I have no more wish to understand, negotiate with, or in any way accomodate sociopathic predators; nor more than I wish to accomodate or understand a rabid wolfhound. I may pity their condition, I may even comprehend their motives. I understand the mechanism of Rabies, after all; that doesn't mean that I allow rabid animals to live.
At the risk of sounding sociopathic myself, I hold the two to be roughly equivalent. A rabid dog, as cute and friendly as he may once have been, needs to die. Right now. Friendly once or not, -NOW- that dog is a potentially lethal threat. Friendly as he was at 5 or 10 years old, a gangbanger, burgaler, or other sociopathic criminal (to say nothing of the REAL nasties, as mentioned above) a potentially violent criminal is a potentially lethal threat, and the response should be identical. I have no qualms about killing someone who, for all I know, is a few seconds away from killing -me- instead. If this individual is carrying or brandishing a weapon, he is threatening my life. Period. I decided, a long time ago, that people who threaten the lives or persons of myself, my family, or my friends -also- need to die. Someone who is so mentally disturbed, so socially and morally unhinged as to feel justified in threatening someone's life in exchange for that other persons' compliance or their property, is no longer fit to live among decent people. I'd be happy if they all went away somewhere (Coventry, maybe?), but since they never have and never will, I simply plan on removing any that are dumb enough to come into my circle, as it were. I don't go looking for them; in fact I go to great lengths to avoid them. However, if they come looking for me, they are in for a very nasty and probably very brief surprise. If they were to run away (hopefully "scared straight") when I drew my weapon, I would do a giddy little Happy Snoopy Dance. The best solution is -always- that the bad guy runs away. But if he hangs around after the gun is drawn, he's just committed the terminal error of being both mean and double-stupid. That kind of idiocy doesn't fly in nature, and it won't fly with me. I am not food, and I will not be eaten.
The problem with assuming that a criminal will let you live if you run/comply/resist w/out a gun is this: you don't know if you will be allowed to live until you're home, behind a locked door. The bad guy might decide to off you at any time; nervousness, an itchy finger, or "just 'cause I felt like it" have all been proffered as the motive for otherwise random shootings in the past. I can be reasonably sure I'll survive the encounter when the former mugger is either running away (the usual, and hoped-for result) or dead on the ground (a much rarer occurance).
Finally, as for statistics:
http://www.jpfo.org/data-docs.htm (It's safer by FAR to resist with a firearm; citations provided.) The 2-3 bits you want about about ten lines down the page.
Edited to add:
"One in a million!" is cold comfort to the person with the misfortune to be the One in question.