I've invented a statistic (and acronym) called PIHN (pronounced "pin"). It stands for "Police-Involved Homicide Number."
PIHN looks at police-involved homicides but takes a city's violence into account. PIHN assumes a (very questionable) direct relationship between homicides in a city and the number police-involved homicides one might expect.
A high PIHN means that there are more police-involved homicides for a given level of violence (and perhaps a poorly trained and/or more trigger-happy police department). A low PIHN means fewer police-involved homicides (perhaps a better trained and less trigger-happy police department).
You too can calculate PIHN! Divide the police-involved homicide rate or number by the average overall homicide rate or number. I used 2003-2012 homicide data from city-data. And then multiply by 100 to get a PIHN greater than 1.