Okay, I will give you the "advantage by mindset". But the homeowner has advantage of terrain, which in my view can offset the criminal's advantage. Even if it's just to evacuate quickly or notify authorities.
Home invasions are somewhat common in USA. However, most intruders are not intent on causing physical harm to the occupants. They seek money or items they can exchange for money/drugs.
Intruders are usually suprised when confronted by occupants, and will exit the premises immediately. There are those criminals who do not react in this manner, whether by "intent" to comit harm, drug use, or other circumstances. It is these cases where an action plan which may involve an elevated level of force may be necessary to protect family members.
I define "action plan" as a means to extract family members and other occupants from the potential conflict situation ( by notification, evacuation, or barricade). "Elevated level of force" is based loosely on commonly accepted principles of defensive action. In VERY RARE circumstances would lethal force be necessary, but I am a firm believer in "be prepared".
Given the hypothetical situation of a home invasion, would I hunt down the buglar and shoot them? Most likely not. Would I have a firearm handy in case the situation presented no other option than to defend myself with lethal force? Yes.
There are quite a few examples of intruders being shot (and sometimes killed) during home invasions.
NRA publications are very good at publisizing actual (and recent) accounts of armed citizens successfully defending themselves against attack. Yes, this accounts for probably less than 1% of all criminal acts purpotrated, but it does indeed happen in USA today.
"Home invasions" or burglary as we call it here are not uncommon. But they seek cash or easy to fence items and hit homes without people. I say it again, if you go up against an armed burglar with your gun, you better shoot him straight away preferably in the back instead of confronting him or doing some kind of "action plan". Put two bullets in his torso as close to the centerline in the chest as you can and one in his head. The golden rule of handguns is that you dont pull it unless you are going to use it. That was the clear message we got before were were checked out on the Glock 19. Do you still want to confront a criminal with your handgun?
Big picture? Handsguns bring very little good to a modern society, but they are big business and Hollywood loves them.
