[taxyz]

I'm not sure if that national average is a good benchmark or not (maybe there is some sort of argument for how urbanized society has become) but my guess would be that there is some density factor. SF is something like 850k people pre-pandemic on 49 square miles. While it's not one of the biggest in absolute amount of people, it is the second(?) densest. I would suspect that a city of same population but 1/4 density would not need the same amount of cops.

update: I am guessing this is what your non-linear part is about; I missed that on first read.

[HWR_14]

It is the 21st densest city in the US, but most of them are small. NYC and Paterson, NJ (150k) are both denser.

I have no idea which way density argues. It means that cops are denser at the same per capita numbers which means their proximity to the highest priority should be closer. So faster emergency response. I don't know why a denser area would need more police, but I could be very wrong on that.

[taxyz]

My argument (guess really) for why density necessitates more cops is that the opportunity for criminals also increases with density.

My thinking goes something like: a line of densely parked cars up Polk street with a bunch of people with their phones out at night making it hard to tell who is holding a flashlight probably means you need more cops patrolling the area to prevent crime vs my now suburban street with a few cars and no one walking at night means it would both be easy to spot opportunistic burglars and unlikely they'd hit up my street mostly for lack of targets.

I, too, could be wrong as I am saying this with no data.

[HWR_14]

You definitely need more cops to patrol the first example, but it also has far more people. It might take 20 times or more as long a street in the suburbs to get the same total people.

[diebeforei485]

> I don't know why a denser area would need more police

Plenty of commuters, shoppers/diners, and criminals from outside SF, so number of police officers per city resident is not a very good metric.