RESEARCH SERIES ON THE RECIDIVISM OF

FEDERAL GUIDELINE OFFENDERS 

RELEASE 3

A COMPARISON OF THE

FEDERAL SENTENCING GUIDELINES

CRIMINAL HISTORY CATEGORY

AND THE U.S. PAROLE COMMISSION

SALIENT FACTOR SCORE

 January 4, 2005
Submitted to the United States Sentencing Commission

RICARDO H. HINOJOSA

Chair

RUBEN CASTILLO

Vice Chair

 

WILLIAM K. SESSIONS, III

Vice Chair

 

JOHN R. STEER

Vice Chair

 

MICHAEL E. HOROWITZ

Commissioner

 

BERYL A. HOWELL

Commissioner

MICHAEL E. O’NEILL

Commissioner

 

EDWARD F. REILLY, JR.

(Ex officio)

 

DEBORAH J. RHODES

(Ex officio)

Prepared by

LINDA DRAZGA MAXFIELD

MILES HARER*

TIMOTHY DRISKO

CHRISTINE KITCHENS

SARA MEACHAM

MATTHEW IACONETTI

*while serving at the U.S. Sentencing Commission
Examples of government use of criminality prediction instruments include the Salient Factor Score of the U.S. 1

Parole Commission, the Risk Prediction Index (RPI) of the Administrative Office of the U.S. Courts, or the Offender

Group Reconviction Scale (OGRS) in the United Kingdom described in Copas and Marshall (1998).

Hoffman and Beck, 1974. 2

Hoffman and Beck (1976) subsequently re-tested the SFS, finding that the SFS retained its predictive accuracy 3

in identifying those at high risk of parole failure. The early studies by Hoffman and Beck (1974, 1976) used a two year

follow-up recidivism period. With the passage of time, the later studies tested the SFS using longer follow-up periods.

Using two, three, and five year follow-up periods, the SFS not only maintained predictive accuracy but actually became

slightly more accurate as the follow-up period length was extended (Hoffman and Beck, 1985).

The Commission explicitly allows that an offender’s prior criminal history is predictive of recidivism. See 4

U.S. Sentencing Commission, 1987: 41-44.

U.S. Sentencing Commission, 2004: Chapter Four, Part A - Criminal History. 5

Page 1 of 34

C

riminal justice practitioners over the years have used various forms of prediction

instruments to help guide prisoner risk decisions, such as whether to sentence a 1

person to prison or probation, or when to parole an offender. Such prediction

instruments do not foresee the future nor predict whether an offender will go back to a life of crime.

Rather, they use a set of observable measures — such as age, frequency of prior offending, or

recency of prior offending — to identify offenders who have the highest probability of recidivating.

 

The U.S. Parole Commission’s re-offending prediction instrument has been in use for the

longest period of time. In its1970s effort to structure discretion and equalize decision making with

a quantified instrument, the U.S. Parole Commission developed a recidivism prediction measure

called the Salient Factor Score (SFS). Early research documents that the SFS (operating as a pilot 2

project in 1972) identified groups of offenders more, or less, likely to recidivate. In addition to its

construction sample of federal prisoners released in 1970, the thorough evaluation employed two

validation samples of federal prisoners also released in 1970. With these successful validation

results, the then U.S. Board of Parole adopted the SFS as its main decision-making instrument in

October 1973. Since that time, the Parole Commission has used empirical recidivism data to guide,

construct, and revise the SFS. Continuing research and validation demonstrates that the SFS is an 3

accurate and reliable recidivism risk assessment tool. 

 

In its work to implement the Sentencing Reform Act of 1984, the U.S. Sentencing

Commission (USSC) developed an empirical recidivism risk prediction instrument as a component

of the federal sentencing guidelines. This instrument, the Criminal History Category (CHC), 4

appears as Chapter Four in the federal Guidelines Manual. Unique in this USSC effort, however, 5

is the identification of two goals for its criminal history instrument: first, to predict recidivism, and
Ibid.: 41. 6

U.S. Sentencing Commission, 2004: Chapter Four, Part A - Criminal History, introductory comment.

7

Apprendi v New Jersey, 120 S. Ct. 2348 (June 26, 2000). 8

Blakely v Washington, 124 S. Ct. 2531 (June 24, 2004). 9

Blumstein et al.: 1986: 188. 10

Page 2 of 34

second, to reflect offender culpability. With this dual purpose, the CHC relies heavily, but not 6

exclusively, upon the empirical foundation of the SFS. For example, both the SFS and the CHC

focus on the number and timing of prior criminal history events. However, the computation strategy

of the individual scores, the time periods employed, and the assignment of points differ.

Nonetheless, the SFS and the CHC remain related in structure. The purpose of this paper is to

describe the differences between the SFS and the CHC, to compare their predictive abilities (both

overall, and component by component), and to suggest alternative formulations of the CHC that

promote maximum predictive accuracy.7

The first section below describes the empirical foundations of the guidelines’ CHC. This

is followed by a component comparison of elements in the CHC and the SFS. The third section

describes the data and methodology used in the analysis. Section D and section E look explicitly at

predictive power, with the first of these sections assessing the predictive power of the individual

components and the second section comparing the total predictive power of each instrument. 

The focus of the paper turns toward the goals of revision and improvement with the final

sections. Section F directly compares the component elements of the two models to determine which

formulation – that of the CHC or that of the SFS – is more predictive. Section G introduces age and

first offender enhancements to the CHC and measures the increases in predictive power. The

conclusion section summarizes the findings and highlights the importance of efficiency and

simplicity in a post-Apprendi and post-Blakely guideline environment. 8 9

This report is part of the USSC Research Series on the Recidivism of Federal Guideline

Offenders.

A. Origins of the Criminal History Category

I

n creating the CHC, USSC reviewed the four prediction measures made prominent in a

mid-1980s criminal careers study conducted by the National Academy of Sciences.10

These four risk assessment scales were the Iowa Assessment Scale, the Rand Inmate

Scale, the U.S. Parole Commission’s Salient Factor Score, and the Proposed INSLAW Scale for

Selecting Career Criminals for Special Prosecution. Although USSC recognized the importance of

accurately measuring prior criminal behavior and future recidivism risk to promote the goals of
U.S. Sentencing Commission, 1987: 41. 11

U.S. Sentencing Commission, 1987: 43; Hoffman and Beck, 1997: 1. 

12

“The [SFS] score and its four risk categories are at the high end of the accuracy range reported in other parole 13

recidivism studies ... In addition, these accuracy measures have been very stable over several validation samples”

(Blumstein et al., 1986: 182); “In many ways, the Salient Factor Score is preferable to the other predictive instruments,

due to its extensive validation and operational use in the criminal justice system” (Janus, 1985:121).

 In 1998, “[t]he Parole Commission revised the Salient Factor Score by increasing the weight given to prior 14

commitments and age at offense, and deleting the drug-abuse item. The revised Salient Factor Score was designated

as SFS 98” (U.S. Parole Commission, 2003a: 33).

28 U.S.C.§ 991(b)(1)(A) mandates USSC to assure that the 18 U.S.C.§3553(a)(2) purposes of sentencing 15

– including protection of the public from further crimes of the offender – are met. The other three purposes of

sentencing are listed in 18 U.S.C.§3553(a)(2) as: providing just punishment, affording adequate deterrence, and

providing adequate educational, vocational, medical, or other corrective treatment. 

Page 3 of 34

crime control, it was constrained by the demanding time schedule of the newly-implemented 11

Sentencing Reform Act. There were inadequate time and resources to evaluate empirically a new

recidivism prediction measure, particularly in light of the Commission’s desire to include the more

subjective culpability perspective along with the recidivism prediction perspective. 

Consequently, the guideline’s criminal history measure did not emanate from its own direct

empirical evidence. To create the CHC, USSC relied on the validity of existent (non-Commission)

data and the validity of existing prediction tools. In deriving the components of the guidelines’

Chapter Four model, USSC elected to focus upon two of the four established recidivism prediction

tools described in the National Academy of Science study. 

First, the Commission adopted a modified version of several elements in the existing SFS.12

The creators of the guidelines criminal history measure, recognizing the Parole Commission’s

prominence in related statistical methodologies, relied heavily upon the recidivism research and the

well-documented validity tests of the SFS. In fact, the SFS reliability has been continuously tested, 13

reformatted, and evaluated throughout its history, with elements dropped when they did not

independently contribute predictive power within its set of factors.14

However, the CHC and SFS do have one essential conceptual difference. As an instrument

of the U.S. Parole Commission, the purpose of the SFS is to assess the likelihood of recidivism. Its

elements are included if they add to predictive accuracy. On the other hand, the goal of the CHC

encompasses more than recidivism prediction. Its second core philosophy involves additional 15

purposes of sentencing: just punishment and deterrence. The introductory section of the Guidelines

Manual’s Chapter Four on criminal history states that to protect society from known criminals, the

CHC should not only take into account recidivism (i.e., the likelihood of re-offending), but also

culpability (i.e., harsher punishments for offenders with aggravated prior criminal backgrounds):

A defendant with a record of prior criminal behavior is more culpable than a first
U.S. Sentencing Commission, 2004: Chapter Four, Part A - Criminal History, introductory comment.

16

Forst et al, 1982: 19-21. 17

U.S. Sentencing Commission, 1987: 43. 18

U.S. Sentencing Commission, 2004: Chapter Four, Part A - Criminal History, introductory comment.

19

Page 4 of 34

offender and thus deserving of a greater punishment. General deterrence of criminal

conduct dictates that a clear message be sent to society that repeated criminal

behavior will aggravate the need for punishment with each recurrence.

16

Because of the close historical relationship between the SFS and the CHC, there have been

numerous speculations concerning their comparative strengths in predicting recidivism. However,

the SFS, with its single-minded recidivism prediction purpose, generally is assumed to be more

predictive than the CHC with its dual culpability and recidivism goals (Schmidt & Garner, 1991;

Hoffman, 1994; Harer, 1994; Hoffman and Beck, 1997). 

Second, the Commission identified one of the nine elements of Proposed INSLAW scale that

targeted violent behavior in the instant offense. The scale’s violence element was adapted to 17

specific uncounted violent prior offenses and included in the CHC model.

From this approach, USSC reasoned that the high SFS predictive power demonstrated by the

SFS, as well as from the Proposed INSLAW scale, would transfer, at least in part, to the nascent

guidelines criminal history measure:

The indirect evidence available to the Commission strongly suggests that the criminal

history score will demonstrate predictive power comparable to that of prediction

instruments currently in use. ... The high correlation between the two instruments

suggests that the criminal history score will have significant predictive power.

18

Thus, with this amalgam of elementsfrom pre-existing prediction instruments, the CHC is currently

the recidivism prediction tool used at federal guideline criminal sentencings to measure offender

culpability, deter criminal conduct, and protect the public from further crimes of the defendant.19

B. Component Comparison of the CHC and the SFS

Not surprisingly, given their historical commonality, the CHC and the SFS have underlying

concepts that look and sound similar. To illustrate this similarity, the practitioner worksheets for

these measures appear in the appendices: the CHC worksheet appears in Appendix A and the SFS

worksheet appears in Appendix B. 

 There are several procedural differences between the CHC and the SFS. One is the time

frame when it is administered. The USSC CHC is computed at the time of sentencing for the instant

offense. The Parole Commission’s SFS is computed during the offender’s incarceration to assist in
U.S. Sentencing Commission, 2004: Chapter Four, §4A1.1(a) through §4A1.1(f). 20

Approximately every five years, the U.S. Parole Commission re-validates and updates the SFS. A current 21

copy of the SFS can be found in Appendix B at the end of this report. Also see U.S. Parole Commission, 2003b: 58.

USSC §4A1.1(a),(b),(c) instruct that three points are added for each prior sentence of imprisonment exceeding 22

one year and one month, two points for each prior sentence of imprisonment between 60 days and 13 months, and one

point for each other prior sentence (up to a total of 4 points). For example, if an hypothetical offender has four prior

convictions, one with a probation-only sentence, two each with a sentence of 6 months of prison, and one with a

Page 5 of 34

parole release determinations.

Not only is there a scaling magnitude difference between the two measures, additionally they

are scaled in opposite directions. 

• Lower SFS values predict higher risks of recidivism within its finite range

of values from zero to ten.

– Scoring at the minimum value of zero on the SFS indicates a very

high recidivism risk.

• Lower CHC values predict lower risks of recidivism. CHC has a lower limit

of zero, but has no upper limit. Some offenders accrue as many as 30, or 40,

or more, points under the CHC.

– Scoring at the minimum value of zero on the CHC indicates a very

low recidivism risk. 

To compute the scores for either the CHC or the SFS, practitioners follow the respective set

of application criteria that attach numbers to the specific instrument components. Exhibit 1

compares the computational structure between the USSC CHC and the Parole Commission SFS. 

The CHC is composed of six guideline computations that quantify criminal history. The current 20

SFS (SFS98) is also composed of six guideline computations (Item A through Item F) that quantify

variables highly associated in predicting recidivism.21

 

To determine and compare the predictive abilities of both the CHC and SFS a brief

understanding of each of their respective components is necessary. 

1. Frequency and Seriousness of Criminal History

 For the first two components listed in Exhibit 1, frequency and seriousness of prior

offending, the SFS and the CHC use different counting techniques. TheCHC adds up to three points

each for separate prior conviction and makes distinctions between prior sentences in one of three

categories: those less than 60 days, between 60 days and 13 months, or more than 13 months. In 22
sentence of 18 months of prison, the offender would receive eight criminal history points (i.e., the first receives one

point, the next two receive 2 points each, and the fourth receives three points.) For the CHC, the higher the score, the

higher the hypothesized risk of recidivism.

The SFS Item A can add between 0 and 3 points, ranging from 0 points when the offender has three or more 23

prior convictions, to three points if the offender has no prior convictions. The SFS Item B can add between 0 and 2

points depending on the number of convictions exceeding 30 days. For example, if an hypothetical offender has four

prior convictions, one with a probation-only sentence, two each with a sentence of 6 months of prison, and one with a

sentence of 18 months of prison, the offender would receive 0 points for these SFS items. This is due to receipt of zero

points from Item A (i.e., a total of four prior convictions) and zero points from Item B (i.e., a total of three prior

convictions with confinements longer than 30 days). For the SFS, the higher the score, the lower the hypothesized risk

of recidivism. 

U.S. Sentencing Commission, 2004: Chapter Four, §4A1.2(e). 24

U.S. Sentencing Commission, 2004: Chapter Four, §4A1.2(d)(2).

25

U.S. Parole Commission, 2003b: 60 (Item A.8). 26

U.S. Sentencing Commission, 2004: Chapter Four, §4A1.2(h),(i); U.S. Parole Commission, 2003b: 60 (Items 27

A.9, A10).

U.S. Sentencing Commission, 2004: Chapter Four, §4A1.2(c); U.S. Parole Commission, 2003b: 59 (Item 28

A.2(b)).

Page 6 of 34

contrast, the SFS only adds points up to a maximum offour prior convictions and distinguishes only

two prior conviction commitment lengths: those 30 days or less, and those more than 30 days.23

The computational rules for both instruments incorporate exclusions for certain prior

offenses. One of these exclusions is a “decay” factor, under which prior offenses occurring before

a designated time period are not counted in the computation. For the CHC, in general there are two

decay periods for adult offenses: 15 years for imposed sentences of 13 months or more, and 10 years

for other sentences. For juvenile sentences, the decay periods is five years. The SFS does not 24 25

count prior convictions that occurred more than ten years prior to the instant offense if that ten-year

period is commitment-free.26

Another exclusion rule involves the jurisdiction of prior convictions. The CHC excludes

foreign convictions and tribal convictions while the SFS includes such offenses.27

Another exclusion rule involves minor offenses. Both the CHC and the SFS exclude minor

traffic offenses (such as speeding), juvenile status offenses (such as truancy), and other minor

offenses such as hitchhiking, public intoxication, or vagrancy. For other misdemeanor or petty

offenses, the conviction is only counted if the sentence involved is at least 30 days of imprisonment

or a one-year or longer sentence of probation. The specific provisions and definitions are similar

between the instruments.

28

 While there are differences in the computation and application of the frequency and

seriousness variables, these respective elements target the same underlying concepts.
Page 7 of 34

2. Instant Offense While Under Criminal Justice Supervision

The “under supervision” element of the CHC and the SFS identify whether the offender was

under any form of criminal justice supervision at the time of the instant federal offense. The

wordings of the provisions are similar. This element captures the higher recidivism likelihood when

the instant offense is committed while the offender is still meeting a sentence obligation for an

earlier offense.

The SFS Item E and the CHC §4A1.1(d) are similar. Guideline §4A1.1(d) instructs the user

to “[a]dd 2 points if the defendant committed the instant offense while under any criminal justice

sentence, including probation, parole, supervised release, imprisonment, work release, or escape

status.” 

 Item E of the SFS allocates one point to those who at the time of their instant offense were

“[n]either on probation, parole, confinement, or escape status . . . nor [were] committed as a

probation, parole, confinement, or escape status violator this time.” 

3. Recency of Prior Offending

Both the CHC and SFS address the time since release from a prior commitment, but

implement it from differing perspectives. For the CHC, the measure identifies an offender who

committed the instant offense less than two years after release from an imposed imprisonment

sentence of 60 days or longer. The SFS focuses on a “crime free period” and identifies as more

likely to recidivate an offender who both (1) has any prior offense with a commitment of 30 days

or longer, and (2) committed the instant offense less than three years after release from the most

recent 30-days-or-longer commitment. 

Note that this recency factor applies independently from the application for criminal justice

supervision (described immediately above). At the time of the instant offense, an offender who

meets the conditions for one of these two factors sometimes might also meet the conditions for both.

4. Prior Violent Offending

USSC guideline §4A1.1(f) may add points to a CHC score if a given crime of violence did

not receive points in the guideline calculation onlybecause of its close relationship to another violent

conviction that did receive points. The CHC “prior violent offending” element was derived from

the Proposed INSLAW Scale. The SFS does not contain a violence component. 

5. Age
Schmidt and Witte, 1988: 87. Schmidt and Witte additionally cite studies that date from the early 1970s and 29

document the strong predictive relationship between recidivism and offender age. 

“While empirical research has shown that other factors are correlated highly with the likelihood of recidivism, 30

e.g., age and drug abuse, for policy reasons they were not included here at this time,” USSG, Ch. 4, Pt. A, intro.

comment. (emphasis added)..

Hoffman and Beck, 1997: 193. 31

Page 8 of 34

Item C and Item F in the SFS target the predictive recidivism power of the offender’s age.

Item C captures the impact of the offender’s age at the instant offense in combination with the

number of prior commitments: the older the defendant and the fewer the number of prior

commitments, then the higher the defendant’s SFS score (thus indicating a lower likelihood of

recidivating.) SFS Item F assigns an additional point to offenders older than 41 years of age,

accounting for a long-established high empirical correlation between age and recidivism. 

29

USSC does not include age as a recidivism factor in the CHC, with the original Commission

members citing its exclusion on policy grounds. However, the introductory commentary to the

guidelines criminal history chapter leaves open the possible reconsideration of its inclusion. Note, 30

however, that the “decay” factor of the CHC is often interpreted as a proxy for age at current

offense.31

From the above component by component comparisons between the SFS and the CHC, a

shared common core can be identified. The SFS items (excluding its age components) target the

same underlying predictors as does the CHC (excluding its violence component). There are

operational variations, particularly involving differences in the rules for calculating each component

and differences in scaling (the SFS scores from high to low recidivism risk in a bounded range from

zero to ten, respectively, while the CHC scores from low to high recidivism risk in an unbounded

range from zero and higher). 

Outside this common core, however, there are two differences. The SFS contains two items

which incorporate offender age as a recidivism predictor. The USSC CHC has no age component,

but includes a violence component motivated by its culpability goal.

The sections that follow introduce empirical data to compare the overall predictive power

of the SFS and the CHC. The analysis strives to attribute differences in predictive power to

particular SFS and CHC components. The next step compares the SFS to modified CHC

instruments that incorporate offender age and offender first offender status as predictive components.

C. The Recidivism Study
Due to alien deportation following conviction for criminal behavior, it is difficult to measure recidivism of 32

noncitizens convicted of federal crimes. 

Details on the structure, methodology, and statistical techniques of the analysis are documented in the project’s 33

companion report, “Background and Methodology of the U.S. Sentencing Commission’s 2003 Recidivism Study.”

While the two-year recidivism follow-up period limit was set at June 1, 2001, the actual collection of FBI 34

“RAP” sheet data did not occur until October 2001. The four month delay between June and October assured that “RAP”

sheet data would reflect all events prior to June 1. The intervening months accounted for administrative processing time

to update fingerprint card information on the FBI datafile, thus minimizing any potential bias due to the states’

differential schedules for reporting data to the FBI.

Page 9 of 34

T

he sections below describe the USSC recidivism study, including data collection

strategy, research definitions, and analysis methods.

1. Recidivism Data 

The recidivism study data are a stratified, random sample of 6,062 U.S. citizens who were

32

sentenced under the federal sentencing guidelines in fiscal year 1992. Data on criminal behavior 33

prior to the federal instant offense, as well as demographic and offender characteristics, were

collected from the federal pre-sentence reports (PSRs) and other court documents submitted to the

Sentencing Commission by U.S. district courts. Prison release date information was extracted from

the SENTRY datafile of the Federal Bureau of Prisons in the U.S. Department of Justice.

Recidivism information was obtained from the “RAP” sheet data of the Federal Bureau of

Investigation’s Criminal Justice Information Services Division office. 

The sample of offenders used in the recidivism analysis represents the 28,519 U.S. citizen

federal offenders in the Commission’s 1992 fiscal year sentencing datafile where the following “twoyear window inclusion” conditions were met:

• a pre-sentence report (PSR) from a fiscal year 1992 sentencing was submitted

to the Sentencing Commission,

• a “RAP” sheet was located on the FBI datafile;

• for offenders receiving prison sentences, the release from prison occurred at

least two years prior to June 1, 2001. 

Given the project schedule for “RAP” sheet collection in October 2001, an offender must

have been released from prison by June 1, 1999. Because the sampled offenders were sentenced in

fiscal year 1992 (i.e., between October 1, 1991 and September 30, 1992), prison sentences as long

as seven years are available for study. The selection of these specific dates reflects the 34

Commission’s interest in the recidivism impact of mandatory minimum sentences. The effect of five

year mandatory minimum sentences can be analyzed using the project’s sampling strategy. 

With the study’s prison release deadline established as June 1, 2001, there were offenders
This figure represents the sum of the sample offenders who by June 1, 2001, were still in prison (8.9%), who 35

had died (0.4%) or had not been released for at least two years (5.4%). Even with these limitations, however, 85.3

percent of the total recidivism sample is included in the analysis reported here. Not included in the analysis are those

offenders with sentences roughly longer than seven years who are disproportionately found in the higher CHCs,

particularly CHC VI.

Disposition information was obtained from the FBI’s criminal history record (“RAP” sheet). 36

Page 10 of 34

in the sample who either were still in prison on this date, or had at this time been released from

prison for less than two years. For the entire recidivism sample, 14.7 percent of sample offenders

are not in the analysis because they had not finished serving their prison time or did not have a twoyear “at risk” window of opportunity.35

2. Defining Recidivism

Recidivism results are presented using one substantive definition. The recidivism definition

used in this analysis includes the first of any one of the three following events during the offenders

first two years back in the community: 

• a re-conviction for a new offense; 

• a re-arrest with no conviction disposition information available on the postrelease criminal history record; or 36

• a supervision revocation (probation or post prison supervision). 

3. Methodology

The use of the recidivism definition addresses the state of post-release criminal behavior

records. Recidivism researchers recognize that the FBI offender “RAP” sheets are the most accurate

and readily available data source for repeat criminal behavior. However, “RAP” sheets can contain

errors or partial information. For example, depending on the reporting policies and practices of local

jurisdictions, arrest dispositions may not always be transferred to the FBI for inclusion on “RAP”

sheets, or offender fingerprints may not be collected for certain types of crimes or offenders.

Consequently, “RAP” sheets will underreport actual criminal behavior, and will under report

convictions resulting from arrests.

Data cited throughout this paper are weighted to represent the entire comparable population

of fiscal year 1992 U.S. citizen offenders sentenced under the federal guidelines. 

Two techniques are used to analyze recidivism rates of federal offenders. The two techniques

are hazard modeling and the receiver operating characteristic. Both are accepted methods for
Quinsey, Harris, Rice, and Cormier, 1998; Swets, Dawes, and Monahan, 2000. 37

Allison, 1995; Hosmer and Lemeshow, 1999; Klein and Moeschberger, 1997. 38

The AUC methodology is summarized in Appendix A, with a detailed explanation in project’s companion 39

report, “Background and Methodology of the U.S. Sentencing Commission’s 2003 Recidivism Study.”

As seen in the Exhibit 2's column labeled “Pr > ChiSq,” the level of statistical significance for CHC elements 40

labeled in the Exhibit as i, ii, iii, and iv is 0.0001, signifying high predictive strength. Element v (violent priors not

otherwise receiving points) is not a statistically significant predictor.

Page 11 of 34

evaluating recidivism. By using both methods, the Commission is able to show the degree to which

the CHC and SFS components predict recidivism and compare in their predictive capabilities.37

Survival analysis, also known as hazard modeling, is a method that can be used to evaluate

the predictive ability of risk assessment tools such as the CHC and SFS. Survival analysis measures

the ability of criminal history to predict how rapidly offenders recidivate during the follow-up

period. The concept of crimes committed per unit of time has its roots in the incapacitation 38

literature, where great effort was expended to identify offenders who frequently committed crimes.

These repeat offenders were individuals committing multiple crimesin a given period,such as daily,

monthly, or yearly. By identifying frequent offenders, they could be targeted for longer prison terms

than offenders who commit crimes less frequently. Incapacitation literature argues that the selective

targeting of frequent offenders would result in a more efficient use of prison resources as a means

of crime reduction. Appendix C provides further explanation of hazard modeling.

Measuring the area under the curve (AUC) is an established technique associated with 39

receiver operating characteristic (ROC) curve analysis. The AUC statistic provides a probability that

an offender’s criminal history is able to predict recidivism. The AUC statistic ranges from a value

of 0.5 (indicating no ability to predict recidivism) to a value of 1.0 (indicating 100 percent accuracy

in predicting recidivism). The greater the AUC, the better the predictive power of the measure being

tested. Appendix D provides further explanation of the AUC method.

The sections below use these methodological techniques to compare the predictive abilities

of the CHC and the SFS respective components. 

D. Predictive Power of the Models’ Elements

Exhibits 2 and 3 display proportional hazard model results for each CHC and SFS element,

predicting days until the primary recidivism measure during the offenders’ first two years at risk in

the community. 

Exhibit 2 presents on the proportional hazard results for CHC elements in predicting days

until the primary recidivism measure. Each of the first five elements (§§4A1.1(a)-(e)) makes an

independent and statistically significant contribution to predictive power. The exception is the 40

sixth element §4A1.1(f) measuring the predictive power of a specific violent offense which did not

otherwise receive criminal history points. 
As seen in the Exhibit 3's column labeled “Pr > ChiSq,” the level of statistical significance for all but one SFS 41

element is 0.0002 or lower, signifying high predictive strength. 

In all the analyses, the SFS scale is reordered such that a high SFS score is positively associated with a high 42

risk of recidivism. 

Significantly different from 0.5 at p<0.05. 43

Page 12 of 34

Exhibit 3 displays the comparable proportional hazard results for the elements of the SFS.

Of the six items, all but one show statistical significance for an independent contribution to 41

predictive power. Item B, measuring the incidence of prior commitment longer than 30 days, not

only lacks statistical significance, and further has an effect opposite to expectation. Its positive sign

suggests that having commitments longer than 30 days decreases the offender’s probability of

recidivism. It is possible that this logically inconsistent result is an artifact of Item B’s high

correlation with Item C, which also measures prior commitments.

E. Comparison of Criminal History Computation and Salient Factor Score

T

he AUC method is used to compare the predictive powers of the CHC and SFS.

Exhibit 4 presents the ROC curves for the SFS and the CHC prediction of the primary

recidivism measure. Also shown are results from tests for a statistically significant 42

difference between the two areas. As displayed in Exhibit 4, the area for the SFS (0.7313), is larger

than that for the CHC (0.6992), a difference that is highly significant. 

43

Overall, the SFS is a better predictor of recidivism than is the CHC. 

The finding is consistent with the focus on prediction that underlies the SFS, and its

successful objective to maximize predictive accuracy. The next stage in the analysis seeks to

determine which separate elements of the SFS account for its higher predictive power over the CHC.

This investigation examines how the predictive power of the SFS elements, both individually and

in combination, compares to the predictive power of the associated CHC elements.

F. Comparison of Element-to-Element Formulations

B

oth the CHC and SFS models contain measures that address frequency, seriousness,

criminal justice sentence status, and recency. The comparative analyses below

examine how the different operationalizations of these components affect their

relative prediction powers. The results of the AUC method appear in the rows of Exhibit 5. To

provide a ready reference, the first row of Exhibit 5 displays the predictive power of the full CHC

versus the full SFS model already documented and described above in Exhibit 4.
The AUC area difference in CHC versus SFS comparison is 0.0124 for the model combining solely the four 44

elements of frequency, seriousness, recency, and under a criminal justice sentence.

Page 13 of 34

1. Frequency and Seriousness Comparison. 

The first reformulation involves a minimalist recidivism prediction model. Looking only at

information on the frequency and seriousness of prior offending, the following comparison is made:

• the CHC elements for frequency and serious of prior offending

(§§4A1.1(a)-(c) in Exhibit 1), and

• the SFS elements for frequency and serious of prior offending (Item A and

B in Exhibit 1). 

The second row of Exhibit 5 displays the results of this comparison. The AUC area

difference shrinks to a verysmall value (0.0065) which, although statistically significant (at the 0.05

level), may have only small policy significance. This finding suggests that while the SFS measures

for frequency and seriousness of prior offending provide statistically stronger predictions of

recidivism, the magnitude of the predictive accuracy difference may not be meaningful for policy

decision-making and its need to consider the practicality and efficiency of data collection. 

2. Frequency, Seriousness, Under Sentence, and Recency Comparison. 

The next comparison focuses on all four of the common elements of the CHC and SFS.

These four common elements are: (i) the frequency of prior offending (as examined above); (ii) the

seriousness of prior offending (as examined above); (iii) the status of the offender being under a

criminal justice sentence at the time of the instant offense (CHC element §4A1.1(d) and SFS Item

E in Exhibit 1); and (iv) the recency of prior offending (CHC element §4A1.1(e) and SFS Item D

in Exhibit 1). 

The predictive power data for these four comparable elements appears in the third row of

Exhibit 5. The AUC difference between the four-component CHC and SFS shrinks by about twothirds, from 0.0321 to 0.0124. While this difference remains statistically significant (at the <0.01

level) favoring the SFS, the smaller difference further questions the extent of its policy significance.

The results of both comparisons above highlight the predictive superiority of the SFS

formulations of the four common recidivism prediction elements. However, the relatively small

magnitude ofthis SFS advantage is noteworthy in the context ofthe full model comparison. The full

model comparison, showing the total benefit of the SFS, appears in row 1 of Exhibit 5. Recall that

in this head-to-head, full CHC versus full SFS all-element comparison, the difference in the AUC

prediction areas is 0.0321. This difference — 0.0321 — in row 1 of Exhibit 5 is more than twice

as large as the area difference for the four-element comparison — 0.0124 — in row 3 of Exhibit 5. 44

The major difference between the full and four-element models is the presence of offender age in

the full model comparison. Consequently, these findings suggest that the offender’s age is a
For this exercise, a CHC age component was created. Using age at the instant offense, the measure adds three 45

points to the total CHC score if the offender was age 20 or younger; adds two points if the offender was age 21-25; adds

one point if the offender was age 26-35; makes no change if the offender was age 36-45; subtracts one point if the

offender was age 46-60, and subtracts two points if the offender was age 60 or older. Any resulting score less than zero

is reset to zero. It is not assumed that this is the most predictive age component that can be constructed but is offered

as an heuristic device to examine the predictive power of an age component in the CHC.

 The predictive power of the CHC “first offender” component is documented in Maxfield et al., 2004b. 46

The postulated first offender element applied in this analysis scores zero points to offenders with no prior 47

arrests; one point to offenders with prior arrests but no prior convictions; one point to those only with “never counted”

minor prior convictions (as listed at §4A1.2(c)(2) and including hitchhiking, loitering, minor traffic infractions, public

intoxication, or vagrancy); or three points to all remaining current offenders. These points are added into the total sum

of criminal history points. It is not assumed that this is the most predictive nor desirable first offender element that can

be constructed. Instead, it is offered solely as an heuristic device to examine the predictive power of a first offender

component in the CHC. This particular formulation is based on the most predictive model explored in the recidivism

series’ report on first offender issues (Maxfield et al., 2004b) and incorporates any arrest that does not result in a

conviction (or for which conviction status is unknown). Although arrests are highly predictive, their use raises potential

legal and ethical issues in policy application.

Page 14 of 34

powerful component of recidivism prediction. This hypothesis motivates the next analyses which

test the power of CHC elements for offender age and first offender status.

G. Predictive Power of Alternative CHC Formulations

T

hese first steps in the USSC investigation to motivate more predictive, formulations

of the CHC are reported in the “Alternative CHC Formulation” section (rows 4, 5, and

6) of Exhibit 5. In this analysis, the full SFS is compared to alternate formations of

the CHC which add an age component and/or a first offender component. 

1. CHC with a Speculative Age Component 

In row 4 of Exhibit 5, a speculative age component is added to the CHC. In the resulting 45

comparison with the CHC, the AUC results demonstrate that the addition of an age element to the

CHC diminishes the SFS predictive advantage. As presented in row 4, the AUC statistics for the

CHC-with-age and the SFS show no statistical difference in recidivism prediction. The addition of

age to the CHC results in the two measures being equally accurate in the prediction of recidivism.

This finding further accentuates the power of age as a factor in the prediction of recidivism. 

2. CHC with a Speculative First Offender Status Component

Row 5 of Exhibit 5 compares the full SFS to the CHC with a speculative first offender

component. When a first offender element is added to the CHC, the difference in predictive 46 47

power compared to the full SFS is decreased substantially: the difference in area is only 0.007.
Page 15 of 34

Nonetheless, this difference is still statistically significant (0.01 level), although of dubious policy

significance. 

These data highlight the significance of a model that adapts for first offender status. Taken

by itself, a CHC with an added first offender component would bring substantial recidivism

prediction improvement by adjusting for offenders with extremely low levels of prior involvement

with the criminal justice system.

3. CHC with Speculative Component for Both Age and First Offender Status

Finally, in row 6 of Exhibit 5, the full SFS is compared to the reformulated CHC that

includes both a speculative age component and first offender component. As displayed in row six,

this alternate formation of the CHC surpasses the SFS in predictive power. The CHC with both

speculative offender age and first offender components is significantly better at predicting

recidivism than is the full SFS. 

H. Conclusion 

T

he analyses above compare the recidivism risk prediction powers of the U.S.

Sentencing Commission’s criminal history category (CHC) and the U.S. Parole

Commission’s Salient Factor Score (SFS). The SFS serves as a historical model for

the CHC, with many components derived from common concepts, although the actual measurement

strategies vary. 

The predictive power comparisons reveal an array of contrasts between the two measures.

First, both measures have components which did not contribute to prediction accuracy. For the

CHC, the element that adds points for prior violent offenses otherwise uncounted did not have

statistical significance. For the SFS, the element that incorporates the number of prior commitments

exceeding 30 days did not have statistical significance.

In their current formulations, the SFS is a statistically better recidivism risk prediction

instrument than is the CHC. The results suggest that, in large part, the greater predictive power of

the SFS is due to its use of offender age as a predictive factor. Supporting this conclusion is the

result achieved when an age component is added to the CHC. With a speculative offender age

provision, the modified CHC eliminates approximately two-thirds of the SFS prediction advantage.

 Pursuing enhanced predictive power for the CHC, the analysis also considers a “first

offender” criminal history element. A first offender adjustment would decrease the guideline’s

criminal history score for offenders with minimal or no prior experience in the criminal justice

system. The data indicate that a speculative first offender adjustment improves the predictive power

of the CHC, although to a lesser degree than observed with an offender age CHC element. However,

the analysis suggests that, taken together and dependant upon the actual policies adopted, the
Apprendi v New Jersey, 120 S. Ct. 2348 (June 26, 2000). See also Blakely v Washington, 124 S. Ct. 2531 48

(June 24, 2004). 

For example, USSG §4A1.2(c) describes the inclusion rules for misdemeanor and petty offenses. 49

For example, §2L1.2 uses the offense of a prior conviction to determine the substantive Specific Offense

50

Characteristic enhancement.

Page 16 of 34

addition of both offender age and first offender components could serve to boost the CHC predictive

power statistically beyond that of the current SFS.

The comparisons of relative predictive power of the CHC and SFS provide interesting

opportunities for analytical speculation. However, the comparison itself is detrimental if it obscures

the more important goal of instrument revision and improvement both for prediction accuracy and

for application efficiency. Meticulous information collection by the probation officer is the basis

for both the CHC and SFS calculations. Efficient revisions to the methods are welcome if in

addition to providing appropriate prediction levels, they also either simplify the data collection

process or assist in its more accurate collection.

The CHC and SFS models share many predictive concepts. These include the frequency,

seriousness, and recency of prior offenses, as well as the offender status under a criminal justice

sentence. The presence of these shared concepts motivates areas of possible guideline simplification.

 For example, when the CHC and SFS formulations for frequencyand seriousness alone are analyzed

(as they are in results reported in row 2 of Exhibit 5), the SFS formulation is found to be statistically

more predictive. The SFS has greater predictive power even though the SFS formulation is more

computationally straightforward. The SFS procedure merely sums up the number of prior

convictions, and commitments exceeding 30 days. In contrast, the CHC formulation is more

complex, requiring the classification of each prior conviction into one of three imposed sentence

length categories and the application of both mathematical addition and multiplication. The analysis

suggests that not only can a reformulation of the CHC be simplified, but that simplified calculations

can additionally be more predictive.

The need for efficient revision of the guidelines CHC may soon become a mandate. The

Apprendi v New Jersey Supreme Court decision states: 

Other than the fact of a prior conviction, any fact that increases the penalty for a

crime beyond the prescribed statutory maximum must be submitted to a jury, and

proved beyond a reasonable doubt.48

The CHC uses several facets of the prior conviction to assign criminal history points. These

attributes include the length of the imposed sentence for each prior offense and the relative timing

between the instant offense and the prior offenses. Additionally, the nature of a prior offense

conviction determines criminal history point assignment for certain offenses, or offense level 49

computation under certain substantive guidelines. If the Supreme Court finds that any of these 50
Page 17 of 34

characteristics of prior offenses are beyond the “fact of a prior conviction,” several components of

the current CHC will require modification. The approach of SFS Element A and its simple count

of prior convictions provides a suggested alternative, and perhaps improved, formulation of a CHC

recidivism prediction measure.

While it may be tempting to proclaim broad conclusions from the results presented, these

conclusions do not suggest that use of the CHC be suspended, nor that it adopt the calculation

provisions of the SFS. However, the analysis does underscore that modifications to the current CHC

could simplify computation, enhance recidivism prediction, and contribute to a resolution of

emergent Apprendi constitutional issues. One of the benefits of the USSC recidivism data is their

availability at this time both for development of a post-Blakely guideline system and for the

empirical fine-tuning desired and foreseen by the original federal Sentencing Commission.
Page 18 of 34

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Page 22 of 34

Exhibit 1

Comparison of Elements in the

Criminal History Computation and the Salient Factor Score

Criminal History

Computation

(U.S. Sentencing

Commission)

Salient Factor

Score SFS98

(U.S. Parole

Commission)

Elements

i

Frequency of Prior

Offending

Count of 

prior

convictions

 (§§4A1.1(a),(b),(c))

Count of prior

commitments

(up to four)

(Item A)

ii Seriousness of Prior

Offending

Individual imposed

sentence lengths of prior

convictions

 (§§4A1.1(a), (b), (c))

Count of prior

commitments of 

30 days or more

(up to three)

 (Item B)

iii Under Criminal Justice

Sentence at Instant

Offense

Instant offense

committed while under

sentence or supervision

(§4A1.1(d))

Instant offense

committed while under

sentence or supervision

(Item E)

iv Recency of Prior

Offending

Two years since release

from 60 days or more

days’ prison imposed

 (§4A1.1(e))

Three years since last

release from 30 days or

more commitment

(Item D)

v Violent Priors

Without Points

Related violent

convictions not receiving

points

(§4A1.1(f))

—

vi Age

—

Age at instant offense

and priors

(Item C);

Over age 41

at instant offense

(Item F)

Source: U.S. Sentencing Commission.
Page 23 of 34

Exhibit 2 

Criminal History Score Elements:

Predicting Days Until Primary Recidivism

Element1

Parameter

Estimate

Standard

Error

ChiSquarePr >

ChiSq

Hazard

Ratio

i, ii Number of Priors

with One Point 

 (§4A1.1(c))

0.25539 0.01145 497.7580 <.0001* 1.291

i, ii Number of Priors

with Two Points

 (§4A1.1(b))

0.04920 0.00651 57.0525 <.0001* 1.050

i, ii Number of Priors

with Three Points

 (§4A1.1(a))

0.04934 0.00410 144.7873 <.0001* 1.051

iii Under Criminal

Justice Sentence

 (§4A1.1(d))

0.17359 0.01666 108.5080 <.0001* 1.190

iv Recency of Priors 

 (§4A1.1(e))

0.42601 0.02865 221.1488 <.0001* 1.531

v Violent Priors

Without Points

 (§4A1.1(f))

-8.56552 56.20198 0.0232 <0.8789 0.000

 Likelihood Ratio Chi-Square 2114.3817 ( p = <.0001)

*Statistically significant at p<.05 or smaller.

See Exhibit 1

1

 Source: U.S. Sentencing Commission
Page 24 of 34

Exhibit 3

 Salient Factor Score (SFS 98):

Predicting Days Until Primary Recidivism

 Element1

Parameter

Estimate

Standard

Error

ChiSquarePr >

ChiSq

Hazard

Ratio

i, ii Number of Priors

(Item A)

-0.42982 0.01588 732.4484 <.0001* 0.651

i, ii Number of

Priors >30 days 

(Item B)

0.01925 0.03134 0.3772 <.5391 1.019

iii Under Criminal

Justice Sentence

(Item E)

-0.13032 0.03440 14.3486 <.0002* 0.878

iv Recency of Priors

(Item D)

-0.33606 0.04536 54.8988 <.0001* 0.715

vi Age At Instant

Offense and Priors 

(Item C)

-0.31103 0.01478 442.6309 <.0001* 0.733

vi Over Age 41 at

Instant Offense

(Item F)

-0.38346 0.04784 64.2358 <.0001* 0.681

Likelihood Ratio Chi-Square 2912.2049 (p = <0.0001)

*Statistically significant at p<.05 or smaller.

See Exhibit 1

1

Source: U.S. Sentencing Commission
Page 25 of 34

Exhibit 4

Comparison of Predictive Power:

Criminal History Category vs. Salient Factor Score

Two Year Primary Recidivism Definition

 Source: U.S. Sentencing Commission
Page 26 of 34

Exhibit 5

Alternate Formations: CHC and SFS Area Under the ROC Comparisons

 Predicting the Primary Recidivism Measure

Recidivism Study 2003

Salient Factor Score Criminal History Category Area Comparison

Row SFS Formulation1

SFS

AUC CHC Formulation1

CHC

AUC

 DifferenceSignificance

Test

1 Full SFS 0.7313 Full CHC 0.6992 0.0321* 149.83 

p=0.0000

Comparison of Similar Elements

2 (i) Frequency and (ii) Seriousness 0.7047 (i) Frequency and (ii) Seriousness 0.6982 0.0065* 10.23 

p = 0.0014

3

(i) Frequency, (ii) Seriousness, (iii)

Under CJ Sentence, (iv) Recency

 0.7116 (i) Frequency, (ii) Seriousness, (iii)

Under CJ Sentence, (iv) Recency

0.6992 0.0124* 39.73 

p = 0.0000

Alternative CHC Formulations

4 Full SFS 0.7313 Full CHC plus Age Element 0.7311 0.0002 2 0.02 

p=0.8929

5 Full SFS 0.7313 Full CHC plus First Offender

Element3 0.7243 0.007* 7.32 p=0.0068

6 Full SFS 0.7313 Full CHC plus Age Element and

First Offender Element4 0.7462 -0.0149* 62.65 p=0.0000

*Statistically significant at p<.05 or smaller.

See Exhibit 1.

1

The age element assigns points for age at the instant offense as follows: age 20 years or younger, add 3 points; age 21-25, add 2 points; age 26-35, add 1 2

point; age 46-60, subtract 1 point; age 60 and older, subtract 2 points. The age component is added to the current CHC and any scores less than zero are set to

zero. 

The first offender element scores 0 points to those with no prior arrests; 1 point to those with prior arrests but no prior convictions; 1 point to those with only 3

“never counted” minor prior convictions as listed in §4A1.2(c)(2); and 2 points to all remaining current CHC. 

This formulation incorporates both the age element and the first offender element and resets any scores less than zero to the value of zero.

4

SOURCE: U.S. Sentencing Commission
Page 27 of 34

Appendix A

Criminal History Worksheet

Defendant______________________________________Docket Number_____________________________________

Enter the Date Defendant Commenced Participation in Instant Offense (Earliest Date of Relevant Conduct)____________________

1. 3 Points for each prior ADULT sentence of imprisonment EXCEEDING ONE YEAR AND ONE MONTH imposed within 15

YEARS of the defendant's commencement of the instant offense OR resulting in incarceration during any part of that 15-YEAR

period. (See §§4A1.1(a) and 4A1.2.)

2. 2 Points for each prior sentence of imprisonment of AT LEAST 60 DAYS resulting from an offense committed ON OR AFTER the

defendant's 18th birthday not counted under §4A1.1(a) imposed within 10 YEARS of the instant offense; and

2 Points for each prior sentence of imprisonment of AT LEAST 60 DAYS resulting from an offense committed BEFORE the

defendant's 18th birthday not counted under §4A1.1(a) from which the defendant was released from confinement within 5 YEARS of

the instant offense. (See §§4A1.1(b) and 4A1.2.)

3. 1 Point for each prior sentence resulting from an offense committed ON OR AFTER the defendant's 18th birthday not counted under

§4A1.1(a) or §4A1.1(b) imposed within 10 YEARS of the instant offense; and

1 Point for each prior sentence resulting from an offense committed BEFORE the defendant's 18th birthday not counted under

§4A1.1(a) or §4A1.1(b) imposed within 5 YEARS of the instant offense. (See §§4A1.1(c) and 4A1.2.)

NOTE: A maximum sum of 4 Points may be given for the prior sentences in Item 3.

 Date of Offense Sentence Release Guideline Criminal

Imposition Date Section History Pts.

**

Indicate with an asterisk those offenses where defendant was sentenced as a juvenile. *

A release date is required in only three instances:

**

a. When a sentence covered under §4A1.1(a) was imposed more than 15 years prior to the commencement of the

instant offense but release from incarceration occurred within such 15-year period;

b. When a sentence counted under §4A1.1(b) was imposed for an offense committed prior to age 18 and more than

5 years prior to the commencement of the instant offense, but release from incarceration occurred within such 5-

year period; and

c. When §4A1.1(e) applies because the defendant was released from custody on a sentence counted under 4A1.1(a)

or 4A1.1 (b) within 2 years of the instant offense or was still in custody on such a sentence at the time of the

instant offense (see Item 6).

4. Sum of Criminal History Points for prior sentences under §§4A1.1(a), 4A1.1(b), and 4A1.1(c) (Items 1,2,3).
Page 28 of 34

Appendix A (continued)

Defendant______________________________________ Docket Number_____________________________

5. 2 Points if the defendant committed the instant offense while under any criminal justice sentence (e.g.,

probation, parole, supervised release, imprisonment, work release, escape status). (See §§4A1.1(d) and 4A1.2.) 

List the type of control and identify the sentence from which control resulted. Otherwise, enter 0 Points.

6. 2 Points if the defendant committed the instant offense LESS THAN 2 YEARS after release from

imprisonment on a sentence counted under §4A1.1(a) or (b), or while in imprisonment or escape status on such

a sentence. However, enter only 1 Point for this item if 2 points were added at Item 5 under §4A1.1(d). (See

§§4A1.1(e) and 4A1.2.) List the date of release and identify the sentence from which release resulted. 

Otherwise, enter 0 Points.

7. 1 Point for each prior sentence resulting from a conviction of a crime of violence that did not receive any points

under §4A1.1(a), (b), or (c) because such sentence was considered related to another sentence resulting from a

conviction of a crime of violence. Provided, that this item does not apply where the sentences are considered

related because the offenses occurred on the same occasion. (See §§4A1.1(f) and 4A1.2.) Identify the crimes

of violence and briefly explain why the cases are considered related. Otherwise, enter 0 Points.

Note: A maximum sum of 3 Points may be given for Item 7.

8. Total Criminal History Points (Sum of Items 4-7)

9. Criminal History Category (Enter here and on Worksheet D, Item 4)

Total Points Criminal History Category

0-1 I

2-3 II

4-6 III

7-9 IV

10-12 V

13 or more VI
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Appendix B

Salient Factor Score (SFS 98)

Item A. PRIOR CONVICTIONS/ADJUDICATIONS (ADULT/JUVENILE) ...................................... _____

None = 3; One = 2; Two or three = 1; Four or more = 0

Item B. PRIOR COMMITMENT(S) OF MORE THAN 30 DAYS (ADULT/JUVENILE) .................. _____

None = 2; One or two = 1; Three or more = 0

Item C. AGE AT CURRENT OFFENSE/PRIOR COMMITMENTS ................................................... _____

26 years or more Three or fewer prior commitments = 3

Four prior commitments = 2

Five or more commitments = 1

22-25 years Three or fewer prior commitments = 2

Four prior commitments = 1

Five or more commitments = 0

20-21 years Three or fewer prior commitments = 1 

 Four prior commitments = 0

19 years or less Any number of prior commitments = 0

Item D. RECENT COMMITMENT FREE PERIOD (THREE YEARS)............................................... _____

No prior commitment of more than 30 days (adult or juvenile) or released to 

 the community from last such commitment at least 3 years prior to the 

commencement of the current offense = 1; Otherwise = 0

Item E. PROBATION/PAROLE/CONFINEMENT/ESCAPE STATUS VIOLATOR THIS TIME... _____

Neither on probation, parole, confinement, or escape status at the time of the 

current offense; nor committed as a probation, parole, confinement, or escape 

status violator this time = 1; Otherwise = 0

Item F. OLDER OFFENDERS........................................................................................................... _____

If the offender was 41 years of age or more at the commencement of the current 

offense (and the total score from Items A - F above is 9 or less) = 1; Otherwise = 0

TOTAL SCORE..................................................................................................................................... _____ 
Allison, 1995; Hosmer and Lemeshow, 1999; Klein and Moeschberger, 1997. 51

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Appendix C

Evaluating Predictive Power with Survival Analysis

S

urvival analysis, also called hazard rate analysis, is a method that can be used to

evaluate the predictive ability of the guidelines’ criminal history measure. Survival

analysis measures the ability of criminal history to predict how rapidly offenders

recidivate during the follow-up period. The concept of crimes committed per unit of time has its

51

roots in the incapacitation literature, where great effort was expended to identify offenders who

committed crimes frequently. These repeat offenders were individuals committing multiple crimes

in a given period, such as daily, monthly, or yearly. By identifying frequent offenders, they could

be targeted for longer prison terms than offenders who commit crimes less frequently. Incapacitation

literature argues that the selective targeting of frequent offenders would result in a more efficient use

of prison resources as a means of crime reduction. 

Survival analysis is used here to examine how well criminal history predicts the number

of crimes offenders will commit during a specific follow-up period. The example below illustrates

its strengths.

Assume a researcher has recidivism data for 200 offenders who were released from prison

all on the same day. Assume that all 200 offenders recidivate during the first two years back in the

community. 

• The first 100 of the offenders all recidivate on the last day of the two

year follow-up, the 730 day. Thus, 100 crimes were committed on th

day 730. The daily rate of crime for this group is 100 crimes divided

by 730 days, or 0.1370 offenses per day. 

• The second 100 of these offenders all recidivate on the first day of the

follow-up period. Thus, 100 crimes were committed on day one. The

daily rate of crime for this group is 100 crimes divided by one day, or

100 offenses per day. 

These two groups have different speeds of offending. Within 730 days, the first group is

expected to commit 100 crimes. During the same 730 day period, however, the second group is

expected to commit 73,000 crimes (assuming, of course, that none are apprehended).

Although an extreme example, it illustrates the concern of crime control advocates with

respect to their goal of protecting the public. This approach argues that criminal history must have

the predictive power to identify offenders who pose a greater risk to public. Survival analysis allows

for this evaluation of the prior criminal history measures. 
AUC denotes the Area Under the Curve analysis from the ROC curve, described in Appendix D. 52

Companion reports in the recidivism project series perform these analyses such as, whether the guideline 53

provision of “recency points” (§4A1.1(e)) adds significantly to predictive power over and above other criminal history

components.

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Survival analysis and the AUC provide different perspectives on recidivism risk. The 52

AUC measures how well prior criminal history predicts whether offenders recidivate or not during

a fixed follow-up period. Given the 100 percent rate of recidivism for both groups in the example,

the AUC would be identical when using criminal history to predict recidivism separately for each

group of offenders. The AUC is not sensitive to the speed at which offenders recidivate and

therefore, does not gauge how well criminal history predicts the frequency of re-offending. 

In contrast, survival models are sensitive to the speed of recidivism and therefore provide

a way to test how well criminal history measures this important aspect of re-offending risk. The

survival curves in Exhibit 5 show, from a survival analysis perspective, the rapidity of recidivism

for each day of the two year follow-up period, for each of the six CHCs (I through VI). Offenders

in CHCs V and VI recidivate most rapidly and therefore if not apprehended, are likely to offend more

frequently during the two year follow-up period than are offenders in CHC I. 

Survival analysis has another advantage over the AUC when used to evaluate criminal

history’s ability to predict recidivism. Multiple regression methods for survival analysis have been

developed that allow simultaneous evaluation of the independent contribution to predictive power

of the various criminal history components. The proportional hazard model estimates whether the 53

independent variables contribute uniquely when predicting the rapidity of recidivism. 
This is a simplified explanation. For the sake of clarity, additional issues involving “true negatives” and 54

“false negatives” are not considered. 

On the graph, the false positive rate is plotted along the x axis and the true positive rate (called the 55

“sensitivity”) is plotted along the y axis. The false positive rate is defined as 1 minus the specificity.

Page 32 of 34

Appendix D

Evaluating Predictive Power with the

Area Under the Receiver Operating Characteristic Curve

D

etermining the area under a specific geometric curve is an established technique for

measuring the predictive power of a measurement instrument. This technique is well

established in diagnostic testing for health disorders when a procedure is used to

determine the presence of a disease. If the diagnostic test accurately predicts the presence of the

disease, this is a “true positive” result. However, the researcher must also know how often a

diagnostic test indicates that a disease is present when in fact the disease is not present. This type

of prediction error is called a “false positive” result. The best prediction tool maximizes true

positives and minimizes false positives. The technique that analyzes predictive accuracy uses a 54

graph that maps the “true positive” rate against the “false positive” rate. The curve of this graph is

called a receiver operating characteristic (ROC) curve. The area under the curve provides a measure

of the predictive power of the prediction instrument. The paragraphs below illustrate how this

technique is used.

ROC analysis is a straightforward application of this technique to recidivism research. Here

the measurement instrument is the offender’s prior criminal history. For this example, assume that

the instrument measures criminal history points. The points are used to predict recidivism. The

analysis must show how often the measure of criminal history points accurately predicts recidivism,

compared to how often the measure of criminal history points predicts recidivism incorrectly. 

Graphically, the data are shown in a rectangular box with the area being one unit, as shown

in the figure below. A diagonal line is drawn from the lower left to the upper right corners, bisecting

the rectangle into two equal parts. The area below the diagonal line measures one half the area of

the box (i.e., 0.5 units) and represents “random” prediction, or no predictive power at all. Any

observation along the diagonal line is equally likely to be a true positive or a false positive. This

line, and the area of the rectangle below it, is the comparison point for the recidivism model. 

When the observed true positive and false positive recidivism data are plotted in this

rectangular box, they form a line that curves upward from the diagonal line. This curved line is the 55

ROC curve. The higher the ROC line curves above the diagonal line (and toward the top and left

side of the rectangle), the greater the area under its curve. The area under the ROC curve represents

the predictive power of the criminal history model. Because the ROC curve is higher than the

diagonal line, the area under the ROC curve is greater than the area under the diagonal line. Thus,

as represented in the figure, the ROC curve improves upon random chance prediction.
Page 33 of 34

The statistic used to measure the predictive power of the criminal history model is the

“AUC”: the Area Under the Curve. The greater the AUC, the better the predictive power of the

measurement instrument. 

The AUC has several desirable qualities as a prediction power gauge. First, and in the

context of prior criminal history predicting recidivism, the AUC is interpreted as the probability that

a randomly chosen known recidivist will have more prior criminal history than a randomly chosen

known non-recidivist. Therefore, the AUC ranges from 0.5 to 1.0. 

• With an AUC of 0.5, a randomly chosen known recidivist has a 50 percent

chance of having more prior criminal history than a randomly chosen nonrecidivist. This would mean that there is no relationship between recidivism

and prior criminal history. 

• With an AUC of 1.0, 100 percent of the randomly chosen recidivists will

have more prior criminal history than the randomly chosen non-recidivists,

meaning that prior criminal history predicts recidivism perfectly. With an

AUC of 1.0, all recidivists would have more prior criminal history than all

non-recidivists. 

AUCs between 0.5 and 1.0 indicate a “better than random” predictive accuracy, but a “less

than perfect” predictive accuracy. For the hypothetical example appearing in the figure above, the

AUC of 0.67 indicates that 67 out of 100 times, randomly chosen recidivists and non-recidivists are

compared, a recidivist would have more prior criminal history than a non-recidivist. This indicates

that while the extent of prior criminal history is a strong predictor of recidivism, it is not a perfect

predictor. The predictive power of a criminal history measure might be improved by adding or
The introductory comments of USSG Ch.4, Pt. A states that “while empirical research has shown that other 56

factors are correlated highly with the likelihood of recidivism, e.g., age and drug abuse, for policy reasons they were

not included here at this time.”

Hanley and McNeil, 1982; Hanley and McNeil, 1983, Delong, Delong, and Clarke-Pearson, 1988. The ability 57

to compare different criminal history models makes AUC an important tool in assessing impacts of changes to the

guidelines’ Chapter Four provisions.

Page 34 of 34

changing its components. However, both legal and policy factors guide the types of characteristics

that can be part of a prediction model.56

The AUC statistic has three additional desirable properties. It is insensitive to the base rate

of recidivism. It can be used across multiple prediction instruments to compare statistically

significant predictive power differences. Finally, the AUC can be graphicallyrepresented allowing 57

visual comparisons among multiple curves calculated from different prediction instruments.