Badly.
I came across this chart from the Prison Policy Initiative, which ranks all the states' incarceration rates and compares them to other countries throughout the world. None of the states fare particularly well. Michigan's rate is higher than the national average, and it's higher than every other country in the world (though not nearly as bad as some other states, such as Louisiana).
PPI notes in its comments on the chart:
Nearly all of the countries with relatively high incarceration rates share the experience of recent large-scale internal conflict. But the United States, which has enjoyed a long history of political stability and hasn’t had a civil war in nearly a century and a half, tops the list. If we compare the incarceration rates of individual U.S. states and territories with that of other nations, for example, we see that 36 states and the District of Columbia have incarceration rates higher than that of Cuba, which is the nation with the second highest incarceration rate in the world.
One big question is whether locking more people up makes Michigan, and the rest of America, any safer. When you look at the list of states with the highest incarceration rates, it's a little difficult to see a correlation. Many of the states with the highest prison populations also have a lot of crime, but not all.
PPI is an advocacy organization, and its stance is that high incarceration rates very clearly do not make us safer. That's not the end of the story, of course. For a deeper look at the relation between incarceration and crime, head over to the University of Chicago's Crime Lab page.