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© 2000 by CRC Press LLC

10.3.2 Performance

Table 10.1

 presents information on crime patterns and CGT test results from

the SFU serial murder data set, including number of crime sites, size of
hunting and search areas, and hit score percentages (the implications of

Figure 10.3

 Geoprofile confidence intervals.

© 2000 by CRC Press LLC

which are discussed below). Case data are divided into victim encounter/body
dump (i.e., there was no victim transport), victim encounter, and body dump
sites. A minimum of five different locations of the same crime site type
connected to a single residence was necessary for a site type to be individually
analyzed (see Rossmo, 1995a, for full study details). 

Table 10.2

 shows the

comparative CGT hit score percentages for those cases where more than one
type of crime site was available for examination. Generally, encounter sites
result in lower hit scores than body dump sites, though in some cases best
performance is achieved from the use of all site types (optimal crime site
selection in geographic profiling is discussed below).

Table 10.1    Crime Site Patterns and CGT Results

Serial Murderer

Crime 

Sites

Hunting Area

Area/Crime 

Site

CGT  Hit 

Score %

Search 

Area

Victim Encounter/Body Dump Sites

Chase

5

8.0 km

2

1.6 km

2

1.7%

0.1 km

2

DeSalvo

14

1256 km

2

89.7 km

2

17.8%

223 km

2

Ramirez

21

6393 km

2

304 km

2

9.8%

625 km

2

Berkowitz

10

816 km

2

81.7 km

2

4.7%

38.2 km

2

Victim Encounter Sites

Olson

15

299 km

2

20.0 km

2

3.0%

9.1 km

2

Buono

9

487 km

2

54.1 km

2

9.4%

45.6 km

2

Bianchi

3.2%

15.6 km

2

Collins

7

62.6 km

2

8.9 km

2

1.1%

0.7 km

2

Dahmer

10

6.8 km

2

0.7 km

2

8.7%

0.6 km

2

Brudos

6

5726 km

2

954 km

2

2.2%

128 km

2

Body Dump Sites

Olson

65

11

14,262 km

2

1,297 km

2

12.5%

1779 km

2

Buono and Bianchi

9

305 km

2

33.94 km

2

9.2%

28.0 km

2

Sutcliffe Res 1

20

9547 km

2

477 km

2

4.9%

465 km

2

Res 2

2.4%

232 km

2

Rifkin

16

25,278 km

2

1580 km

2

7.2%

1829 km

2

Collins

66

7

368 km

2

52.54 km

2

23.8%

87.6 km

2

Wuornos Body 

6 

16,980 km

2

2830 km

2

3.8%

643 km

2

Vehicle

7

14,970 km

2

2139 km

2

5.4%

813 km

2

65

The hit score percentage and search area for Agassiz Mountain Prison was 2.5% (352

km

2

); aspects of the case suggest this location was a significant offender anchor point.

66

The hit score percentage and search area for Eastern Michigan University was 15% (55.3

km

2

); aspects of the case suggest this location was a significant offender anchor point.

© 2000 by CRC Press LLC

10.3.3 Validity, Reliability, and Utility

10.3.3.1 Validity

For geographic profiling to distinguish itself from geomancy, it should meet
certain standards. Scientific methodologies must fulfil three important
criteria — validity, reliability, and utility (see Oldfield, 1995). Specification
of a methodology’s limitations is also important (Poythress et al., 1993). The
CGT model works on the assumption that a relationship, modeled on some
form of distance-decay function, exists between crime location and offender
residence. The process can be thought of as a mathematical method for
assigning a series of scores to the various points on the map representing a
criminal’s hunting area. For the CGT model to be valid, the score it assigns
to the point containing the offender’s residence (referred to as the “hit score”)
should be relatively high; that is, there should be few points within the
hunting area with equal or higher scores. This relationship can be shown as
a distribution curve indicating the number of points with various scores (see

Figure 10.4

, derived from the CGT analysis of the Olson case). A uniform

distribution assigns the same score to every point, producing a horizontal
line. (If 

N

 is the total number of points on a map, then the probability

associated with each point is 1/

N

.)

The success of the CGT model is measured by the hit score percentage —

the ratio of the total number of points with scores equal or higher to the hit
score, to the total number of points within the hunting area. This is equivalent
to the percentage of the total area that must be searched before the offender’s
residence is found, assuming an optimal search process (i.e., one that started
in the locations with the highest scores and then worked down). The extent of
the search area — the territory police have to search in order to find the offender
— is equal to the size of the hunting area multiplied by the hit score percentage.
The mean hit score percentage is 50% with a uniform distribution. This means

Table 10.2    CGT Comparative Site Type Results

67

Serial Murderer

CGT Hit Score %

(Encounter Sites)

CGT Hit Score %

(Body Dump Sites)

CGT Hit Score %

(All Sites)

Chase

1.7%

1.1%

Olson

3.0%

12.5%

1.3%

Buono and Bianchi

9.4%

9.2%

6.3%

Collins

1.1%

23.8%

1.2%

Wuornos

5.4%

3.8%

10.8%

Brudos

2.2%

2.9%

Mean

4.2%

10.2%

3.9%

67

Combined locations for Chase include body dump and vehicle drop sites; for Collins, 

encounter, murder, and body dump sites; and for Wuornos, body dump and vehicle 
drop sites.

© 2000 by CRC Press LLC

that, on average, any police system based on this distribution can expect to
locate an offender in half of the hunting area. Investigating suspects alphabet-
ically, tips chronologically, or canvassing from the northwest to the southeast
are all examples of such systems.

The validity of the CGT model can be determined by plotting groupings

of hit score percentages against those from a uniform distribution (i.e., what
is expected by chance) in a Lorenz curve, and then applying an index of
dissimilarity or concentration. One such measure is the Gini coefficient
(Goodall, 1987; Taylor, 1977). In this case it is equal to:

(10.12)

where:

G

  is the Gini coefficient;

N

  is the total number of observations;

x

n

 is 

the 

n

th member of the uniform percentage frequency; and

y

n

 is 

the 

n

th member of the hit score percentage frequency.

The Gini coefficient ranges from 0 to 100, with 0 indicating exact cor-

respondence between the two sets of percentage frequencies, and 100 indi-

Figure 10.4

 CGT score distribution.

G

x

y

n

n

n

N

=

−

=

∑

2

1

© 2000 by CRC Press LLC

cating a complete lack of correspondence. The more successful or valid the
CGT model, the closer the Gini coefficient is to 100. The distribution of CGT
hit score percentages found in the SFU serial murder study was compared
to that expected by chance (testing and learning data sets were different).
Specific CGT hit score percentages used in calculating the index of dissimi-
larity are marked in bold in

 Table 10.1

. Degree of offender choice was the

basis for determining which score to use when different scenarios were avail-
able. This meant that encounter sites were preferred over body dump sites,
unless the former were unknown or the target backcloth was patchy (e.g., a
red-light district). Also, the dominant residence was used in cases involving
more than one offender. Based on 5% intervals, the Gini coefficient for the
study sample equals 85, indicating a high level of validity.

An alternative measure of performance can be obtained by doubling the

mean hit score percentage; the lower this value the greater the predictive
power of the model. This measure ranges from 0, indicating optimal perfor-
mance, to 1, the value expected by chance. The mean hit score percentage
for the above cases is 6.0%, therefore this measure is equal to approximately
0.12. All else being equal, this suggests an area search conducted through a
geoprofile would find, on average, the offender’s residence in 12% of the time
that a random search would take. The relative performance of the CGT model
is therefore approximately 830% (100/12).

Results of the SFU serial murder study show a mean CGT hit score

percentage of 6.0% and a median of 4.2% (standard deviation = 4.8); the
average number of crime locations was 11.6 (see 

Table 10.1

). Performance

ranged from a low of 1.1% to a high of 17.8%. A review of solved operational
cases by the Vancouver Police Department Geographic Profiling Section
found similar results, with a mean CGT hit score percentage of 5.5% and a
median of 4.8% (standard deviation = 4.6); the average number of crime
locations was 19.1. Performance ranged from a low of 0.2% to a high of
17.2%. 

Figure 10.5

 shows the distribution of CGT hit score percentages for

the SFU serial murder data and a sample of VPD operational cases.

The theoretical maximum efficiency of the CGT model was estimated

through Monte Carlo testing, using a computer program to generate random
crime site coordinates based on a fixed-buffered distance-decay function.

65

The testing produced the “learning curve” in 

Figure 10.6

, which displays the

relationship between number of crime sites and median hit score percentage
(standard deviation is also shown). Because the distribution is not normal
(see 

Figure 10.5

) the median is a better indicator of typical performance than

the mean. Functions based on these curves are used in geographic profiling

65 

This function produces a pattern similar to Rengert’s (1996) bull’s-eye distribution. The

CGT model showed a small drop in performance when tested on other forms of crime site
geography (teardrop, bimodal, or uniform spatial patterns).