Chicago would be a great experiment for privatizing the police force, IMO.
Heyjackass.com reports 795 homicides for 2016 total, with police shootings (11) and self defense (11) not included.
http://heyjackass.com/category/2016-stats/
Big city policed departments have always been political tools of the City government. Crime reduction was always a secondary add on, in the U.S.
Some other countries were not as bad, such as England, I have been told.