Length of Incarceration and Recidivism

UNITED STATES SENTENCING COMMISSION
Charles R. Breyer

Commissioner

Danny C. Reeves

Commissioner

Patricia K. Cushwa

Ex Officio

Candice C. Wong

Ex Officio

Kenneth P. Cohen 

Staff Director

Glenn R. Schmitt

Director

Office of Research and Data

April 2020

United States Sentencing Commission

One Columbus Circle, N.E.

Washington, DC 20002

www.ussc.gov
	 	 Ryan Cotter, Ph.D.

 

 Deputy Director

	 	 	 Office of Research and Data	

EXECUTIVE SUMMARY RESEARCH FINDINGS APPENDICES

2 INTRODUCTION 

4 KEY FINDINGS

5 METHODOLOGY

11 RESEARCH DESIGN 1A

12 RESEARCH DESIGN 1B

13 RESEARCH DESIGN 2

16 RESEARCH DESIGN 1A

20 RESEARCH DESIGN 1B

24 RESEARCH DESIGN 2

28 COMPARING MODELS

30 CONCLUSION

31 APPENDIX A

Comparing Models

33 APPENDIX B

Research Design 1A

39 APPENDIX C

Research Design 1B

45 APPENDIX D

Research Design 2

51 ENDNOTES

TABLE OF CONTENTS

i

 o

EXECUTIVE SUMMARY

The purpose of this report is to examine the relationship between length of incarceration and recidivism. 

In this section, you will find information on the United States Sentencing Commission’s previous recidivism 

research, key findings, and methodology.
INTRODUCTION

The United States Sentencing Commission began studying 

recidivism shortly after the enactment of the Sentencing Reform 

Act (SRA) of 1984.1 Considerations of recidivism by federal 

offenders were central to the Commission’s initial work. Past 

studies, together with ongoing multi-year research on this 

subject, advance the Commission’s mission to conduct research 

on sentencing issues related to the purposes of sentencing 

set forth in the SRA.2 Exemplifying this, the criminal history 

provisions in the Guidelines Manual were developed, in part, 

based on information regarding federal offenders’ risk of 

recidivism. Information about recidivism is also relevant to 

the Commission’s obligation to formulate sentencing policy 

that “reflect[s], to the extent practicable, advancement[s] in 

knowledge of human behavior as it relates to the criminal justice 

process.”3

In 2016, the Commission began its current multi-publication 

recidivism series. The first publication, Recidivism Among 

Federal Offenders: A Comprehensive Overview (2016), examined 

recidivism among more than 25,000 federal offenders who 

were either released from federal prison or placed on a term of 

probation in 2005.4 The Commission’s report, The Past Predicts 

the Future: Criminal History and Recidivism of Federal Offenders

(2017), studied the relationship between criminal history and 

recidivism.5 The Commission’s report, The Effects of Aging on 

Recidivism Among Federal Offenders (2017), analyzed the impact 

of aging on federal offender recidivism.6 The Commission 

also released three reports that examined recidivism among 

specific groups of federal offenders: Recidivism Among Federal 

Drug Trafficking Offenders (2017), Recidivism Among Federal 

Violent Offenders (2019), and Recidivism Among Federal Firearms 

Offenders (2019).7

This study, the seventh in the recidivism series, examines the 

relationship between length of incarceration and recidivism. 

The Commission has commented on the effect of length of 

incarceration on recidivism in two of the prior publications in 

this series. In the Recidivism Among Federal Offenders report, 

the Commission found that offenders sentenced to relatively 

short terms of imprisonment — less than six months — had a 

lower recidivism rate than offenders serving longer sentences. 

Offenders sentenced to less than six months had a recidivism 

rate of 37.5 percent while offenders serving longer sentences 

had relatively stable recidivism rates ranging from 50.8 percent 

to 55.5 percent.8 That study, however, did not control for factors 

that have been shown to be associated with recidivism, such as 

the type of instant federal offense of conviction, criminal history 

of the offender, or age of the offender at the time of release. In 

the Recidivism Among Federal Drug Trafficking Offenders report,

the Commission found that there was little apparent association 

between the offender’s sentence and recidivism rate.9

2
Specifically, the recidivism rate for drug trafficking offenders 

sentenced to less than six months was only slightly lower 

than the recidivism rate for drug trafficking offenders serving 

longer sentences, 40.6 percent compared to a range of 47.8 

percent to 55.6 percent. However, when the Criminal History 

Category of the drug trafficking offenders was considered, as 

the sentence length increased, the recidivism rate decreased. 

The Commission opined that the inverse relationship between 

sentence length and likelihood of recidivism within each 

Criminal History Category was likely attributable, at least in part, 

to the effect that age has on recidivism. This report expands on, 

and refines, these prior analyses to more thoroughly examine 

the relationship between length of incarceration and recidivism. 

In doing so, this report empirically explores three potential 

relationships that may exist between length of incarceration and 

recidivism: deterrent, criminogenic, or no effect (See Table 1).

Empirical research on the relationship between length of 

incarceration and recidivism is limited and insufficient for 

developing federal sentencing policy.11 There are a limited 

number of studies on the subject and they present mixed 

results.12 Further, a number of these studies are dated (e.g., 

conducted prior to 2000), use less rigorous research designs, or 

present results on the relationship between incarceration and 

recidivism as a sub-analysis within a broader study.13 Further, a 

number of the prior studies have methodological deficiencies 

relating to not controlling for offender age and, therefore, are 

not considered valid studies.14

The most recent study utilizing a rigorous research design was 

conducted by Professor Benjamin Meade and colleagues.15

In their study, the authors found a deterrent effect for state 

offenders incarcerated for 61 months or longer compared 

to a similar group of offenders serving shorter periods of 

incarceration.16 However, it is not known the degree to 

which their finding would generalize to the federal offender 

population.

The purpose of this report is to add to the limited research 

examining the effect of incarceration on reoffending within the 

federal population and thereby inform policy makers.17

Rela%onship Descrip%on

Incarcera'on is a specific deterrent. As the length of incarcera%on increases, the likelihood of 

recidivism decreases. 

Incarcera'on is criminogenic. As the length of incarcera%on increases, the likelihood of 

recidivism increases. 

No effect. No sta%s%cally significant rela%onship between length of 

incarcera'on and recidivism is iden'fied.10

TABLE 1.

Three Potential Relationships Between Length of Incarceration and Recidivism10

3
KEY FINDINGS

The Commission consistently found that incarceration lengths 

of more than 120 months had a deterrent effect. 

Each of the research designs estimated that offenders 

incarcerated for more than 120 months were less likely to 

recidivate eight years after release. In the two models with the 

larger sample sizes, offenders incarcerated for more than 120 

months were approximately 30 percent less likely to recidivate 

relative to a comparison group receiving less incarceration. 

In the third model, offenders incarcerated for more than 120 

months were approximately 45 percent less likely to recidivate 

relative to a comparison group receiving less incarceration. 

In two models, the deterrent effect extended to incarceration 

lengths of more than 60 months. 

Specifically, offenders incarcerated for more than 60 months 

up to 120 months were approximately 17 percent less likely to 

recidivate relative to a comparison group sentenced to a shorter 

period of incarceration. 

For incarceration lengths of 60 months or less, the Commission 

did not find any statistically significant criminogenic or 

deterrent effect. 

When focusing on the shortest period of incarceration studied 

(12 to 24 months), the research designs yielded varying results, 

neither of which were statistically significant nor sufficiently 

reliable to make evidence-based conclusions.

Models 1A, 1B, and 2

Incarcera'on lengths of 

greater than 120 months

had a deterrent effect 

in all models. 

0 60 120 or more

Length of Incarcera'on (in months)

Models 1B and 2

Incarcera'on lengths of 

greater than 60 months

up to 120 months 

had a deterrent effect 

in two models.

4
METHODOLOGY

This study utilized two research designs to analyze the relationship between length of incarceration and recidivism. Research design one 

focused on creating precisely matched comparison groups. Research design two focused on creating similar comparison groups while 

retaining a larger sample size.

Study Cohort

The study examines 25,431 federal offenders who were 

released into the community, either from federal prison or on 

probation, in calendar year 2005, and:

 - who are citizens;

 - whose pre-sentence investigation report was submitted 

 to the Commission; 

 - who have valid FBI numbers;

 - who were not reported dead, escaped, or detained; and

 - whose federal sentence was not vacated.

The data was supplemented with Federal Bureau of 

Investigation criminal history records information to measure 

offenders’ recidivism rates. 

Recidivism

Recidivism “refers to a person’s relapse into criminal behavior, 

often after the person receives sanctions or undergoes 

intervention for a previous crime.”18 Recidivism measures can 

provide policy makers with information regarding the relative 

threat to public safety posed by various types of offenders, and 

the effectiveness of public safety initiatives in deterring crime 

and rehabilitating offenders.19 Recidivism measures are used 

by numerous public safety agencies to measure performance 

and inform policy decisions on issues such as pretrial detention, 

prisoner classification and programming, and offender 

supervision in the community.20

Two principal research choices can affect the relative magnitude 

of recidivism as measured in any study. First, researchers must 

determine which events will be considered as evidence of 

reversion to criminal behavior. Recidivism is typically measured 

by criminal acts that resulted in the rearrest, reconviction, or 

reincarceration of the offender over a specified period of time.21

Second, researchers must decide the time period in which 

recidivism events are counted. The period of time over which 

events are counted following release into the community is the 

5
“follow-up period.” Recidivism analysis begins with a starting 

event, such as release from prison into the community, following 

which events, such as arrests, are recorded until the close of 

the follow-up period. In some studies, follow-up periods may 

be quite short (e.g., six months), while other studies follow 

offenders for substantially longer periods (e.g., several years). 

Longer follow-up periods tend to correspond with higher 

recidivism rates because offenders are tracked for lengthier 

periods of time. Consequently, longer follow-up periods provide 

a more accurate estimate of recidivism or desistance from crime. 

The Commission selected an eight-year follow-up period and 

identified rearrest as the recidivism event. Rearrest is the most 

reliably reported measure of recidivism and, consequently, is the 

primary indicator utilized by researchers.22 Rearrest classifies 

a person as a recidivist if he or she has been arrested for a 

new crime after being released into the community directly on 

probation or after serving a term of imprisonment. Rearrest 

also includes arrests for alleged violations of supervised release, 

probation, or state parole.23 Thus, any rearrest, apart from minor 

traffic offenses, was considered recidivism. 

Study Groups

This study analyzes five ordered study groups receiving 

different lengths of incarceration (see Figure 1). The length of 

incarceration interval for each study group was determined 

based on natural timeframes and available sample size. The first 

three study groups are composed of offenders sentenced within 

one-year intervals: more than 24 months up to 36 months; more 

than 36 months up to 48 months; and more than 48 months 

up to 60 months. The fourth and fifth groups required larger 

timeframes due to a smaller number of offenders in each group. 

The decision to use five-to-ten and greater than ten years as the 

boundaries was to align with five-year clustering often seen in 

federal mandatory minimum sentences.24

Each study group is compared to a similar group of offenders 

who served shorter lengths of incarceration. The recidivism 

rate for individuals in the study groups were compared to 

the recidivism rate for individuals in the comparison groups. 

Exemplifying this, the recidivism rate for the study group 

incarcerated for more than 24 months up to 36 months was 

compared to a similar group of individuals serving periods 

of incarceration of 24 months or shorter. This process was 

replicated for each of the five study groups. 

6
Study Group Length of Incarcera%on

1 >24-36 months

2 >36-48 months

3 >48-60 months

4 >60-120 months

5 >120 months

24 36 48 60 120 or more

Length of Incarcera'on (in months)

Study 

Group 1

Study 

Group 2

Study 

Group 3

Study 

Group 4

Study 

Group 5

FIGURE 1. 

Study Group Length of Incarcera%on

1 >24-36 months

2 >36-48 months

3 >48-60 months

4 >60-120 months

5 >120 months

24 36 48 60 120 or more

Length of Incarcera'on (in months)

Study 

Group 1

Study 

Group 2

Study 

Group 3

Study 

Group 4

Study 

Group 5

7
Doubly Robust Estimation

This study utilizes a two-stage process to analyze the effect 

of length of incarceration on recidivism. As detailed in the 

next section, the first step focuses on developing similar 

comparison groups for each study group through the use of 

matching and weighting techniques. In the second stage of the 

analysis, an outcome regression model—in this case multiple 

logistic regression—was used to estimate the effect of length of 

incarceration on recidivism.25 This two-stage process of creating 

comparison groups and then utilizing regression modeling results 

in a doubly robust estimation, which is particularly powerful in 

that only one of the two models needs to be correctly specified 

to obtain unbiased estimates.26

Comparison Groups Using Matching and Weighting

The first stage of the analysis focuses on creating a similar 

comparison group for each study group. When creating a 

comparison group, researchers must consider two important 

factors: the necessary degree of similarity between study 

and comparison groups, and sample size. The study group 

and comparison group must be sufficiently similar on select 

attributes to isolate the effect of the variable of interest (i.e.,

length of incarceration) on the outcome variable (i.e., recidivism). 

Colloquially, this is often described as comparing applesto-apples. The attributes selected by the researcher, called 

control variables, are generally important variables that are 

perceived to influence the outcome. For example, if the study 

and comparison groups have similar proportions of males, any 

difference in recidivism rates observed would not be attributed 

to gender. Here, the researcher would have controlled for 

gender in their model. Ideally, groups being compared would be 

identical on all attributes except for the variable of interest. 

Sample size is also important because statistical tests require 

sample sizes large enough to detect existing relationships. This 

is referred to as power in statistics. Larger unbiased samples 

provide better estimates of how similar individuals not involved 

in the study will perform (i.e., generalizable results). Therefore, 

in addition to similarity between groups, researchers must be 

cognizant of ensuring a sufficient sample size exists to detect 

a relationship between the variables of interest and outcome 

variable. 

In this study, the Commission used a combination of matching 

and weighting to create comparison groups. Matching creates 

a comparison group by identifying individuals who are similar 

on key attributes determined by the researcher. The researcher 

specifies the level of precision for matches.27 As the level of 

precision increases, it becomes more difficult to identify matches 

and, therefore, the sample size shrinks. Thus, researchers must 

balance the level of precision in matching with the subsequent 

sample size. With weighting, individuals in the comparison 

group who are similar to individuals in the study group are given 

more weight than individuals who are dissimilar. As the level of 

8
similarity between matches increases, the weights increase.28

One advantage of weighting, as compared to matching with a 

high degree of precision (e.g., exact matching), is that it often 

results in a larger simple size because individuals with some 

dissimilarity will remain in the study but receive less weight.

The Commission chose to determine the length of incarceration 

for each study group and then create a matched comparison 

group for each study group. By determining the study groups’ 

length of incarceration first and then developing comparison 

groups second, this study preserves the natural characteristics 

of offenders serving various lengths of incarceration. For 

example, in general, fraud offenders receive shorter sentences 

than drug trafficking offenders. This means the composition 

of offenders serving sentences longer than 120 months will, 

understandably, be different than the composition of offenders 

serving sentences of 24 to 36 months of incarceration.29 While 

there will be some variation in the characteristics of offenders 

in each study group (i.e., at various lengths of incarceration), the 

differences between study groups and comparison groups will 

be minimal due to matching or weighting. 

With either matching or weighting, the first step is to determine 

which attributes must be controlled for. Researchers have 

identified five principal attributes that studies examining length 

of incarceration and recidivism must address: age, gender, 

race, prior criminal history, and instant offense type.30 These 

prior recidivism studies have principally examined offenders 

sentenced in state courts. In its prior research studies, the 

Commission has confirmed that these factors are also associated 

with the recidivism of federal offenders. Specifically, as an 

offender’s age-at-release increases recidivism decreases;31

male offenders have higher recidivism rates than female 

offenders;32 as an offender’s criminal history category increases 

their recidivism rate increases;33 and type of instant offense is 

associated with recidivism (e.g., drug trafficking offenders have 

higher recidivism rates than fraud offenders).34

The Commission’s prior research also identified associations 

between education level, violence, weapons offenses, and 

recidivism. The Commission found that offenders with higher 

levels of education have lower recidivism rates than offenders 

with lower levels of education.35 The Commission also found 

that offenders who used violence in conjunction with the instant 

offense or who used violence in prior offenses have higher rates 

of recidivism than offenders who have never used violence in 

connection with an offense.36 Additionally, the Commission 

found that offenders who commit weapons offenses have higher 

recidivism rates than offenders who commit other offenses.37

Based on the Commission’s prior research, and that conducted 

by other researchers, this report controls for the attributes listed 

in Table 2.

9
This study controls for the attributes in Table 2 by ensuring 

the study and comparison groups are similar via matching or 

weighting and, subsequently, through a regression model. 

Consequently, any identified differences in recidivism rates 

between the study and comparison groups would not be 

attributed to the characteristics listed in Table 2. 

This study used two research designs to develop similar 

comparison groups. The objective of the first design was to 

develop precisely matched comparison groups to analyze the 

effect of incarceration on recidivism. The objective of the 

second design was to develop comparison groups that were 

similar while retaining larger sample sizes to increase statistical 

power. 

Control AGributes and Variables

 age-at-release high school comple'on

 gender violent offense

 race weapons offense

 criminal history category (CHC) substan'al assistance departure

 instant offense type (sentencing guideline) safety valve adjustment

TABLE 2.

10
RESEARCH DESIGN 1 (A & B)

The first research design utilized matching to develop a 

comparison group that exactly matched all characteristics in 

Table 2 except for age-at-release, which could vary by one 

year.38 For example, if an individual in the study group had an 

age-at-release of 40, their match would be between the ages 

39 to 41 at release. Thus, the study and comparison groups 

were almost identically matched on all attributes in Table 2. 

In addition to the precise matching, individuals in the 

comparison group had to have a sentence of incarceration 

that was at least 12 months shorter than their match in the 

study group. This limitation avoids matching individuals 

with lengths of incarceration that are not meaningfully 

distinguishable, for example comparing an individual 

incarcerated for 49 months with an individual incarcerated for 

48 months. 

The Commission utilized two variations of research design 

one. In the first variation, Research Design 1A, in addition to 

having a sentence of incarceration at least 12 months shorter 

than their match, individuals in the comparison group could 

have no more than 36 months shorter length of incarceration 

(see Figure 2). The second restriction minimizes any concern 

that there may be attributes not accounted for in the design 

0 12 48 60

Length of Incarcera'on (in months)

Comparison Group Study Group

Offenders sentenced to 

at least 12, 

but not more than 36, 

months less than their match

Offenders sentenced to 

greater than 48 

up to 60 months

FIGURE 2. RESEARCH DESIGN 1A

11
that impact length of incarceration. In other words, if two 

offenders are identically matched on all attributes in Table 2 

but receive drastically different lengths of incarceration, it is 

possible that the difference in incarceration length is due to an 

unidentified attribute not accounted for in the research design. 

By requiring the comparison group to have similar lengths 

of incarceration (i.e., no more than 36 months shorter), any 

attributes that were not formally controlled for, such as drug 

weight, should be similar. Thus, in Research Design 1A, the 

comparison group is comprised of individuals precisely matched 

on the attributes listed in Table 2 who had a sentence that was 

at least 12 months, but not more than 36 months, shorter than 

their match in the study group.

In the second variation of research design one, Research 

Design 1B, the 36 months maximum difference in the length of 

incarceration restriction was removed (see Figure 3). Removing 

this restriction recognizes that setting a 36 month limit excludes 

the possibility that greater differences in incarceration length 

more often result from the exercise of judicial discretion than 

the impact of an unidentified attribute. Further, removing 

this restriction addresses the concern that by applying the 

limitation, the marginal improvement in the exactness of the 

match between the two groups unduly limits the sample size 

and, consequently, the statistical power of the research design. 

Therefore, in Research Design 1B, the comparison group 

comprised individuals who matched on all attributes listed 

in Table 2 with an incarceration sentence at least 12 months 

shorter. 

0 48 60

Length of Incarcera'on (in months)

Comparison Group Study Group

Offenders sentenced to 

at least 12 months less than their match

Offenders sentenced to 

greater than 48 

up to 60 months

FIGURE 3. RESEARCH DESIGN 1B

12
RESEARCH DESIGN 2

Research Design 2 utilized a combination of matching 

and weighting to create comparison groups. Specifically, 

the following attributes were matched exactly: age-atrelease, gender, race, criminal history category, and primary 

sentencing guideline. Weighting was used to balance the 

remaining attributes: high school completion, violent offense, 

weapons offense, substantial assistance, and safety valve 

adjustment. After weighting, the study and comparison 

groups were assessed to confirm the groups were sufficiently 

similar.39

While the second research design controlled for the attributes 

listed in Table 2, it excluded the requirement that matches have 

incarceration lengths at least 12 months, but not more than 36 

months, shorter. That is, the comparison group could include any 

individuals receiving a shorter period of incarceration (see Figure 

4). 

0 48 60

Length of Incarcera'on (in months)

Comparison Group Study Group

Offenders sentenced to 

greater than 0 months 

up to 48 months

Offenders sentenced to 

greater than 48 

up to 60 months

FIGURE 4. RESEARCH DESIGN 2

13
Regression Modeling

After establishing the comparison groups, multiple logistic 

regression was used to estimate the relationship between 

length of incarceration and recidivism. Logistic regression is a 

modeling technique used to analyze the relationship between 

attributes (e.g., length of incarceration, age, gender, etc.) and 

a binary response variable (e.g., recidivism).40 In this study, 

logistic regression was used to analyze the relationship between 

length of incarceration and recidivism while controlling for the 

attributes listed in Table 2. 

Logistic regression estimates the effects of variables on an 

outcome which is often reported as an odds ratio. In this study, 

the odds ratio represents the odds of recidivism for the study 

group as compared to the odds of recidivism for the comparison 

group. An odds ratio of one indicates no difference in recidivism 

between the groups. An odds ratio less than one indicates the 

study group had lower odds of recidivism than the comparison 

group. An odds ratio greater than one indicates the study group 

had greater odds of recidivism than the comparison group.41

In addition to producing an estimate, each estimate is tested 

for statistical significance. Testing estimates for statistical 

significance can be analogized to the burden of proof 

consideration in a criminal trial. The significance test begins with 

the premise that there is no relationship between the variables 

being tested, in this study length of incarceration and recidivism, 

similar to the premise that a defendant is innocent until proven 

guilty. In statistics, this presumption of innocence is referred to 

as the null hypothesis. The researcher collects data, or evidence, 

which is then judged to determine if the results of the analysis 

could have happened by random chance (i.e., null hypothesis) or 

if the evidence suggest the relationship observed exists beyond 

a reasonable doubt. In statistics, the threshold of beyond 

reasonable doubt is usually numerically defined with a p-value. 

The p-value numerically defines the degree of evidence required 

to reject the null hypothesis and determine that a relationship 

between the variables exists beyond a reasonable doubt. In this 

study, the Commission used the conventional threshold of 0.05 

to denote statistical significance. The threshold of less than 0.05 

means that for an estimate to be statistically significant, the 

data collected must indicate a less than 5 percent chance that 

the null hypothesis is true (i.e., that there is no true relationship 

between the variables). 

The Commission considers findings that do not achieve a 

p-value less than 0.05 to be unreliable for policy making. 

Therefore, the Commission will not rely on a finding that length 

of incarceration has a deterrent or criminogenic effect if the 

p-value is 0.05 or greater.

14
RESEARCH FINDINGS

This section of the report explores three potential relationships that may exist between length of 

incarceration and recidivism (incarceration as having a deterrent effect, a criminogenic effect, or no effect 

on recidivism).
RESEARCH DESIGN 1A

In Research Design 1A, all attributes in Table 2 were exactly 

matched except for age-at-release, which could vary by one year. 

After matching, the sample size for Research Design 1A was 4,930 

offenders across the five study groups (see Figure 5).

Figure 6 provides information on the average length of 

incarceration for each study and comparison group. Differences 

in the average length of incarceration range from 18.6 to 24.8 

months. As expected, the average lengths of incarceration for the 

comparison groups are greater than 12, but not greater than 36, 

months shorter than the average length of incarceration for the 

corresponding study groups. 

As noted, the Commission identified the study groups first 

and then created comparison groups in order to preserve the 

natural composition of offenders sentenced to various lengths of 

incarceration. Thus, in each study group, a matched or weighted 

comparison group of similar individuals was created. Between the 

study groups at various length of incarceration, there were some 

differences in the composition of offenders, as was expected. 

As the length of incarceration increased, the proportion of 

males increased, the proportion of Black offenders increased, 

the severity of CHC increased, and the proportion of §2D1.1 

offenders increased (see Table 3). 

>24-36 months >36-48 months >48-60 months >60-120 months >120 months

 147 Offenders Each

 701 Offenders Each

 511 Offenders Each

 644 Offenders Each

 462 Offenders Each

Study Group

Comparison Group

Total Sample Size: 

4,930 Offenders

FIGURE 5. SAMPLE SIZE

>24-36 months >36-48 months >48-60 months >60-120 months >120 months

 147 Offenders Each

 701 Offenders Each

 511 Offenders Each

 644 Offenders Each

 462 Offenders Each

Study Group

Comparison Group

Total Sample Size: 

4,930 Offenders

>24 to 36 months

>36 to 48 months

>48 to 60 months

>60 to 120 months

>120 months

125.5 months

58.8 months

32.1 months

19.8 months

12.1 months

149.7 months

83.6 months

56.5 months

42.1 months

30.7 months

FIGURE 6. AVERAGE LENGTH OF INCARCERATION

16
Age (years)

Mean 36.3 35.5 35.4 36.5 38.8

Gender (%)

Male 82.7 85.6 91.2 93.4 96.6

Female 17.3 14.4 8.8 6.6 3.4

Race (%)

White 74.5 73.1 66.9 47.8 27.2

Black 24.0 23.4 31.9 51.5 72.8

Other 1.5 3.4 1.2 0.7 0.0

Criminal History Category (%)

Category I 65.4 59.8 46.0 38.5 27.9

Category II 12.6 10.4 15.3 13.4 14.3

Category III 13.0 14.9 18.6 17.1 17.0

Category IV 4.1 8.1 10.6 12.1 8.8

Category V 1.3 3.9 3.7 7.3 10.9

Category VI 3.7 3.0 5.9 11.6 21.1

Primary Guideline (%)

§2D1.1 35.5 51.1 67.3 76.2 84.4

§2B1.1 24.9 6.8 0.0 0.0 0.0

§2K2.1 18.8 26.1 19.6 10.6 0.0

§2F1.1 11.3 9.3 0.0 0.0 0.0

§2B3.1 0.0 0.0 0.0 9.4 0.0

Other 9.5 6.7 13.1 3.9 15.6

ATTRIBUTES

LENGTH OF INCARCERATION

>24-36 months >36-48 months >48-60 months >60-120 months >120 months

TABLE 3. 

17
For each of the five study cohorts, multiple logistic regression 

was used to analyze the relationship between length of 

incarceration and recidivism while controlling for the attributes 

in Table 2. In Research Design 1A, one study group was 

identified as having a statistically significant relationship 

between length of incarceration and recidivism. Individuals 

serving sentences of more than 120 months incarceration had 

a statistically significant deterrent relationship between length 

of incarceration and recidivism. The regression model estimated 

individuals incarcerated for more than 120 months were 

approximately 45 percent less likely to recidivate as compared 

to a matched comparison group receiving an incarceration 

sentence that was at least 12 months shorter, but not more than 

36 months shorter (see Figure 7).42 This finding, a statistically 

significant deterrent relationship for offenders incarcerated 

for more than 120 months, was consistent across each of the 

research designs. In addition to estimating the likelihood of 

recidivism, time to rearrest was analyzed. The average time to 

rearrest for the study group was 962 days while the average 

time to rearrest for the comparison group was 946 days.43

In Research Design 1A, the model estimated that offenders 

sentenced to more than 24 to 36 months were 24 percent more 

likely to recidivate relative to a comparison group receiving a 

shorter sentence of incarceration (see Figure 8). This finding 

was not statistically significant, however, and is not sufficiently 

reliable for policy making. Further, as discussed below, there are 

substantial differences in the estimated effect of incarceration 

on recidivism for offenders in this study group across the three 

models. Therefore, no conclusion can be drawn as to the effect 

of length of incarceration on recidivism for offenders in this 

group. 

Example of Matched Offenders in Research Design 1A: 

(sentenced to at least 12 months shorter but not more than 36 months shorter than their match)

Comparison Group 

Offender

Study Group 

Offender

140-month 

sentence

0 120 or more

Length of Incarcera'on (in months)

120-month 

sentence

20-month 

difference

FIGURE 7. 

18
Criminogenic E

ffect Deterrent E

ffect

Recidivism Odds

indicates sta<s<cally significant

 indicates not sta<s<cally significant

*

Length of Incarcera%on

15% less likely

45% less likely

-1% less likely

1% more likely

24% more likely

-50

0

50

>24-36 months>36-48 months>48-60 months

>60-120 months

>120 months

*

FIGURE 8.

19
As discussed above, in Research Design 1B, the 36 month 

maximum difference in length of incarceration restriction was 

removed. Thus, for example, an individual incarcerated for 120 

months could be compared to an individual incarcerated for 12 

months. This restriction affected all study groups except for 

the first study group, those offenders with a sentence longer 

than 24 months up to 36 months.44 Once the restriction was 

removed, the pool of individuals available for comparison 

increased and, therefore, the overall sample size increased. After 

matching, the sample size for Research Design 1B was 9,524 (see

Figure 9), almost double the sample size for Research Design 1A.

Figure 10 provides information on the average length of 

incarceration for each study and comparison group. Differences 

in the average length of incarceration range from 18.6 to 97.8 

months. As expected, once the 36 month maximum difference 

in length of incarceration restriction was removed, the 

differences in average length of incarceration between study 

and comparison groups increased as compared to Research 

Design 1A. 

As noted, the Commission identified the study groups first and 

then created comparison groups second in order to preserve 

the natural composition of offenders sentenced to various 

lengths of incarceration. Thus, in each study group, a matched 

or weighted comparison group of similar individuals was created. 

Between the study groups at various length of incarceration, as 

RESEARCH DESIGN 1B

>24 to 36 months

>36 to 48 months

>48 to 60 months

>60 to 120 months

>120 months

75.3 months

43.6 months

26.5 months

19.0 months

12.1 months

173.1 months

89.8 months

56.7 months

42.3 months

30.7 months

FIGURE 10. AVERAGE LENGTH OF INCARCERATION

>24-36 months >36-48 months >48-60 months >60-120 months >120 months

 1,110 Offenders Each

 1,794 Offenders Each

 718 Offenders Each 678 Offenders Each

 462 Offenders Each

Study Group

Comparison Group

Total Sample Size: 

9,524 Offenders

FIGURE 9. SAMPLE SIZE

>24-36 months >36-48 months >48-60 months >60-120 months >120 months

 1,110 Offenders Each

 1,794 Offenders Each

 718 Offenders Each 678 Offenders Each

 462 Offenders Each

Study Group

Comparison Group

Total Sample Size: 

9,524 Offenders

20
Age (years)

Mean 36.3 35.7 35.2 36.7 39.7

Gender (%)

Male 82.7 85.8 89.1 92.9 96.5

Female 17.3 14.2 10.9 7.1 3.5

Race (%)

White 74.5 73.6 71.0 54.6 36.9

Black 24.0 23.0 27.6 44.3 62.4

Other 1.5 3.4 1.4 1.1 0.6

Criminal History Category (%)

Category I 65.4 60.2 49.9 41.9 28.6

Category II 12.6 10.3 14.9 12.9 13.7

Category III 13.0 15.0 19.1 18.5 18.9

Category IV 4.1 7.8 8.1 10.8 11.5

Category V 1.3 3.7 3.1 6.7 6.6

Category VI 3.7 2.9 5.0 9.3 20.7

Primary Guideline (%)

§2D1.1 35.5 51.9 69.6 78.6 84.4

§2B1.1 24.9 6.9 0.0 0.0 0.0

§2K2.1 18.8 25.4 16.3 10.8 5.5

§2F1.1 11.3 9.3 4.9 1.5 0.0

§2B3.1 0.0 0.0 0.0 6.2 9.1

Other 9.5 6.5 9.2 2.9 1.0

LENGTH OF INCARCERATION

ATTRIBUTES >24-36 months >36-48 months >48-60 months >60-120 months >120 months

TABLE 4. 

21
expected, there were some differences in the composition of 

offenders. Consistent with Research Design 1A, as the length of 

incarceration increased, the proportion of males increased, the 

proportion of Black offenders increased, the severity of CHC 

increased, and the proportion of §2D1.1 offenders increased 

(see Table 4). 

In Research Design 1B, two study groups were identified as 

having statistically significant relationships between length 

of incarceration and recidivism. Individuals incarcerated for 

more than 120 months had a statistically significant deterrent 

relationship between length of incarceration and recidivism 

(see Figure 11). The regression model estimated individuals 

incarcerated for more than 120 months were approximately 

30 percent less likely to recidivate as compared to a matched 

comparison group receiving at least 12 months shorter 

incarceration (see Figure 12).

45 In addition to estimating the 

likelihood of recidivism, time to rearrest was analyzed. The 

average time to rearrest for the study group was 955 days while 

the average time to rearrest for the comparison group was 847 

days.46

Individuals incarcerated for a period of more than 60 up to 

120 months had a statistically significant deterrent relationship 

between length of incarceration and recidivism. The regression 

model estimated individuals incarcerated for more than 60 

up to 120 months were approximately 16 percent less likely 

to recidivate as compared to a matched comparison group 

receiving an incarceration sentence that was at least 12 months 

shorter. In addition to estimating the likelihood of recidivism, 

time to rearrest was analyzed. The average time to rearrest for 

the study group was 938 days while the average time to rearrest 

for the comparison group was 880 days.47

As noted, offenders in study group one (greater than 24 to 36 

months) were the exact same in Research Designs 1A and 1B. 

Consequently, the model estimate for the first study group is the 

same for Research Designs 1A and 1B. Specifically, the model 

estimated that offenders sentenced to more than 24 months 

up to 36 months were 24 percent more likely to recidivate as 

compared to offenders whose sentence was at least 12 months 

shorter (see Figure 12). As discussed above, however, this finding 

was not statistically significant and is not sufficiently reliable for 

policy making. Further, as discussed below, there are substantial 

differences in the estimated effect of incarceration on recidivism 

for offenders in this study group between Research Designs 

1A, 1B, and 2. Therefore, no conclusions can be drawn from the 

data about this group. 

Example of Matched Offenders in Research Design 1B: 

(sentenced to at least 12 months shorter than their match)

Comparison Group 

Offender

Study Group 

Offender

140-month 

sentence

0 120 or more

Length of Incarcera'on (in months)

80-month 

sentence

60-month 

difference

FIGURE 11.

22
-50

0

50

>24-36 months>36-48 months>48-60 months

>60-120 months

>120 months

16% less likely

30% less likely

2% less likely 5% less likely

24% more likely

Criminogenic E

ffect Deterrent E

ffect

Recidivism Odds

* indicates sta<s<cally significant

 indicates not sta<s<cally significant

Length of Incarcera%on

*

*

FIGURE 12.

23
RESEARCH DESIGN 2

Research Design 2 focused on developing similar comparison 

groups while retaining a larger sample size. This design used 

a combination of matching and weighting to create the 

comparison groups. The comparison groups included individuals 

matched or weighted on all attributes listed in Table 2 who had 

a shorter length of incarceration.48 The objective of Research 

Design 2, to create similar comparison groups and retain a larger 

sample size, was achieved. The total sample size for Research 

Design 2 was 16,800, much larger than the sample sizes of 

either Research Design 1A or 1B (see Figure 13). 

Figure 14 provides information on the average length of 

incarceration for each study and comparison group. Differences 

in the average length of incarceration range from 14.6 to 100.3 

months. The difference in average length of incarceration 

between study and comparison groups in Research Design 2 is 

comparable to the differences identified in Research Design 1B. 

As noted, the Commission identified the study groups first and 

then created comparison groups second in order to preserve the 

natural composition of offenders sentenced to various lengths of 

incarceration. Thus, in each study group, a matched or weighted 

comparison group of similar individuals was created. Between 

the study groups at various length of incarceration, as expected, 

there were some differences in the composition of offenders. 

Consistent with the prior research designs, as the length of 

incarceration increased, the proportion of males increased, the 

FIGURE 13. SAMPLE SIZE

>24-36 months >36-48 months >48-60 months >60-120 months >120 months

 1,135 Offenders

 2,006 Offenders

 1,182 Offenders

 1,449 Offenders

 1,272 Offenders

 1,495 Offenders

 2,968 Offenders

 1,489 Offenders

 2,012 Offenders

 1,792 Offenders

Study Group

Comparison Group

Total Sample Size: 

16,800 Offenders

>24 to 36 months

>36 to 48 months

>48 to 60 months

>60 to 120 months

>120 months

69.6 months

38.6 months

30.2 months

22.4 months

15.7 months

169.9 months

87.2 months

57.0 months

41.6 months

30.3 months

FIGURE 14. AVERAGE LENGTH OF INCARCERATION

24
Age (years)

Mean 35.2 35.2 35.5 36.7 40.0

Gender (%)

Male 87.2 88.6 92.5 93.5 96.6

Female 12.8 11.4 7.5 6.5 3.4

Race (%)

White 72.4 65.1 62.0 49.0 35.3

Black 25.8 32.6 37.0 50.1 64.1

Other 1.7 2.3 1.0 0.9 0.7

Criminal History Category (%)

Category I 57.8 57.2 42.4 38.0 28.7

Category II 12.9 9.7 15.4 12.8 13.3

Category III 16.8 14.3 21.0 19.7 18.7

Category IV 7.1 10.4 10.4 11.2 11.2

Category V 2.3 3.3 4.1 6.6 5.8

Category VI 3.1 5.1 6.6 11.8 22.3

Primary Guideline (%)

§2D1.1 50.1 65.9 74.7 82.6 84.2

§2B1.1 9.9 3.4 0.0 0.0 0.0

§2K2.1 22.9 21.3 14.4 10.2 6.4

§2F1.1 6.9 4.1 3.0 1.0 0.0

§2B3.1 0.0 0.0 3.1 3.9 8.6

§2G2.4 4.2 0.0 0.0 0.0 0.0

Other 6.0 5.3 4.8 1.3 0.9

LENGTH OF INCARCERATION

ATTRIBUTES >24-36 months >36-48 months >48-60 months >60-120 months >120 months

TABLE 5. 

25
proportion of Black offenders increased, the severity of CHC 

increased, and the proportion of §2D1.1 offenders increased 

(see Table 5). 

In Research Design 2, two study cohorts were identified as 

having statistically significant relationships between length 

of incarceration and recidivism. Individuals incarcerated for 

more than 120 months had a statistically significant deterrent 

relationship between length of incarceration and recidivism. 

The regression model estimated individuals incarcerated for 

more than 120 months were approximately 29 percent less 

likely to recidivate relative to a comparison group receiving a 

shorter sentence of incarceration.

49 In addition to estimating 

the likelihood of recidivism, time to rearrest was analyzed. The 

average time to rearrest for the study group was 956 days while 

the average time to rearrest for the comparison group was 951 

days.50

Individuals incarcerated for periods of more than 60 months 

up to 120 months also had a statistically significant deterrent 

relationship between length of incarceration and recidivism 

(see Figure 15). The regression model estimated that these 

individuals were 18 percent less likely to recidivate relative to a 

comparison group receiving a shorter sentence of incarceration 

(see Figure 16). In addition to estimating the likelihood of 

recidivism, time to rearrest was analyzed. The average time to 

rearrest for the study group was 955 days while the average 

time to rearrest for the comparison group was 893 days.51

In Research Design 2, the model estimated that offenders 

sentenced to more than 24 months up to 36 months were three 

percent more likely to recidivate (see Figure 16). This finding, 

however, was not statistically significant and is not sufficiently 

reliable for policy making. Further, this estimate is substantially 

different from the model estimates for Research Designs 1A and 

1B (3% as compared to 24%). Therefore, no conclusions can be 

drawn from this data about this group. 

Comparison Group 

Offender

Study Group 

Offender

61-month 

sentence

0 60 120

Length of Incarcera'on (in months)

Example of Matched Offenders in Research Design 2: 

(sentenced to a term shorter than their match)

24-month 

sentence

FIGURE 15. 

26
-50

0

50

>24-36 months>36-48 months>48-60 months

>60-120 months

>120 months

Criminogenic E

ffect Deterrent E

ffect

Recidivism Odds

* indicates sta<s<cally significant

 indicates not sta<s<cally significant

Length of Incarcera%on

*

* 18% less likely

29% less likely

5% less likely 6% less likely

3% more likely

FIGURE 16. 

27
Each of the research models identified statistically significant 

deterrent relationships between length of incarceration and 

recidivism for individuals incarcerated for more than 120 

months. Additionally, Research Designs 1B and 2 identified 

statistically significant deterrent relationships for individuals 

incarcerated for more than 60 up to 120 months. In comparing 

the regression models, there is a high degree of similarity 

between the statistically significant estimates for Research 

Designs 1B and 2 (the designs with larger sample sizes). 

Collectively, across all of the regression models, there appears 

to be consistency in the overall trend towards a deterrent effect 

for individuals incarcerated for longer than 60 months. 

No statistically significant relationship between length of 

incarceration and recidivism was identified for offenders 

incarcerated for 60 months or less. The first study group, 

offenders sentenced to more than 24 to 36 months, were the 

only group of offenders with a sentence shorter than 60 months 

where any model estimated an effect on recidivism. However, as 

previously discussed, none of the model estimates for this study 

group were statistically significant and the estimates varied 

substantially. Consequently, because none of the estimates 

were statistically significant and the estimates varied widely 

between the models, the Commission has no basis to conclude 

that incarceration for more than 24 months up to 36 months 

has any effect on recidivism as compared to shorter periods of 

incarceration. 

Figure 17 plots the estimated likelihood of recidivism for each 

of the study cohorts across the various research designs.52 The 

horizontal axis plots each of the study cohorts, the vertical axis 

represents the likelihood of recidivism, and the red horizontal 

line at zero demarcates an increased likelihood of recidivism 

(above the line) with a decreased likelihood of recidivism (below 

the line). Statistically significant estimates are denoted by 

asterisk shapes. As Figure 17 illustrates, significant estimates 

for offenders incarcerated for greater than 60 to 120 months, 

and greater than 120 months, substantially overlap for Research 

Designs 1B and 2. 

COMPARING MODELS

28
FIGURE 17. 

-50

0

50

>24-36 months >36-48 months >48-60 months >60-120 months >120 months

*

* 18% less likely 

>60-120 months

29% less likely 

>120 months

5% less likely 6% less likely

3% more likely

*

 indicates sta<s<cally significant

Recidivism Odds

-50

0

50

>24-36 months >36-48 months >48-60 months >60-120 months >120 months

*

Criminogenic E

ffect Deterrent E

ffect

15% less likely

45% less likely 

>120 months

1% less likely

1% more likely

24% more likely

-50

0

50

>24-36 months >36-48 months >48-60 months >60-120 months >120 months

16% less likely 

>60-120 months

30% less likely 

>120 months

2% less likely 5% less likely

24% more likely

*

*

MODEL 1A MODEL 1B MODEL 2

29
The Commission initiated this study to better understand 

the relationship between length of incarceration and 

recidivism for federal offenders. There are three potential 

relationships between length of incarceration and recidivism: 

deterrent, criminogenic, and no effect. The Commission 

found a statistically significant deterrent effect for offenders 

incarcerated for more than 60 months when compared to 

similar offenders incarcerated for shorter periods of time. The 

Commission found no statistically significant effect for offenders 

sentenced to 60 months or less. Consequently, the Commission 

has no basis to conclude that incarceration for 60 months or less 

has a criminogenic or deterrent effect. 

To analyze the relationship between length of incarceration 

and recidivism, five study cohorts were examined through 

three models. In all three models, offenders incarcerated for 

more than 120 months were identified as having a statistically 

significant deterrent relationship between incarceration and 

recidivism. For Research Designs 1B and 2, the models with 

larger sample sizes, offenders incarcerated for more than 

120 months were estimated to be approximately 30 percent 

less likely to recidivate than those serving shorter periods of 

incarceration.53 For Research Design 1A, offenders incarcerated 

for more than 120 months were estimated to be 45 percent 

less likely to recidivate. In two models, Research Designs 1B 

and 2, offenders incarcerated for more than 60 to 120 months 

were identified as having a statistically significant deterrent 

relationship between incarceration and recidivism. Specifically, 

offenders incarcerated for more than 60 months up to 120 

months were estimated to be approximately 17 percent less 

likely to recidivate.54

In conclusion, this study suggests an inverse relationship 

between length of incarceration and recidivism for offenders 

serving more than 60 months incarceration. Federal offenders 

incarcerated for longer than 60 months had a lower recidivism 

rate than offenders with similar characteristics receiving shorter 

lengths of incarceration.

CONCLUSION

30
APPENDIX A

Appendix A provides information on the regression model estimates, in the form of odds ratios, for each 

of the five study groups across the various research designs. Only the estimate for the effect of length of 

incarceration on recidivism is presented. For the full regression models, see Appendices B, C, and D.
Research Designs

 Design 1A

Research Design 1A used matching to develop comparison groups that exactly 

matched all aRributes in Table 2 with the excep'on of age-at-release, which could 

vary by one year. Addi'onally, matches were required to have been sentenced to at 

least 12 months, but not more than 36 months, less incarcera'on.

 Design 1B

Research Design 1B is the same as Research Design 1A, with the excep'on that 

individuals in the comparison group could have periods of incarcera'on that were 

more than 36 months shorter.

 Design 2

Research Design 2 used matching and weigh'ng to develop comparison groups 

similar on the aRributes listed in Table 2 while retaining a larger sample size. There 

were no restric'ons on length of incarcera'on for the comparison group (e.g., a 

minimum 12 months less incarcera'on or a maximum of 36 less incarcera'on).

TABLE A-1. 

Odds Ra%o for Each Research Design

>24-36 

months

>36-48 

months

>48-60 

months

>60-120 

months

>120 

months

 Design 1A: 

 Odds Ra%o 1.24 0.99 1.01 0.85 0.55*

 Design 1B: 

 Odds Ra%o 1.24 0.98 0.95 0.84* 0.70*

 Design 2: 

 Odds Ra%o 1.03 0.95 0.94 0.82* 0.71*

TABLE A-2. 

32
APPENDIX B

Appendix B provides information on the full regression model for Research Design 1A, including: 

estimate, standard error, Z value, p-value, odds ratio, and 95 percent confidence interval for the odds 

ratio. 
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 2.001 0.393 5.095 0.000

Research Group

 Study vs. Comparison 0.217 0.151 1.432 0.152 1.24 0.92 1.67

Age-at-Release

 Age -0.056 0.008 -7.005 0.000 0.94 0.93 0.96

Gender

 Female vs. Male -0.784 0.218 -3.591 0.000 0.46 0.30 0.70

Race

 Black vs. White 0.546 0.195 2.808 0.005 1.73 1.18 2.53

 Other vs. White -0.419 0.693 -0.605 0.545 0.66 0.14 2.35

High School Completion

 Yes vs. No -0.524 0.192 -2.727 0.006 0.59 0.40 0.86

Criminal History Category

 CHC II vs. CHC I 1.081 0.259 4.173 0.000 2.95 1.78 4.93

 CHC III vs. CHC I 1.023 0.266 3.841 0.000 2.78 1.66 4.71

 CHC IV vs. CHC I 1.377 0.419 3.282 0.001 3.96 1.79 9.39

 CHC V vs. CHC I 1.531 0.694 2.206 0.027 4.62 1.30 21.70

 CHC VI vs. CHC I 2.412 0.523 4.611 0.000 11.15 4.32 34.87

Guideline

 §2B1.1 vs. §2D1.1 -0.351 0.311 -1.130 0.259 0.70 0.38 1.29

 §2K2.1 vs. §2D1.1 -0.293 0.316 -0.924 0.355 0.75 0.40 1.38

 §2F1.1 vs. §2D1.1 -0.825 0.384 -2.151 0.031 0.44 0.20 0.92

 Other vs. §2D1.1 -0.002 0.368 -0.005 0.996 1.00 0.48 2.05

Violence

 Yes vs. No 0.392 0.597 0.657 0.511 1.48 0.45 4.83

Weapons Adjustment

 Yes vs. No 0.282 0.788 0.358 0.720 1.33 0.29 7.07

Substantial Assistance

 Yes vs. No -0.337 0.225 -1.502 0.133 0.71 0.46 1.11

Safety Valve

 Yes vs. No 0.044 0.290 0.153 0.879 1.04 0.59 1.85

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 1A

Study Cohort: >24-36 months

 95% CI

Response Variable: recidivism (rearrest)

 -516.592 (df = 20)

0.19

924

TABLE B-1. 

34
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.233 0.336 3.671 0.000

Research Group

 Study vs. Comparison -0.008 0.127 -0.059 0.953 0.99 0.77 1.27

Age-at-Release

 Age -0.043 0.007 -6.115 0.000 0.96 0.94 0.97

Gender

 Female vs. Male -0.694 0.187 -3.705 0.000 0.50 0.34 0.72

Race

 Black vs. White 0.547 0.163 3.360 0.001 1.73 1.26 2.38

 Other vs. White 0.100 0.352 0.283 0.777 1.10 0.55 2.21

High School Completion

 Yes vs. No -0.292 0.139 -2.104 0.035 0.75 0.57 0.98

Criminal History Category

 CHC II vs. CHC I 0.615 0.246 2.494 0.013 1.85 1.14 3.00

 CHC III vs. CHC I 1.137 0.240 4.732 0.000 3.12 1.95 5.02

 CHC IV vs. CHC I 1.479 0.322 4.591 0.000 4.39 2.37 8.40

 CHC V vs. CHC I 2.162 0.478 4.528 0.000 8.69 3.63 24.31

 CHC VI vs. CHC I 3.518 0.764 4.606 0.000 33.70 9.36 217.39

Guideline

 §2B1.1 vs. §2D1.1 -0.229 0.340 -0.673 0.501 0.80 0.41 1.55

 §2K2.1 vs. §2D1.1 0.185 0.243 0.764 0.445 1.20 0.75 1.94

 §2F1.1 vs. §2D1.1 -0.615 0.328 -1.875 0.061 0.54 0.28 1.02

 Other vs. §2D1.1 0.096 0.327 0.293 0.770 1.10 0.58 2.09

Violence

 Yes vs. No 0.332 0.348 0.955 0.340 1.39 0.71 2.80

Weapons Adjustment

 Yes vs. No 0.240 0.471 0.511 0.609 1.27 0.51 3.27

Substantial Assistance

 Yes vs. No -0.212 0.168 -1.261 0.207 0.81 0.58 1.12

Safety Valve

 Yes vs. No 0.135 0.237 0.570 0.569 1.15 0.72 1.82

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 1A

Study Cohort: >36-48 months

 95% CI

Response Variable: recidivism (rearrest)

 -732.066 (df = 20)

0.18

1,288

TABLE B-2. 

35
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.468 0.376 3.902 0.000

Research Group

 Study vs. Comparison 0.010 0.142 0.067 0.947 1.01 0.76 1.33

Age-at-Release

 Age -0.048 0.008 -5.758 0.000 0.95 0.94 0.97

Gender

 Female vs. Male -0.692 0.253 -2.729 0.006 0.50 0.30 0.82

Race

 Black vs. White 0.557 0.168 3.318 0.001 1.75 1.26 2.43

 Other vs. White 0.762 0.640 1.191 0.234 2.14 0.61 7.96

High School Completion

 Yes vs. No -0.347 0.153 -2.268 0.023 0.71 0.52 0.95

Criminal History Category

 CHC II vs. CHC I 0.700 0.247 2.838 0.005 2.01 1.25 3.28

 CHC III vs. CHC I 1.210 0.249 4.867 0.000 3.35 2.07 5.49

 CHC IV vs. CHC I 1.649 0.326 5.060 0.000 5.20 2.78 10.00

 CHC V vs. CHC I 1.817 0.484 3.750 0.000 6.15 2.50 17.04

 CHC VI vs. CHC I 2.524 0.464 5.442 0.000 12.48 5.29 33.30

Guideline

 §2K2.1 vs. §2D1.1 -0.298 0.259 -1.153 0.249 0.74 0.45 1.23

 Other vs. §2D1.1 -0.248 0.280 -0.887 0.375 0.78 0.45 1.35

Violence

 Yes vs. No 0.776 0.355 2.183 0.029 2.17 1.09 4.42

Weapons Adjustment

 Yes vs. No 0.361 0.295 1.223 0.221 1.44 0.81 2.58

Substantial Assistance

 Yes vs. No -0.220 0.173 -1.274 0.203 0.80 0.57 1.13

Safety Valve

 Yes vs. No -0.016 0.235 -0.068 0.946 0.98 0.62 1.56

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 1A

Study Cohort: >48-60 months

 95% CI

Response Variable: recidivism (rearrest)

-582.255 (df = 18)

0.17

1,022

TABLE B-3. 

36
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.837 0.378 4.866 0.000

Research Group

 Study vs. Comparison -0.163 0.121 -1.339 0.181 0.85 0.67 1.08

Age-at-Release

 Age -0.066 0.008 -8.044 0.000 0.94 0.92 0.95

Gender

 Female vs. Male -0.569 0.256 -2.220 0.026 0.57 0.34 0.93

Race

 Black vs. White 0.369 0.128 2.882 0.004 1.45 1.12 1.86

 Other vs. White 0.866 0.763 1.136 0.256 2.38 0.56 12.29

High School Completion

 Yes vs. No -0.324 0.130 -2.482 0.013 0.72 0.56 0.93

Criminal History Category

 CHC II vs. CHC I 0.853 0.225 3.790 0.000 2.35 1.51 3.66

 CHC III vs. CHC I 0.929 0.212 4.387 0.000 2.53 1.68 3.85

 CHC IV vs. CHC I 1.712 0.256 6.689 0.000 5.54 3.38 9.23

 CHC V vs. CHC I 1.299 0.313 4.146 0.000 3.67 2.00 6.85

 CHC VI vs. CHC I 2.023 0.277 7.299 0.000 7.56 4.43 13.16

Guideline

 §2K2.1 vs. §2D1.1 1.081 0.300 3.601 0.000 2.95 1.67 5.42

 §2B3.1 vs. §2D1.1 0.900 0.871 1.033 0.301 2.46 0.33 11.80

 Other vs. §2D1.1 0.655 0.370 1.769 0.077 1.92 0.92 3.95

Violence

 Yes vs. No -0.568 0.842 -0.675 0.500 0.57 0.13 4.03

Weapons Adjustment

 Yes vs. No 0.136 0.195 0.695 0.487 1.15 0.78 1.68

Substantial Assistance

 Yes vs. No -0.219 0.143 -1.529 0.126 0.80 0.61 1.06

Safety Valve

 Yes vs. No 0.299 0.221 1.351 0.177 1.35 0.88 2.08

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 1A

Study Cohort: >60-120 months

 95% CI

Response Variable: recidivism (rearrest)

-797.333 (df = 19)

0.17

1,402

TABLE B-4. 

37
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 0.664 1.001 0.663 0.507

Research Group

 Study vs. Comparison -0.592 0.267 -2.216 0.027 0.55 0.33 0.93

Age-at-Release

 Age -0.029 0.020 -1.455 0.146 0.97 0.93 1.01

Gender

 Female vs. Male -1.468 1.120 -1.311 0.190 0.23 0.01 1.46

Race

 Black vs. White 0.483 0.339 1.425 0.154 1.62 0.83 3.16

High School Completion

 Yes vs. No -0.783 0.294 -2.665 0.008 0.46 0.26 0.81

Criminal History Category

 CHC II vs. CHC I 1.391 0.447 3.112 0.002 4.02 1.70 9.88

 CHC III vs. CHC I 1.247 0.424 2.937 0.003 3.48 1.53 8.13

 CHC IV vs. CHC I 1.309 0.526 2.489 0.013 3.70 1.35 10.74

 CHC V vs. CHC I 1.876 0.539 3.483 0.000 6.53 2.34 19.55

 CHC VI vs. CHC I 2.177 0.464 4.695 0.000 8.82 3.63 22.50

Guideline

 Other vs. §2D1.1 1.561 0.973 1.604 0.109 4.76 0.76 40.43

Violence

 Yes vs. No -1.267 1.040 -1.218 0.223 0.28 0.03 2.02

Weapons Adjustment

 Yes vs. No 0.153 0.359 0.427 0.669 1.17 0.58 2.37

Substantial Assistance

 Yes vs. No -0.780 0.361 -2.161 0.031 0.46 0.22 0.92

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 1A

Study Cohort: >120 months

 95% CI

Response Variable: recidivism (rearrest)

-167.619 (df = 15)

0.17

294

TABLE B-5. 

38
APPENDIX C

Appendix C provides information on the full regression model for Research Design 1B, including: 

estimate, standard error, Z value, p-value, odds ratio, and 95 percent confidence interval for the odds 

ratio. 
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 2.001 0.393 5.095 0.000

Research Group

 Study vs. Comparison 0.217 0.151 1.432 0.152 1.24 0.92 1.67

Age-at-Release

 Age -0.056 0.008 -7.005 0.000 0.94 0.93 0.96

Gender

 Female vs. Male -0.784 0.218 -3.591 0.000 0.46 0.30 0.70

Race

 Black vs. White 0.546 0.195 2.808 0.005 1.73 1.18 2.53

 Other vs. White -0.419 0.693 -0.605 0.545 0.66 0.14 2.35

High School Completion

 Yes vs. No -0.524 0.192 -2.727 0.006 0.59 0.40 0.86

Criminal History Category

 CHC II vs. CHC I 1.081 0.259 4.173 0.000 2.95 1.78 4.93

 CHC III vs. CHC I 1.023 0.266 3.841 0.000 2.78 1.66 4.71

 CHC IV vs. CHC I 1.377 0.419 3.282 0.001 3.96 1.79 9.39

 CHC V vs. CHC I 1.531 0.694 2.206 0.027 4.62 1.30 21.70

 CHC VI vs. CHC I 2.412 0.523 4.611 0.000 11.15 4.32 34.87

Guideline

 §2B1.1 vs. §2D1.1 -0.351 0.311 -1.130 0.259 0.70 0.38 1.29

 §2K2.1 vs. §2D1.1 -0.293 0.316 -0.924 0.355 0.75 0.40 1.38

 §2F1.1 vs. §2D1.1 -0.825 0.384 -2.151 0.031 0.44 0.20 0.92

 Other vs. §2D1.1 -0.002 0.368 -0.005 0.996 1.00 0.48 2.05

Violence

 Yes vs. No 0.392 0.597 0.657 0.511 1.48 0.45 4.83

Weapons Adjustment

 Yes vs. No 0.282 0.788 0.358 0.720 1.33 0.29 7.07

Substantial Assistance

 Yes vs. No -0.337 0.225 -1.502 0.133 0.71 0.46 1.11

Safety Valve

 Yes vs. No 0.044 0.290 0.153 0.879 1.04 0.59 1.85

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 1B

Study Cohort: >24-36 months

 95% CI

Response Variable: recidivism (rearrest)

 -516.592 (df = 20)

0.19

924

TABLE C-1. 

40
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.380 0.327 4.225 0.000

Research Group

 Study vs. Comparison -0.015 0.124 -0.119 0.905 0.98 0.77 1.26

Age-at-Release

 Age -0.043 0.007 -6.461 0.000 0.96 0.94 0.97

Gender

 Female vs. Male -0.714 0.184 -3.872 0.000 0.49 0.34 0.70

Race

 Black vs. White 0.547 0.160 3.417 0.001 1.73 1.26 2.37

 Other vs. White 0.060 0.344 0.175 0.861 1.06 0.54 2.08

High School Completion

 Yes vs. No -0.326 0.136 -2.403 0.016 0.72 0.55 0.94

Criminal History Category

 CHC II vs. CHC I 0.647 0.241 2.682 0.007 1.91 1.19 3.07

 CHC III vs. CHC I 1.091 0.234 4.672 0.000 2.98 1.89 4.72

 CHC IV vs. CHC I 1.411 0.315 4.482 0.000 4.10 2.24 7.72

 CHC V vs. CHC I 2.158 0.476 4.529 0.000 8.65 3.63 24.18

 CHC VI vs. CHC I 3.598 0.764 4.709 0.000 36.54 10.14 235.95

Guideline

 §2B1.1 vs. §2D1.1 -0.341 0.332 -1.027 0.304 0.71 0.37 1.36

 §2K2.1 vs. §2D1.1 0.120 0.234 0.511 0.609 1.13 0.71 1.78

 §2F1.1 vs. §2D1.1 -0.669 0.319 -2.099 0.036 0.51 0.27 0.95

 Other vs. §2D1.1 0.035 0.322 0.110 0.912 1.04 0.55 1.94

Violence

 Yes vs. No 0.354 0.347 1.019 0.308 1.43 0.73 2.86

Weapons Adjustment

 Yes vs. No 0.061 0.449 0.136 0.892 1.06 0.44 2.59

Substantial Assistance

 Yes vs. No -0.300 0.164 -1.822 0.069 0.74 0.54 1.02

Safety Valve

 Yes vs. No 0.065 0.229 0.282 0.778 1.07 0.68 1.67

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 1B

Study Cohort: >36-48 months

 95% CI

Response Variable: recidivism (rearrest)

 -768.934 (df = 20)

0.18

1,356

TABLE C-2. 

41
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.663 0.294 5.653 0.000

Research Group

 Study vs. Comparison -0.050 0.118 -0.420 0.674 0.95 0.76 1.20

Age-at-Release

 Age -0.050 0.007 -7.366 0.000 0.95 0.94 0.96

Gender

 Female vs. Male -0.684 0.193 -3.545 0.000 0.50 0.34 0.73

Race

 Black vs. White 0.538 0.145 3.706 0.000 1.71 1.29 2.28

 Other vs. White 0.703 0.499 1.408 0.159 2.02 0.77 5.56

High School Completion

 Yes vs. No -0.348 0.129 -2.698 0.007 0.71 0.55 0.91

Criminal History Category

 CHC II vs. CHC I 0.597 0.206 2.900 0.004 1.82 1.22 2.73

 CHC III vs. CHC I 1.021 0.201 5.080 0.000 2.78 1.88 4.13

 CHC IV vs. CHC I 1.409 0.291 4.851 0.000 4.09 2.34 7.32

 CHC V vs. CHC I 1.637 0.436 3.758 0.000 5.14 2.29 12.85

 CHC VI vs. CHC I 2.383 0.417 5.712 0.000 10.83 5.02 26.24

Guideline

 §2K2.1 vs. §2D1.1 -0.129 0.221 -0.582 0.560 0.88 0.57 1.36

 §2F1.1 vs. §2D1.1 -0.364 0.331 -1.101 0.271 0.70 0.36 1.32

 Other vs. §2D1.1 0.065 0.266 0.244 0.807 1.07 0.63 1.80

Violence

 Yes vs. No 0.460 0.334 1.378 0.168 1.58 0.83 3.08

Weapons Adjustment

 Yes vs. No 0.289 0.268 1.076 0.282 1.34 0.79 2.27

Substantial Assistance

 Yes vs. No -0.157 0.146 -1.082 0.279 0.85 0.64 1.14

Safety Valve

 Yes vs. No -0.029 0.190 -0.154 0.877 0.97 0.67 1.41

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 1B

Study Cohort: >48-60 months

 95% CI

Response Variable: recidivism (rearrest)

 -836.399 (df = 19)

0.15

1,436

TABLE C-3. 

42
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.823 0.216 8.450 0.000

Research Group

 Study vs. Comparison -0.170 0.074 -2.292 0.022 0.84 0.73 0.98

Age-at-Release

 Age -0.055 0.005 -11.861 0.000 0.95 0.94 0.96

Gender

 Female vs. Male -0.411 0.147 -2.793 0.005 0.66 0.50 0.88

Race

 Black vs. White 0.248 0.077 3.198 0.001 1.28 1.10 1.49

 Other vs. White 0.475 0.365 1.302 0.193 1.61 0.80 3.36

High School Completion

 Yes vs. No -0.411 0.078 -5.300 0.000 0.66 0.57 0.77

Criminal History Category

 CHC II vs. CHC I 0.642 0.138 4.656 0.000 1.90 1.45 2.49

 CHC III vs. CHC I 0.857 0.129 6.647 0.000 2.36 1.83 3.04

 CHC IV vs. CHC I 1.218 0.156 7.797 0.000 3.38 2.50 4.61

 CHC V vs. CHC I 1.397 0.195 7.176 0.000 4.04 2.77 5.95

 CHC VI vs. CHC I 1.795 0.180 9.989 0.000 6.02 4.25 8.61

Guideline

 §2K2.1 vs. §2D1.1 0.526 0.161 3.256 0.001 1.69 1.24 2.33

 §2B3.1 vs. §2D1.1 -0.040 0.472 -0.084 0.933 0.96 0.36 2.34

 §2F1.1 vs. §2D1.1 0.005 0.342 0.015 0.988 1.00 0.50 1.93

 Other vs. §2D1.1 0.034 0.261 0.132 0.895 1.03 0.62 1.71

Violence

 Yes vs. No 0.299 0.443 0.674 0.500 1.35 0.59 3.41

Weapons Adjustment

 Yes vs. No 0.200 0.127 1.574 0.115 1.22 0.95 1.57

Substantial Assistance

 Yes vs. No -0.309 0.090 -3.430 0.001 0.73 0.62 0.88

Safety Valve

 Yes vs. No -0.044 0.130 -0.336 0.737 0.96 0.74 1.24

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 1B

Study Cohort: >60-120 months

 95% CI

Response Variable: recidivism (rearrest)

 -2120.155 (df = 20)

0.14

3,588

TABLE C-4. 

43
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.625 0.303 5.372 0.000

Research Group

 Study vs. Comparison -0.360 0.094 -3.820 0.000 0.70 0.58 0.84

Age-at-Release

 Age -0.054 0.006 -8.519 0.000 0.95 0.94 0.96

Gender

 Female vs. Male -0.650 0.282 -2.309 0.021 0.52 0.29 0.89

Race

 Black vs. White 0.190 0.104 1.821 0.069 1.21 0.98 1.48

 Other vs. White 0.465 0.598 0.779 0.436 1.59 0.49 5.34

High School Completion

 Yes vs. No -0.199 0.098 -2.039 0.041 0.82 0.68 0.99

Criminal History Category

 CHC II vs. CHC I 0.461 0.154 2.993 0.003 1.58 1.17 2.14

 CHC III vs. CHC I 0.839 0.142 5.916 0.000 2.31 1.75 3.06

 CHC IV vs. CHC I 1.245 0.173 7.201 0.000 3.47 2.48 4.89

 CHC V vs. CHC I 1.669 0.229 7.274 0.000 5.31 3.42 8.41

 CHC VI vs. CHC I 1.757 0.162 10.876 0.000 5.80 4.24 7.98

Guideline

 §2K2.1 vs. §2D1.1 0.763 0.251 3.040 0.002 2.15 1.33 3.57

 §2B3.1 vs. §2D1.1 0.585 0.637 0.919 0.358 1.80 0.51 6.44

 Other vs. §2D1.1 0.263 0.485 0.543 0.587 1.30 0.49 3.34

Violence

 Yes vs. No -0.002 0.618 -0.003 0.997 1.00 0.29 3.42

Weapons Adjustment

 Yes vs. No -0.087 0.116 -0.746 0.456 0.92 0.73 1.15

Substantial Assistance

 Yes vs. No 0.070 0.130 0.542 0.588 1.07 0.83 1.38

Safety Valve

 Yes vs. No 0.165 0.272 0.607 0.544 1.18 0.69 2.00

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 1B

Study Cohort: >120 months

 95% CI

Response Variable: recidivism (rearrest)

 -1320.811 (df = 19)

0.14

2,220

TABLE C-5. 

44
APPENDIX D

Appendix D provides information on the full regression model for Research Design 2, including: 

estimate, standard error, Z value, p-value, odds ratio, and 95 percent confidence interval for the odds 

ratio.
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.812 0.220 8.251 0.000

Research Group

 Study vs. Comparison 0.034 0.084 0.406 0.684 1.03 0.88 1.22

Age-at-Release

 Age -0.053 0.005 -11.521 0.000 0.95 0.94 0.96

Gender

 Female vs. Male -0.611 0.128 -4.782 0.000 0.54 0.42 0.70

Race

 Black vs. White 0.357 0.106 3.370 0.001 1.43 1.16 1.76

 Other vs. White 0.081 0.316 0.257 0.797 1.08 0.58 2.02

High School Completion

 Yes vs. No -0.605 0.092 -6.596 0.000 0.55 0.46 0.65

Criminal History Category

 CHC II vs. CHC I 0.751 0.150 5.012 0.000 2.12 1.58 2.84

 CHC III vs. CHC I 1.114 0.151 7.384 0.000 3.04 2.27 4.10

 CHC IV vs. CHC I 1.783 0.220 8.094 0.000 5.95 3.90 9.27

 CHC V vs. CHC I 1.971 0.348 5.664 0.000 7.17 3.75 14.83

 CHC VI vs. CHC I 2.523 0.345 7.308 0.000 12.46 6.58 25.75

Guideline

 §2B1.1 vs. §2D1.1 -0.114 0.184 -0.618 0.536 0.89 0.62 1.28

 §2K2.1 vs. §2D1.1 0.135 0.146 0.927 0.354 1.15 0.86 1.52

 §2F1.1 vs. §2D1.1 -0.396 0.222 -1.782 0.075 0.67 0.43 1.03

 §2G2.4 vs. §2D1.1 0.372 0.237 1.568 0.117 1.45 0.91 2.31

 Other vs. §2D1.1 -0.177 0.213 -0.831 0.406 0.84 0.55 1.27

Violence

 Yes vs. No 0.488 0.228 2.139 0.032 1.63 1.04 2.56

Weapons Adjustment

 Yes vs. No 0.588 0.297 1.983 0.047 1.80 1.01 3.25

Substantial Assistance

 Yes vs. No 0.020 0.101 0.196 0.844 1.02 0.84 1.25

Safety Valve

 Yes vs. No 0.032 0.145 0.221 0.825 1.03 0.78 1.37

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 2

Study Cohort: >24-36 months

 95% CI

Response Variable: recidivism (rearrest)

0.14

3,064

 -1812.253 (df = 21)

TABLE D-1. 

46
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.527 0.216 7.081 0.000

Research Group

 Study vs. Comparison -0.054 0.077 -0.699 0.485 0.95 0.81 1.10

Age-at-Release

 Age -0.049 0.004 -10.894 0.000 0.95 0.94 0.96

Gender

 Female vs. Male -0.438 0.120 -3.644 0.000 0.64 0.51 0.82

Race

 Black vs. White 0.157 0.086 1.825 0.068 1.17 0.99 1.38

 Other vs. White 0.212 0.244 0.868 0.385 1.24 0.76 2.00

High School Completion

 Yes vs. No -0.379 0.080 -4.712 0.000 0.68 0.58 0.80

Criminal History Category

 CHC II vs. CHC I 0.792 0.158 5.004 0.000 2.21 1.62 3.02

 CHC III vs. CHC I 0.994 0.150 6.624 0.000 2.70 2.02 3.63

 CHC IV vs. CHC I 1.451 0.187 7.770 0.000 4.27 2.97 6.18

 CHC V vs. CHC I 2.029 0.308 6.587 0.000 7.60 4.27 14.38

 CHC VI vs. CHC I 2.585 0.276 9.377 0.000 13.26 7.91 23.41

Guideline

 §2B1.1 vs. §2D1.1 -0.003 0.256 -0.013 0.990 1.00 0.60 1.65

 §2K2.1 vs. §2D1.1 0.289 0.135 2.142 0.032 1.34 1.02 1.74

 §2F1.1 vs. §2D1.1 -0.423 0.248 -1.705 0.088 0.66 0.40 1.06

 Other vs. §2D1.1 0.042 0.206 0.203 0.839 1.04 0.69 1.56

Violence

 Yes vs. No 0.009 0.219 0.042 0.967 1.01 0.66 1.55

Weapons Adjustment

 Yes vs. No 0.365 0.208 1.756 0.079 1.44 0.96 2.17

Substantial Assistance

 Yes vs. No -0.111 0.097 -1.149 0.251 0.90 0.74 1.08

Safety Valve

 Yes vs. No 0.032 0.133 0.242 0.808 1.03 0.80 1.34

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 2

Study Cohort: >36-48 months

 95% CI

Response Variable: recidivism (rearrest)

 -2108.683 (df = 20)

0.19

3,461

TABLE D-2. 

47
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.808 0.228 7.930 0.000

Research Group

 Study vs. Comparison -0.063 0.087 -0.722 0.471 0.94 0.79 1.11

Age-at-Release

 Age -0.053 0.005 -10.117 0.000 0.95 0.94 0.96

Gender

 Female vs. Male -0.670 0.168 -3.994 0.000 0.51 0.37 0.71

Race

 Black vs. White 0.197 0.094 2.088 0.037 1.22 1.01 1.46

 Other vs. White 0.279 0.417 0.670 0.503 1.32 0.59 3.05

High School Completion

 Yes vs. No -0.210 0.090 -2.331 0.020 0.81 0.68 0.97

Criminal History Category

 CHC II vs. CHC I 0.531 0.144 3.693 0.000 1.70 1.28 2.26

 CHC III vs. CHC I 0.600 0.135 4.437 0.000 1.82 1.40 2.38

 CHC IV vs. CHC I 1.388 0.190 7.292 0.000 4.01 2.77 5.86

 CHC V vs. CHC I 1.545 0.280 5.519 0.000 4.69 2.75 8.29

 CHC VI vs. CHC I 2.045 0.253 8.087 0.000 7.73 4.78 12.93

Guideline

 §2K2.1 vs. §2D1.1 0.076 0.159 0.475 0.635 1.08 0.79 1.48

 §2B3.1 vs. §2D1.1 0.508 0.373 1.364 0.173 1.66 0.80 3.47

 §2F1.1 vs. §2D1.1 -0.466 0.284 -1.638 0.101 0.63 0.36 1.08

 Other vs. §2D1.1 -0.499 0.227 -2.202 0.028 0.61 0.39 0.94

Violence

 Yes vs. No 0.248 0.261 0.948 0.343 1.28 0.77 2.16

Weapons Adjustment

 Yes vs. No 0.066 0.163 0.405 0.685 1.07 0.78 1.47

Substantial Assistance

 Yes vs. No -0.105 0.103 -1.023 0.307 0.90 0.74 1.10

Safety Valve

 Yes vs. No -0.213 0.136 -1.566 0.117 0.81 0.62 1.05

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 2

Study Cohort: >48-60 months

 95% CI

Response Variable: recidivism (rearrest)

 -1707.807 (df = 20)

0.16

2,671

TABLE D-3. 

48
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.740 0.190 9.168 0.000

Research Group

 Study vs. Comparison -0.198 0.065 -3.036 0.002 0.82 0.72 0.93

Age-at-Release

 Age -0.055 0.004 -13.588 0.000 0.95 0.94 0.95

Gender

 Female vs. Male -0.521 0.132 -3.947 0.000 0.59 0.46 0.77

Race

 Black vs. White 0.267 0.067 4.007 0.000 1.31 1.15 1.49

 Other vs. White 0.601 0.325 1.847 0.065 1.82 0.97 3.50

High School Completion

 Yes vs. No -0.345 0.066 -5.247 0.000 0.71 0.62 0.81

Criminal History Category

 CHC II vs. CHC I 0.632 0.114 5.539 0.000 1.88 1.50 2.36

 CHC III vs. CHC I 0.969 0.105 9.239 0.000 2.64 2.15 3.24

 CHC IV vs. CHC I 1.370 0.130 10.580 0.000 3.94 3.06 5.08

 CHC V vs. CHC I 1.628 0.171 9.494 0.000 5.09 3.66 7.17

 CHC VI vs. CHC I 2.012 0.145 13.870 0.000 7.48 5.64 9.97

Guideline

 §2K2.1 vs. §2D1.1 0.487 0.144 3.372 0.001 1.63 1.23 2.17

 §2B3.1 vs. §2D1.1 0.160 0.315 0.508 0.612 1.17 0.63 2.16

 §2F1.1 vs. §2D1.1 -0.166 0.380 -0.437 0.662 0.85 0.39 1.74

 §2S1.1 vs. §2D1.1 -0.713 0.442 -1.614 0.106 0.49 0.19 1.09

 Other vs. §2D1.1 0.177 0.306 0.577 0.564 1.19 0.65 2.16

Violence

 Yes vs. No 0.123 0.268 0.459 0.646 1.13 0.68 1.94

Weapons Adjustment

 Yes vs. No 0.231 0.101 2.294 0.022 1.26 1.03 1.54

Substantial Assistance

 Yes vs. No -0.244 0.074 -3.310 0.001 0.78 0.68 0.90

Safety Valve

 Yes vs. No 0.076 0.108 0.702 0.483 1.08 0.87 1.33

-2 Log Likelihood

McFadden Pseudo R2

N

Response Variable: recidivism (rearrest)

 -3063.791 (df = 21)

0.16

4,974

Research Design 2

Study Cohort: >60-120 months

 95% CI

TABLE D-4. 

49
Term Estimate Standard Error Z Value p-value Odds Ratio Lower Upper

 (Intercept) 1.753 0.288 6.075 0.000

Research Group

 Study vs. Comparison -0.348 0.088 -3.948 0.000 0.71 0.59 0.84

Age-at-Release

 Age -0.052 0.006 -8.950 0.000 0.95 0.94 0.96

Gender

 Female vs. Male -1.125 0.286 -3.933 0.000 0.32 0.18 0.56

Race

 Black vs. White 0.149 0.099 1.515 0.130 1.16 0.96 1.41

 Other vs. White 0.208 0.500 0.417 0.677 1.23 0.45 3.28

High School Completion

 Yes vs. No -0.328 0.090 -3.663 0.000 0.72 0.60 0.86

Criminal History Category

 CHC II vs. CHC I 0.336 0.142 2.374 0.018 1.40 1.06 1.85

 CHC III vs. CHC I 0.789 0.130 6.087 0.000 2.20 1.71 2.84

 CHC IV vs. CHC I 1.065 0.158 6.744 0.000 2.90 2.13 3.96

 CHC V vs. CHC I 1.516 0.216 7.016 0.000 4.55 3.00 7.02

 CHC VI vs. CHC I 1.752 0.145 12.098 0.000 5.77 4.35 7.68

Guideline

 §2K2.1 vs. §2D1.1 0.852 0.225 3.787 0.000 2.34 1.52 3.69

 §2B3.1 vs. §2D1.1 0.503 0.349 1.441 0.149 1.65 0.83 3.27

 Other vs. §2D1.1 -0.140 0.483 -0.290 0.772 0.87 0.32 2.19

Violence

 Yes vs. No 0.125 0.310 0.404 0.686 1.13 0.62 2.10

Weapons Adjustment

 Yes vs. No -0.054 0.106 -0.510 0.610 0.95 0.77 1.17

Substantial Assistance

 Yes vs. No -0.092 0.115 -0.798 0.425 0.91 0.73 1.14

Safety Valve

 Yes vs. No 0.277 0.259 1.067 0.286 1.32 0.79 2.18

-2 Log Likelihood

McFadden Pseudo R2

N

Research Design 2

Study Cohort: >120 months

 95% CI

Response Variable: recidivism (rearrest)

 -1724.626 (df = 19)

0.14

2,630

TABLE D-5. 

50
ENDNOTES
1 See U.S. Sentencing Comm’n, Supplementary Report On The Initial Sentencing Guidelines And Policy Statements 41–44 (1987), http://www.ussc.gov/sites/

default/files/pdf/guidelines-manual/1987/manual-pdf/1987_Supplementary_Report_Initial_Sentencing_Guidelines.pdf; U.S. Sentencing Comm’n, Recidivism

Among Offenders Receiving Retroactive Sentence Reductions: The 2007 Crack Cocaine Amendment (2014), https:www.ussc.gov/sites/default/files/pdf/researchand-publications/research-projects-and-surveys/miscellaneous/20140527_Recidivism_2007_Crack_Cocaine_Amendment.pdf; U.S. Sentencing Comm’n, Report

to Congress: Federal Child Pornography Offenses 293–310 (2012), https://www.ussc.gov/sites/default/files/pdf/news/congressional-testimony-and-reports/

sex-offense-topics/201212-federal-child-pornography-offenses/Full_Report_to_Congress.pdf; U.S. Sentencing Comm’n, A Comparison Of The Federal Sentencing

Guidelines Criminal History Category And The U.S. Parole Commission Salient Factor Score (2005), http://www.ussc.gov/sites/default/files/pdf/research-andpublications/research-publications/2005/20050104_Recidivism_Salient_Factor_Computation.pdf; U.S. Sentencing Comm’n, Recidivism And The “First Offender”

(2004), https://www.ussc.gov/sites/default/files/pdf/research-and-publications/research-publications/2004/200405_Recidivism_First_Offender.pdf; U.S. 

Sentencing Comm’n, Measuring Recidivism: The Criminal History Computation Of The Federal Sentencing Guidelines (2004), https://www.ussc.gov/sites/default/

files/pdf/research-and-publications/research-publications/2004/200405_Recidivism_Criminal_History.pdf.

2 18 U.S.C. § 3553(a)(2)(C).

3 28 U.S.C. § 991(b)(1)(C).

4 U.S. Sentencing Comm’n, Recidivism Among Federal Offenders: A Comprehensive Overview (2016), https://www.ussc.gov/sites/default/files/pdf/researchand-publications/research-publications/2016/recidivism_overview.pdf [hereinafter Recidivism Overview Report].

5 U.S. Sentencing Comm’n, The Past Predicts The Future: Criminal History and Recidivism of Federal Offenders (2017), https://www.ussc.gov/sites/default/

files/pdf/research-and-publications/research-publications/2017/20170309_Recidivism-CH.pdf [hereinafter Criminal History Report].

6 U.S. Sentencing Comm’n, The Effects of Aging on Recidivism Among Federal Offenders (2017), https://www.ussc.gov/sites/default/files/pdf/research-andpublications/research-publications/2017/20171207_Recidivism-Age.pdf [hereinafter Age and Recidivism Report].

7 U.S. Sentencing Comm’n, Recidivism Among Federal Drug Trafficking Offenders (2017), https://www.ussc.gov/sites/default/files/pdf/researchand-publications/research-publications/2017/20170221_Recidivism-Drugs.pdf [hereinafter Drug Trafficking and Recidivism Report]; U.S. Sentencing

Comm’n, Recidivism Among Federal Violent Offenders (2019), https://www.ussc.gov/sites/default/files/pdf/research-and-publications/researchpublications/2019/20190124_Recidivism_Violence.pdf [hereinafter Violence Report]; U.S. Sentencing Comm’n, Recidivism Among Federal Firearms Offenders

(2019), https://www.ussc.gov/sites/default/files/pdf/research-and-publications/research-publications/2019/20190627_Recidivism_Firearms.pdf [hereinafter 

Firearms Report].

8 See Recidivism Overview Report, supra note 4, at 22.

9 See Drug Trafficking and Recidivism Report, supra note 7, at 18.

52
10 While various statistical models may predict either a deterrent or criminogenic relationship between length of incarceration and recidivism, those 

relationships may not be statistically significant. Statistical significance indicates that the relationship observed, deterrent, or criminogenic, is unlikely to be a 

false positive (i.e., indicating there is a relationship when, in fact, there is not). Statistical significance is important in that it provides a degree of certainty that 

an observed relationship is, in fact, not a false positive. Thus, it is possible that no statistically significant relationship between length of incarceration and 

recidivism is identified. 

11 See Daniel S. Nagin et al., Imprisonment and Reoffending, 38 Crime & Just. 115, 121 (2009).

12 See Dorothy R. Jaman et al., Parole Outcome as a Function of Time Served, 12 Brit. J. Of Criminology 5 (1972); Elizabeth Deschenes et al.,

Intensive Community Supervision In Minnesota: A Dual Experiment In Prison Diversion And Enhanced Supervised Release (1995); Thomas A. Loughran et al., Estimating 

a Dose-Response Relationship Between Length of Stay and Future Recidivism in Serious Juvenile Offenders, 47 Criminology 699 (2009); Benjamin Meade et al., 

Estimating a Dose-Response Relationship Between Time Served in Prison and Recidivism, 50 J. Res. Crime & Delinq. 525 (2013). 

13 Nagin et al., supra note 11, at 169, in the majority of regression studies examining length of incarceration and recidivism, time served was included as a 

control variable, rather than explanatory variable, in the study.

14 Nagin and his colleagues note that in in many nonexperimental studies, insufficient control for the relationship between age and reoffending rates could 

substantially bias estimates and therefore are insufficient for use in public policy. Id. at 121, 175. 

15 Meade et al., supra note 12.

16 Id.

17 Nagin et al., supra note 11, at 121 concludes, “existing research [on the impact of imprisonment and subsequent recidivism] is not nearly sufficient for 

making firm evidence-based conclusions for either science or public policy.”

18 See U.S. Dept. of Justice, Nat’l Inst. Of Justice, Recidivism, https://web.archive.org/web/20160120175242/http://www.nij.gov/topics/corrections/

recidivism/pages/welcome.aspx (Jan. 20, 2016); Michael D. Maltz, Recidivism 1, 54 (2001). According to Maltz, “recidivism, in a criminal justice context, can be 

defined as the reversion of an individual to criminal behavior after he or she has been convicted of a prior offense, sentenced, and (presumably) corrected”. 

Recidivism is derived from the Latin recidere, to fall back, representing an individual who, after release from custody for having committed a crime, is not 

rehabilitated and, instead, relapses into former criminal behavior patterns. 

19 Maltz, supra note 18, at 7–20; see also Ryan King & Brian Elderboom, Improving Recidivism as a Performance Measure, Urban Inst. (2014), https://www.bja.

gov/Publications/UI-ImprovingRecidivism.pdf. 

20 See Christopher T. Lowenkamp et al., Investigating The Impact Of Pretrial Detention On Sentencing Outcomes (2013), https://craftmediabucket.

s3.amazonaws.com/uploads/PDFs/LJAF_Report_state-sentencing_FNL.pdf.

53
21 Maltz, supra note 18 (“[R]ecidivism is measured by criminal acts that resulted in rearrest, reconviction or return to prison.”); See also U.S. Dept. of Justice,

Nat’l Inst. Of Justice, Measuring Recidivism, https://web.archive.org/web/20160129195540/http://www.nij.gov/topics/corrections/recidivism/pages/measuring.

aspx (Jan. 29, 2016).

22 See Maltz, supra note 18, at 60. 

23 Arrests for alleged violations of probation, supervised release, or state parole (as well as actual revocations of any of these types of supervision) were 

counted as rearrests. 

24 See, e.g., 18 U.S.C. § 924(c)(1)(A)(i) (providing a five year mandatory minimum for offenders convicted of using or carrying a firearm during and in relation 

to, or possessing a firearm in furtherance of, a crime of violence or drug trafficking crime); 18 U.S.C. § 2252(b)(1) (providing a five year mandatory minimum 

for offenders convicted of receipt, distribution, and possession with the intent to distribute or sell child pornography); U.S. Sentencing Comm’n, An Overview of

Mandatory Minimum Penalties in the Federal Criminal Justice System (2017), https://www.ussc.gov/sites/default/files/pdf/research-and-publications/researchpublications/2017/20170711_Mand-Min.pdf.

25 This two-stage process of creating comparison groups and then utilizing regression modeling results in a doubly robust estimation. Doubly robust 

estimation is particularly powerful in that only one of the two models needs to be correctly specified to obtain unbiased estimates. See Michele Jonsson Funk et 

al., Doubly Robust Estimation of Causal Effects, 7 Am. J. Epidemiology 761–767 (2011). 

26 See Michele Jonsson Funk et al., Doubly Robust Estimation of Causal Effects, 7 Am. J. Epidemiology 761 (2011). 

27 The level of precision in matches can be specified by the researcher through a distance caliper. The distance caliper acts as a threshold defining the 

degree of matching precision.

28 Weights were created using a logistic link function with linear propensity score.

29 See Meade et al., supra note 12. In some studies, the researchers first matched all offenders on certain characteristics and then second identified various 

study groups based on length of incarceration. While this design creates study groups that balance on matched characteristics, it does not preserve the natural 

composition of offenders serving various lengths of incarceration. The Commission chose to first identify study groups and second create matched comparison 

groups to preserve the natural composition of offenders sentenced to various lengths of incarceration. 

30 Nagin et al., supra note 11, at 142, identified five principal attributes that studies examining length of incarceration and recidivism must address: age, 

sex, race, instant offense type, and prior criminal history. 

31 See Age and Recidivism Report, supra note 6, at 3; Recidivism Overview Report, supra note 4, at A-1. 

32 See Recidivism Overview Report, supra note 4, at A-1. 

54
33 See Criminal History Report, supra note 5; Recidivism Overview Report, supra note 4, at A-1. 

34 See Recidivism Overview Report, supra note 4, at A-1. 

35 See Recidivism Overview Report, supra note 4, at A-1. 

36 See Violence Report, supra note 7, at 3.

37 See Firearms Report, supra note 7, at 4; Recidivism Overview Report, supra note 4, at A-1.

38 Research design one used non-bipartite distance matching with Mahalanobis Distances as the distance metric. By utilizing an extremely small 

distance caliper, 0.1, age-at-release was the only attribute that could vary, and it was restricted to vary by only one year. Offender age is highly correlated with 

recidivism and, therefore, it is important that offenders being compared do not have large differences in age-at-release. By only allowing age-at-release to vary 

by one year, this study controls for any potential effects age might have on recidivism rates.

39 The threshold for weighting balance was 0.1 standardized mean differences. This means the study and comparison groups could not have a 

standardized mean difference greater than 0.1 after weighting. While there is no universally agreed upon convention regarding what threshold indicates 

substantial imbalance between groups, a standardized mean difference greater than 0.1 has been suggested to indicate difference between groups. See Peter 

C. Austin, An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies, 46 Multivariate Behav. Res. 399 (2011). 

40 See Federal Judicial Center, Reference Manual on Scientific Evidence 303 (2011) (Reference Guide on Multiple Regression) for an overview of regression 

modeling.

41 Appendix A provides odds ratios for each research model. 

42 For the full regression models, including estimates for all study cohorts, see Appendix B. 

43 The average time to rearrest was not statistically significantly different. Welch’s two sample t-test was used to test for statistical significance; 

t = -0.15, df = 145, p = 0.88.

44 As noted in Research Design 1B, the 36 month maximum difference restriction was excluded. This exclusion did not affect the first study group, 

offenders sentenced to more than 24 months up to 36 months, because this study group was already naturally bound to offenders with a maximum sentence 

difference of 36 months (i.e., for study group one, the maximum possible sentence is 36 months and the lowest possible sentence is one day).

45 For the full regression models, including estimates for all study cohorts, see Appendix C.

55
46 The average time to rearrest was not statistically significantly different. Welch’s two sample t-test was used to test for statistical significance; 

t = -0.21, df = 1180, p = 0.83.

47 The average time to rearrest was not statistically significantly different. A Welch’s two sample t-test was used to test for statistical significance; 

t = -1.71, df = 1930, p = 0.09.

48 For each of the study cohorts, balance was achieved between the study and comparison groups, with a maximum standardized mean difference of 0.1.

49 For the full regression models, including estimates for all study cohorts, see Appendix D.

50 The average time to rearrest was not statistically significantly different. Welch’s two sample t-test was used to test for statistical significance; 

t = -0.13, df = 1398, p = 0.89.

51 The average time to rearrest was statistically significantly different. Welch’s two sample t-test was used to test for statistical significance; 

t = -2.11, df = 2485, p = 0.04.

52 See Appendix A, Table A-2, for the odds ratios for each study level across the three models. 

53 Research Design 1B estimated 30% less likely to recidivate; Research Design 2 estimated 29% less likely to recidivate.

54 Research Design 1B estimated 16% less likely to recidivate; Research Design 2 estimated 18% less likely to recidivate.

56