The American Left seems to believe that police don't reduce crime, they commit it.
This meta-analysis of 12 qualifying studies reports that increasing the number of sworn officers in a police force indeed reduces crime.
The impact differs depending on the type of crime. Most crime is done no one is looking, so police patrol might not be so relevant for crimes like rape.
Police presence seems most effective for car theft or assaults. Since cars are often stolen while parked in a public place, more patrolling might make a difference.
Assaults also happen frequently in public places like bars. The typical scenario is when one young drinking guy insults another young drinking guy, and mutual combat begins. Lots of cops around might make people think twice about starting a public brawl.
Keep in mind that the study found the impact of police force size to be fairly small. It helps, but not that much.
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