It looks like there are roughly two different slopes, and the US is on the same incarcerated rate / homicide rate slope as the others in its same more-strict group. We stand out because we have more homicides to begin with.
Discussion
Here’s the graph
That’s incarceration rate per 100k vs homicide rate per 100k according to the sources I posted earlier up in the replies. Zoomed in to see countries with <10 homicides per 100k
Looks like countries vary in how steep their line is, but there are roughly two modes - strict, and not. The US is roughly in the middle of the strict mode distribution as seen in that graph. I doubt we want to switch to be be in the middle of the not strict distribution, but if we were we’d incarcerate at a rate if 110 per 100k while keeping our homicide rate of 4.96 per 100k
