Madman are few in numbers.You would feel better if someone were stabbed, or run down? Maybe beaten with a ball bat? A person intent on doing violence, will do violence. You can't escape the will of a madman. But you can draw your weapon, and put 2 in his chest, and be judged by a jury of your peers, and found not guilty, because you exercised your Constitutional right, to defend yourself.
But guns can will make the basic average offender step up from stealing cellphones to car-jacking ad attacking local stores.