The optimal amount of violence in society

I've been wondering what is an optimal amount of street violence in a society, or rather how it can be calculated for any given society.

I mean the realistic optimal amount. The unrealistic one is zero, of course.

A good citizen is not supposed to use violence for anything except serious self-defense in a situation where it is not possible to extricate oneself otherwise. You are not supposed to hit a person who forcibly pushes you out of a line at a sausage stand, a person whose hand you find in your pocket looking for your wallet, a person who has grabbed your tits, a person who has just kicked or punched you without causing any actual damage and is trying to get away, a person who has grabbed your purse and it trying to rip it out of your hands, etc. Not responding with violence in such situations is, for the most part, the law, the custom and the sensible thing to do. And the societies where people always respond to such things with violence are usually not very nice places to live in.

There is another side to this, however: all these things can, for the most part, be done with impunity. You can push people out of lines, hit them, grab their purses or tits, etc., and you are not likely to be punished. Some of these things are illegal, but it's unlikely that you will ever be found. The police will most likely not bother to look for you if you punch somebody in the face without causing an injury or even a visible bruise. They might look more for a purse-snatcher, but even then they are usually only caught after many purses.

I have a theory that one of the factors that stops people from doing such minor acts of violent assholicity to each other is the risk that the victim or some bystander will in fact hit them back. It's not the main factor (I hope that most people are raised to be decent to the extent of not hitting the person next to them in a sausage stand line), but it probably is a bigger factor than fear of police. I strongly suspect that if there were a society where thugs knew for sure that people are not going to hit them back, we'd see a lot more thuggery and it would not be a pleasant place to live in, either.

Since I think that a certain level of aggression among the general population tends both to increase and curb street violence, I am wondering what would be the optimal level of aggression (perceived aggressiveness level is more important here than the actual one) that would be high enough to scare most thugs into behaving themselves most of the time, but would not be high enough to generate a lot of violence by itself.