I see this repeated a lot but im not so sure its that simple. Here is an interesting article https://www.pewtrusts.org/en/research-and-analysis/articles/2014/09/weighing-imprisonment-and-crime#:~:text=Rosenfeld%3A%20The%20best%20we%20can,25%20percent%20of%20the%20reduction which seems to suggest that increased carceration does have a "moderate" effect on crime.