Ponder reality:
The vast majority of the time, police respond after a citizen calls - most likely the person trying to kill you has either succeeded, dropped or fled.
After you (or a witness) calls they will show up 3, 6, (30) minutes later, you either saved yourself or not.
When you are at a Mart, restaurant, parking lot, ____, you encounter the same people (psychos, criminals) as police, most of the time you make first contact.
If some psycho is inclined to rob a person do you think they will go for a uniformed officer or a civilian?
Stack the odds in your favor: carry a pistol that you can shoot accurately, quickly, repeatedly, with ammunition designed to incapacitate quickest.