I fail to see how "per capita per square mile" is a useful measure.

_Anything_ measured in that way would show densely populated area vastly outnumbering rural areas, perhaps with the exclusion of things that essentially don't exist in cites, such as "number of farms per capita per square mile".

The measure appears to be concocted specifically for Lying With Statistics™.

Should proximity to potential assailants not be taken into account?

The "murders per capita per square mile" metric really gets to the heart of the question on every American's mind: what percentage of face-to-face interactions are murders?

If you wanted to track that you'd need to do the opposite of what GP is suggesting.

That is, a dense urban area would have more face-to-face interactions than a sparse rural one. Given two areas with equal levels of per-capita violence, it would then follow that the more sparsely populated one would have more violence per face-to-face interaction, not less.

Right, I guess you'd actually want a measurement like "murders per population density" or "murders per (person per square mile)". Or, as it's more commonly known, murder-hectares per capita.

Murder-hectares per square capita? Murder-capitas per hectare? I'm not actually sure how the dimensional analysis works out.

This is absolutely absurd. We're talking about the US here, so it would be murder-acres, and that just sounds like a country club you really shouldn't join.

Wouldn't that assume that murderers do some kind of random walk, and randomly kill some person they happen to get close by?

I'm sure there are those, too, but IIRC in most violent crime the attacker and the victim know each other. Do people have substantially bigger social circles in cities?

I think I'm hung up on the same thing, chief.

Why per capita per square mile instead of per capita? Why do the miles enter into it? Because of more interactions? I'd like to see just the numbers per capita. I suspect they're fairly close.

Because violent felonies such as homicide proximity is the requisite factor in victimhood. ie The victim must be located near the killer.

Given 1 homicide in 100k for 100sq miles called "rural" vs 1 homicide in 100k for 5 sq miles called "urban", your odds of being in proximity of a homicide are much higher in the urban area. 20 times more likely.

I live in lower Manhattan, and there have been many shootings within a mile of me in the past year, even a few within two blocks of me, but because the per-capita numbers are so low, I'm pretty unconcerned about being shot, and so it doesn't really bother that I'm near the shootings. I don't really see how standardizing by (people * area) does you any good in capturing public safety, or even perceived public safety

Being further away from killers that I'm equally likely to be victims of isn't any more comforting.

> Because violent felonies such as homicide proximity is the requisite factor in victimhood

This doesn't stand up. Crime statistics are measured after the crimes happen; whatever effect might be due to proximity has already taken place.

Consider: in your example you say two places have equal per-capita homicide rates but one is 20x denser. It follows that the denser area will have 20x more people "in proximity" to any given homicide, and therefore that P(victim|proximity) must be 20x lower compared to the rural place.

The way you've done the math only makes sense if everyone "in proximity" of a homicide was equally likely to be a victim, but given equal per-capita rates that can't be the case.