Aotearoa / New Zealand

Not necessarily. If you have a 50% recidivism rate but hold less people in prison, crime rates will go up even if the rate doesn't change, simply because there are more people out of prison. Even if the recidivism rate goes down you may have more crime. But if over time the lower recidivism rate means less people go back to prison, over time you should see overall crime drop. This is probably a generatonal time period though. Short term higher crime rates for longer term gain.