Seena Fazel and Achim Wolf published an article titled A Systematic Review of Criminal Recidivism Rates Worldwide: Current Difficulties and Recommendations for Best Practice (Fazel & Wolf, 2015) and the article concluded that
Recidivism data are currently not valid for international comparisons. Justice Departments should consider using the reporting guidelines developed in this paper to report their data.
The references section of this article also lists articles, reports and statistics available including an article on "the prediction of criminal and violent recidivism among mentally disordered offenders".
UK Statistics
The Ministry of Justice (part of the UK Government), produces regular statistical reports on reoffending rates within the UK. The Government Collection of Proven Reoffending Statistics contains quarterly reports for periods covering January 2009 through to March 2016 — the last report covering January 2016 to March 2016 is dated 25th January 2018. Without comparing reports from that date with older reports against this article, I cannot say whether the recommendations were followed by the UK Government.
US Statistics
The Bureau of Justice Statistics (BJS) collects criminal history data from the FBI and state record repositories to study recidivism patterns of various offenders, including persons on probation or discharged from prison.
The latest study of state prisoners estimated the recidivism patterns of about 400,000 persons released from state prisons in 30 states in 2005. The findings from the 2005 study cannot be directly compared to those from BJS's previous prisoner recidivism studies due to changes in the demographic characteristics and criminal histories of the U.S. prison population, an increase in the number of states in the study, and improvements made to the quality and completeness of the nation’s criminal history records since the mid-1990s. BJS has also used criminal history records to examine the recidivism of persons placed on federal community supervision in 2005.
In addition to recidivism statistics based on criminal history records, BJS collects administrative data through the Annual Surveys of Probation and Parole to examine the rate at which offenders are at risk of being incarcerated for a new offense or for violating the conditions of their supervision.
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References
Fazel, S., & Wolf, A. (2015). A Systematic Review of Criminal Recidivism Rates Worldwide: Current Difficulties and Recommendations for Best Practice. PLoS ONE, 10(6):e0130390.
DOI: 10.1371/journal.pone.0130390 PMCID: PMC4472929