Here is an NPR story about a study that you might find interesting. Some relevant quotes:
"Williams and his colleagues find adding a new police officer to a city prevents between 0.06 and 0.1 homicides, which means that the average city would need to hire between 10 and 17 new police officers to save one life a year. They estimate that costs taxpayers annually between $1.3 and $2.2 million. The federal government puts the value of a statistical life at
around $10 million (
Planet Money did a whole episode on how that number was chosen). So, Williams says, from that perspective, investing in more police officers to save lives provides a pretty good bang for the buck. Adding more police, they find, also reduces other serious crimes, like robbery, rape, and aggravated assault.
Even more, Williams and his coauthors find that, in the average city, larger police forces result in Black lives saved at about twice the rate of white lives saved (relative to their percentage of the population). When you consider African Americans are much more likely to live in dense, poverty-stricken areas with high homicide rates — leading to more opportunities for police officers to potentially prevent victimization — that may help explain this finding."
"While they find serious crimes fall after the average city expands its police force, the economists find that
arrests for serious crimes also fall. The simultaneous reduction of both serious crime and
arrests for serious crime suggests it's not arrests that are driving the reduction. Instead, it suggests merely having more police officers around drives it. These findings are consistent with other research that finds concentrating police in "hotspot" crime areas appears to be an effective way to reduce crime."
To your point:
"The economists also find troubling evidence that suggests cities with the largest populations of Black people — like many of those in the South and Midwest — don't see the same policing benefits as the average cities in their study. Adding additional police officers in these cities doesn't seem to lower the homicide rate. Meanwhile, more police officers in these cities seems to result in even more arrests of Black people for low-level crimes. The authors believe it supports a narrative that "Black communities are simultaneously over and under-policed." The economists don't have a solid explanation for why bigger police forces appear to lead to worse outcomes in these cities, and they plan to investigate these findings more deeply in future research."
NPR Story