Partially Specified Actuarial
Tables and the Poor
Performance of Static-99R
Richard Wollert Ph.D.
Washington State Vancouver
rwwollert@aol.com
http://richardwollert.com
360.737.7712
Jacqueline Waggoner Ed.D.
University of Portland
waggoner@up.edu
wordpress.up.edu/waggoner
503.943.8012
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Actuarial Instruments for Sex
Offender Risk Assessment

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
Contain “risk items” correlated with
sexual recidivism.
Each risk item is subdivided into
categories.
An offender is assigned to only 1
category per risk item.
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Actuarial Manual



Sets forth criteria for assigning offenders
to item categories.
Contains coding rules that weight each
category.
Some categories scored as zero, some
as 1 or more, a few as – 1 or less.
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Actuarial Manual


An offender is assigned to a “risk group”
per his score.
Some groups include a range of scores.
We call them “bins.”
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One-Way Model (Once Called “Partial
Specification” but Dropped as a Misnomer)

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Tries to capture the effects of risk factors
on recidivism with a single number.
First generation actuarials were one-way
models.
The 10-item Static-99 is an example.
Offenders got one point for “current age
less than 25.” No points if older.
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One-way Actuarial Table for Static-99 Score Bins and
Point Scores (from Hanson & Thornton, 2000, p. 129).
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The “Age Invariance Effect”
(Hirschi & Gottfredson, 1983)

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Sexual recidivism declines with age throughout
life (Hanson, 2002).
The decline is linear.
The effect applies to all risk bins (Wollert, 2006;
Hanson, 2006).
Static-99 combined bin-wise rates for all ages.
This masked the fact that different age groups
have different recidivism rates.
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Static-99 Underestimated Young Offender Rates
(-%) and Overestimated Old Offender Rates (+%)
Even With Optimum (Unweighted) Scaling
L
Age Groups [*=differences that fall below (-) or exceed (+) the .05 CI]
Bins
18-29
L
-2.0%*
ML
-1.7%
MH
H
30-39
40-49
50-59
60-70+
-1.4%
+.5%
+.8%
+2.4%*
-.6%
+1.3%*
+1.0%
+3.5%*
-4.9%*
-3.9%*
+4.7%*
+1.6%
+8.4%
-6.4%*
-3.4%
+1.8%
+5.3%
+15.3%*
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The MATS-1 (Wollert et al., 2010) Took Into
Account the Linearity of Age Invariance and
Addressed the Estimation Errors of Static-99

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MATS-1 = “Multisample Age-Stratified Table of
Sexual Recidivism Rates.”
Removes age item from Static-99, so it has 9
“non-age predictor” (NAP) items.
Recidivism focus is on an offender’s age and
NAP score (able to capture interactions).
Also called a “two-way” model.
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MATS-1 Recidivism Rates
Age Groups
Scores
18-39.9
40-49.9
50-59.9
60 and Over
7.6
4.0
2.6
2.0
Medium
17.3
8.0
6.4
2.5
High
36.2
25.5
23.2
6.4
All Levels
13.2
7.6
5.6
2.7
Low
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Static-99R Is A One-Way Model Designed
To Account For The Age Effect
Described in Helmus et al., 2012.
 Age-weighting was used.
 18-34 group: One point added.
 40-59 group: One point subtracted.
 60-70+ group: Three points subtracted.

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Static-99R Performed Poorly
Construction sample ROC = .708.
 Validation sample ROC = .720.
 Static-99 validation sample ROC = .713.
 Recidivism rate for the Static-99R high
bin < 27%.

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How Age-Weighting Undermined Static-99R’s
Performance: Part 1 of a 3 Part Story

243 young offenders were moved to the
highest risk bin from lower Static-99 bins
because they received an extra point.
is “upscale dilution.” Less dangerous
offenders are mixed with more dangerous
offenders = high bins have lower rates
(Waggoner et al., 2008).
 This
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How Static-99R’s Performance Was
Undermined by Age-Weighting: Part 2.

230 old offenders were taken out of the high
bin and moved to lower bins because they
received negative points.
is “downscale enrichment.” More
dangerous offenders are mixed with less
dangerous offenders = low bins have higher
rates.
 This
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How Static-99R’s Performance Was
Undermined by Age-Weighting: Part 3.
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The numbers of recidivists and nonrecidivists in
each bin were about the same for Static-99 and
Static-99R when offender data were pooled
across age groups.

It is impossible to obtain accuracy differences
using ROC tests when the binwise distributions
of recidivists and nonrecidivists for two tests are
about the same.
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The Number of Recidivists and Nonrecidivists In
Each Static-99 and Static-99R Bin Were Similar
Bins
Number of
Recidivists
Number of
Nonrecidivists
Recidivism
Rate (5-years)
L-99
98
2,282
.041 (.034-.050)
L-99R
113
2,723
.040 (.033-.048)
ML-99
185
2,500
.069 (.060-.079)
ML-99R
166
2,043
.075 (.065-.087)
MH-99
265
1,565
.145 (.129-.162)
MH-99R
248
1,589
.135 (.120-.151)
H-99
308
903
.254 (.231-.280)
H-99R
326
898
.266 (.242-.292)
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Static-99R Bins Underestimate
Recidivism for Young Offenders and
Overestimate It for Old Offenders.
Age Groups [*=differences that fall below (-) or exceed (+) the .05 CI]
Bins
18-29
30-39
L
-2.1%*
-1.5%
ML
-1.1%
MH
H
40-49
50-59
60-70+
+.4%
+.7%
+2.3%*
0
+1.9%*
+1.6%
+4.1%*
-5.9%*
-4.9%*
+3.7%*
+.6%
+7.4%
-5.2%*
-2.2%
+3.0%
+6.5%
+16.5%*
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Discussion

Age-weighting did not enhance Static-99R.

Like Static-99, it underestimates young
offender rates and overestimates old
offender rates.
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A Solution to Age-Weighting Problems:
Convert Static-99R to a 2-Way Model
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Take all the age points out of Static-99R.
Stratify Static-99R NAP bins by age in one table.
Use external data and frequency or Bayesian
math to construct another table like the first.
Assign the cells in Table 1 to bins on the basis of
the cell-wise recidivism rates in Table 2.
 e.g., cells with very large rates in Table 2
make up Table 1’s “high” bin category, etc.
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References
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Hanson, R. K. (2002). Recidivism and age. Journal of Interpersonal
Violence,17, 1046-1062.
Hanson, R. K. (2006). Does Static-99 predict recidivism among older
sexual offenders? Sexual Abuse: A Journal of Research and
Treatment, 18, 343-355.
Hanson, R. K. & Thornton, D. (2000). Improving risk assessments
for sex offenders: A comparison of three actuarial scales. Law
and Human Behavior, 24, 119-136.
Helmus, L., Thornton, D., Hanson, R. K., & Babchishin, K. M. (2012).
Improving the predictive accuracy of the Static-99 and Static-2002
with older sex offenders: Revised age weights. Sexual Abuse: A
Journal of Research and Treatment, 24(1), 64-101. DOI:
10.1177/1079063211409951.
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References
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Hirschi, T. & Gottfredson, M. (1983). Age and the explanation of crime.
American Journal of Sociology, 89, 552-584.
Waggoner, J., Wollert, R., & Cramer, E. (2008). A respecification of
Hanson’s updated Static-99 experience table that controls for the
effects of age on sexual recidivism among young offenders. Law,
Probability and Risk, 7, 305-312.
Wollert, R. (2006). Low base rates limit expert certainty when current
actuarial tests are used to identify sexually violent predators: An
application of Bayes’s Theorem. Psychology, Public Policy, and
Law, 12, 56-85.
Wollert, R. (2007, August). Validation of a Bayesian Method for
Assessing Sexual Recidivism Risk. Presented in San Francisco at
the 2007 APA conference. http://www.richardwollert.com
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References

Wollert, R., Cramer, E., Waggoner, J., Skelton, A., & Vess, J.
(2010). Recent research (N=9,305) underscores the
importance of using age-stratified actuarial tables in sex
offender risk assessments. Sexual Abuse: A Journal of
Research and Treatment, 22, 471-490. DOI:
10.1177/1079063210384633.
Acknowledgements
The authors are indebted to Brian Abbott, David Cooke, Ted Donaldson,
Elliot Cramer, and Diane Lytton for reading and commenting on previous
versions of this presentation.
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