 to .4 corresponds to a large change in the response of an attacker. Now he doesn't just bleed a bit more--he can't even pull the trigger again! How to explain such a nonlinearity in the relation between projectile diameter and effectiveness? Such a nonlinearity might exist, but it would need to be investigated and documented before I could beleve in it.