If someone like that is getting fucked with by the biggest gang in NYC, you know there's a problem.
The police are there to preserve disorder, but they have lost sight of this. Now, there are two types of cops; the protect and serve kind, and the us against them kind. Sadly, the latter seems to be taking over. I'm afraid this doesn't end well. The nightmare scenario is some kid walking up to a cop on the 4th of July and asking for baseball cards with a toy in his hand that is mistaken for a gun.
The real question here is what are we going to do about it?
http://marginalrevolution.com/marginalrevolution/2012/12/pol...
Other places have too few (Oakland PD should be at least 2x and really 5x what it has). The fundamental problem is poor places have less budget and also higher need for policing.
Various transit agencies, universities, etc. should probably not operate their own substandard police forces, but use non-sworn security and have a decent working relationship with the local PD.
EDIT: ~4 officers per 10k would also be lower than essentially any other country in the world(2).
1. http://www.governing.com/gov-data/safety-justice/law-enforce...
2. http://en.wikipedia.org/wiki/List_of_countries_by_number_of_...
Now what I'm also curious about - would you expect high population density to increase or decrease the number of police needed per capita? Off hand, I would be inclined to think lower population density would need higher police per capita, but here it seems to be the reverse (possibly reflecting the coffers rather than the needs, though).
You have the somewhat obvious want of a visible police officer ranging an area to deter criminal activity such as shoplifting/vandalism/mugging.
But you also want the police in an area to deal with domestic dispute type crimes which you'd expect to increase at least linearly with density, possibly more so as the closer you are to your neighbors the more you may see them and the more their behavior may impact you. Which may mean that you need several more cops to respond to concurrent incidents even if the average rate of incidents is lower than what a single cop could deal with.
That's without getting in to any other issues such as bureaucracy needs/wants of larger departments. Or the odds of more dense areas being more culturally diverse/allowing higher differentials in income against distance.
So after that I think it would be quite hard to judge what would be required.