Recidivism is usually defined, in corrections circles, as a prison inmate being rearrested for a new offense within a given period of time.
Measurement methods vary, but historically the rearrest rate has been quite high. Take, for example, the recent New York Times article on state-level efforts to help ex-inmates to find jobs upon release. The recidivism rate given there is 2 of every 3 released inmates within three years.
States have much to gain, though, by investing money in offender re-entry. As the Times piece points out, it costs about $35,000 to incarcerate someone for a year - more than it takes to send someone to the University of Michigan.