Try looking at the research on this one:  http://www.sentencingproject.org/wp-content/uploads/2016/01/Deterrence-in-Criminal-Justice.pdf 
"Ideally, from a deterrence perspective, the more severe the imposed sentence, the less likely offenders should be to re-offend.  A 1999 study tested this assumption in a meta-analysis reviewing 50 studies dating back to 1958 involving a total of 336,052 offenders with various offenses and criminal histories. Controlling for risk factors such as criminal history and substance abuse, the authors assessed the relationship between length of time in prison and recidivism, and found that longer prison sentences were associated with a three percent increase in recidivism." (Bottom of page 6).