[w______roy]

It's not "likelihood of getting caught" because even if you have a 1 in 5 shot at getting away with a crime, desperate folks (or folks with a shaky understanding of probability) will still take the risk. It has to be "certainty of getting caught" which requires more than just more police, but also public messaging, education, etc. See: https://www.ojp.gov/pdffiles1/nij/247350.pdf

[bryanlarsen]

Interestingly, that's the link I would use to support my point. From your link:

1. The certainty of being caught is a vastly more powerful deterrent than the punishment.

2. Sending an individual convicted of a crime to prison isn’t a very effective way to deter crime.

3. Police deter crime by increasing the perception that criminals will be caught and punished.

4. Increasing the severity of punishment does little to deter crime.

[w______roy]

Well of course I read the things I link. To clarify, my points are:

1. "Likelihood" ≠ "Certainty" - I might think there's a high chance of getting caught, but unless I'm overwhelmingly certain that I'll get busted, I'll still take a risk. This is an important distinction, because it's not as though there's a linear correlation between likelihood of getting caught and crime rate.

2. This perception can be increased in ways other than just investing in police. A city could invest in cameras and signs that say "you're on camera." They could take out advertisements showing the conviction rate for particular crimes. They could hire rehabilitated offenders to share their stories with kids. The list goes on, there are plenty of ways to spend that money that might be more effective than giving it to police departments.