It is? Please elaborate. No disrespect meant, but I'm curious why attaining fairly solid COM hits in a civilian self-defense situation is a statistical impossibility.
Not impossible. Just unlikely.
If you have to shoot someone, it is highly likely that you'll be within six feet of them. Hence you will not be able to extend your arms toward them, as that will create an opportunity for them to grab your gun. You will likely be holding your gun between waist and chest high when you fire. You will hence not be able to use the sights. Hence you will not be able to aim, at least not in a conventional manor. By the way, the perp will likely be moving, and you should be moving, too. Look at "shot placement" in that perspective.
Additionally, even at longer range, where sights could be used, target fixation frequently causes people to ignore the sights. It's hard to take your eyes off someone who is threatening your life.
The average shot fired in self defense MISSES THE ASSAILANT ENTIRELY. That's why I get so amused when the "over penetration" crowd comes out.
You mention COM hits, and that is good. Targeting COM is what you should expect to have to try. You will instinctively do that, anyway, as COM will be the largest target available during your extreme situation. SD shoot training should include some shots fired from waist high at short range, like 5 feet.
Also, do not shoot once, then pause to analyze the effect. Most handguns are poor stoppers; you should expect to continue firing until you get a positive reaction from the assailant, i.e., they collapse or run, so that they are no longer a threat to you. Your first shot is unlikely to stop the assailant, and you won't know whether it was because it didn't stop them, or your shot missed entirely.
The above is why I say "shot placement" in a self defense situation is a fantasy. You'll be damn lucky just to hit them!
Haven't reloaded in decades but it might be time. Thanks to the OP for dusting off my cobwebs. 
