Eventually, I hope the deterrent effect would cause fewer crimes to be committed in the first place

There's no evidence whatsoever that it works that way. It seems to to be that high rates for jailing people and high rates for violent crime in a society go along with each other.

If you don't think you are going to get caught the penalties you would face if you were caught just aren't relevant. Once you do get caught and jailed you're in an environment that makes it more likely that you are going to get "re-educated" by that very environment to reoffend.