Well, we know the number of police officers per capita in the US is about average, compared to other developed countries.
Yet, it is more violent than any of those. Why?
Perhaps because income inequality in the US is higher than other developed countries as well.
It is hard to tell when we are not insiders.
Europe gun laws are stricter so police dont need to spread out and have as many emergencies like in the US,that might be one of the factors counting.(people also might call the cops more quickly because they expect more people to carry weapons)
I do not really know about income inequality but those i know that lived in the US for some years talked about the payment for work being higher than here while also having less tax,that ofcourse might be biased information .