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# Policing Chronic and Temporary Hot Spots of Violent Crime: A Controlled
Field Experiment

Dylan J. Fitzpatrick  Carnegie Mellon University  Wilpen Gorr  Carnegie Mellon
University  Daniel B. Neill  New York University

###### Abstract

Hot-spot-based policing programs aim to deter crime through increased
proactive patrols at high-crime locations. While most hot spot programs target
easily identified chronic hot spots, we introduce models for predicting
temporary hot spots to address effectiveness and equity objectives for crime
prevention, and present findings from a crossover experiment evaluating
application of hot spot predictions to prevent serious violent crime in
Pittsburgh, PA. Over a 12-month experimental period, the Pittsburgh Bureau of
Police assigned uniformed patrol officers to weekly predicted chronic and
temporary hot spots of serious violent crimes comprising 0.5 percent of the
city’s area. We find statistically and practically significant reductions in
serious violent crime counts within treatment hot spots as compared to control
hot spots, with an overall reduction of 25.3 percent in the FBI-classified
Part 1 Violent (P1V) crimes of homicide, rape, robbery, and aggravated
assault, and a 39.7 percent reduction of African-American and other non-white
victims of P1V crimes. We find that temporary hot spots increase spatial
dispersion of patrols and have a greater percentage reduction in P1V crimes
than chronic hot spots but fewer total number of crimes prevented. Only foot
patrols, not car patrols, had statistically significant crime reductions in
hot spots. We find no evidence of crime displacement; instead, we find weakly
statistically significant spillover of crime prevention benefits to adjacent
areas. In addition, we find no evidence that the community-oriented hot spot
patrols produced over-policing arrests of minority or other populations.

###### keywords:

crime hot spots $|$ proactive policing $|$ predictive policing

In recent years, police agencies have demonstrated an increased willingness to
devote resources to proactive policing strategies for preventing crime (1). In
contrast to reactive policing, which prioritizes responding to 911 emergency
requests for police response and investigating crimes that have already been
committed, proactive policing aims to identify predictable high-crime patterns
and to take actions in regard to those patterns to prevent crimes (2). Most
recently, in the U.S., discussion of the potential benefits and harms of
proactive policing has become part of a wider debate about the role of police
and their impacts on the communities they serve, sparked by multiple instances
of police brutality against minorities and widespread protests against
systemic racism in policing as part of the Black Lives Matter movement (3).

Here we present results from a controlled experiment of proactive policing
which contributes several pieces of evidence to this debate, quantifying the
crime prevention benefits of proactive patrols targeting predicted “hot spots”
of serious violent crime, and confirming that certain undesirable outcomes
(over-policing arrests of racial minorities) did not occur in the study
period. We emphasize that these impacts are critically dependent on the
community-oriented approach taken by police patrolling predicted hot spots,
while aggressive policing practices may substantially harm individuals and
communities. In the discussion below, we note other critical issues to be
addressed while evaluating the potential impacts of proactive policing, as
well as describing a set of best practices intended to maximize benefits and
minimize harms.

### Crime prevention at crime hot spots

While certain high-crime patterns may involve specific persons, our research
concerns high-crime areas rather than individuals. A primary police
intervention for preventing crimes in such areas is frequent, targeted patrols
with police presence deterring criminals from committing crimes (4, 5, 6, 7).
The Part 1 Violent (P1V) crimes of homicide, rape, aggravated assault, and
robbery are the most serious offenses occurring in a city and are the target
crimes for our study (excluding domestic incidents).

An established finding in the criminology literature is that crimes do not
occur uniformly across cities, but instead concentrate in micro-places, or
“hot spots.” Hot spots range from single intersections or storefronts to a few
city blocks and represent optimal locations for committing crimes (8, 9, 10,
11, 12). Crime hot spots make up a small fraction of the total area of a city
yet produce disproportionately many calls for police response to a range of
violent, property, and disorder crimes.

Enforcement actions such as stops, searches, and arrests can prevent crime by
directly incapacitating potential offenders (1). Incapacitation may have
immediate effects on crime (13) or longer-term effects if prolific offenders
are removed from a community. However, it has been shown that aggressive
policing practices, including frequent stops, summonses, and arrests for low-
level crimes, have adverse impacts on community health (14), police-community
relations (15), and racial equity. Minorities can suffer from “over-policing”
with aggressive enforcement. An example is the “broken windows” approach to
policing that advocates zero tolerance to disorder behavior in the belief that
it would reduce crime. Strict enforcement leads to disproportionate harassment
and arrest of minority persons and erodes public trust in police (16).

Guardian actions, such as increased police presence through patrols and
community-policing methods, deter crime by removing opportunities to commit
crime and increasing the perceived risk of crime commission, even though
patrols generally do not involve direct contact with potential offenders (5,
17). A substantial body of evidence reveals that sending proactive patrols to
selected crime hot spots for guardianship reduces crime in those areas, but
the amount of observed crime reduction varies considerably across studies to
date (15). A meta study on guardian actions in the form of community-oriented
policing and problem solving versus enforcement actions in hot spots found
guardianship to have larger effect sizes (18). Spatial diffusion of patrol
benefits is supported by several studies showing that the deterrent effect
from police presence diffuses into areas near patrolled hot spots (19, 20,
21).

During the 1980s and 1990s, foot patrols were used in large areas of cities,
such as entire police beats. Such patrols improved the public’s perceptions of
safety, livability, and positive attitudes toward police but showed no crime
reduction effects (22, 23). Seminal work by Ratcliffe et al. in Philadelphia
(24), followed by replications by Novak et al. in Kansas City, MO (25) and
Piza in Newark, NJ (26), found significant reductions in serious violent
crimes with controlled experiments applying saturation (full-time) foot
patrols to micro-places. Saturation patrols are costly, so Haberman and Stiver
(27) applied only two hours of foot patrol per shift in Dayton, OH, and did
not find a significant reduction in violent crime. In contrast, our paper
provides evidence that foot patrols achieve statistically significant
reductions in serious violent crime, using only the discretionary time of
regular patrol officers for short-duration patrols.

### Chronic and temporary hot spots

Most hot spot studies focus on the impact of patrolling a fixed set of static
hot spots pre-selected using simple tabulations of crimes by location, crime
density maps, crime intelligence, or expert knowledge from police. These
chronic hot spots most often are large commercial areas and adjacent
residential areas, and result in a high concentration and volume of crime that
persist over the course of years and even decades (28, 29). However, a growing
body of evidence finds that other hot spots are dynamic, with crime clusters
exhibiting on-and-off behavior over short periods of time (30, 6, 28, 31).
Temporary hot spots represent flare-ups of crime resulting from short-term
phenomena, such as escalating gang disputes or repeat crimes by transient
individuals. Temporary hot spots tend to be widely distributed throughout a
city including small commercial areas and residential areas (28). Our research
uses prediction and selection of chronic and temporary hot spots as two policy
levers for police to address effectiveness and equity of crime prevention.

### Effectiveness and equity objectives

Police command staff must weigh resource and manpower constraints when making
decisions about how to distribute limited patrols throughout a city. While
most research on crime hot spots has used effectiveness in forecasting and
reducing crimes as the sole objective, we also include equity in the
distribution of crime prevention services by police across a city as an
additional objective. Equity is an important objective for public goods, and
especially for primary goods such as public safety (32).

For evaluating effectiveness of hot spot forecasting methods, we use plots of
percentage of a city’s crimes predicted in hot spots versus percentage area of
a city in hot spots (33, 34, 28, 35), here termed “prediction tradeoff
curves”. These curves are upward sloping with marginally decreasing returns
from increased patrols, and are directly useful for comparing accuracy of
alternative prediction models, incorporating resource limitations of police,
and showing tradeoffs between effectiveness and equity objectives. See SI:
Evaluation of Prediction Methods on Historical Data for example curves for our
models.

The underlying principles of equity are that “like needs should receive like
attention and resources… and greater needs should receive greater attention
and resources… [where the thing needed] is instrumental, a necessary condition
if a more ultimate objective is to be met” (32). Equity in crime prevention
across a city, as measured by the spatial dispersion of areas selected as hot
spots across time, is an important consideration for police (15, 28, 31). The
ultimate objective for crime prevention is a high level and equal distribution
of public safety for all (36). Experiments, such as the one reported in this
paper, confirm the instrumentality of proactive patrols in hot spots for
increasing public safety in all parts of the city where target crimes are
predictable. See SI: Equity in the Allocation of Crime Prevention Services by
Police for further explanation of these principles applied to crime prevention
and how we developed corresponding tools for policy makers to improve equity.

As a basis for measures of equity, we use a hot spot program’s “footprint,”
its spatial distribution of hot spots over a year that have been patrolled at
least for a week. With an equal number of chronic and temporary hot spots in a
program, we expect the footprint of temporary hot spots to be much larger and
widely distributed than that for chronic hot spots. We also use an entropy
index to summarize spatial dispersion of chronic versus temporary hot spots.

### Crime forecasting models and methods

Although simple methods can accurately identify chronic hot spots, the
emerging crime patterns of temporary hot spots require sophisticated spatio-
temporal forecasting models. While such models are intended to predict
temporary hot spots, they also predict chronic hot spots if using crime volume
as the dependent variable. Instead, our temporary hot spot model forecasts
deviations from baseline crime levels, thereby yielding temporary hot spots
and occasionally flare-ups at chronic hot spots.

To date, predictive policing studies have focused on a single method for
forecasting hot spots and have not included a rigorous model selection step in
which multiple forecasting methods for hot spots are compared. Our study uses
a grid of Pittsburgh consisting of cells 500 feet on a side as potential hot
spots. Through an analysis of five years of historical reported crime
incidents and 911 data ending in 2016, we selected forecast models that most
accurately forecasted chronic and temporary hot spots of P1V crimes from a set
of ten candidate models from the crime hot spot and forecasting literature
(See Materials and Methods). Most accurate for chronic hot spots was a simple
12-month moving average of serious violent crimes by grid cell. Most accurate
for temporary hot spots was a single-layer, fully-connected neural network
model with time-lagged dependent and independent variables made up of selected
crimes and 911 call for service counts from a two-year moving window of data.

### Field Study

Pittsburgh, PA is a city of 300,268 population with 64.9% white (non-
Hispanic), 22.8% African American, 5.7% Asian, and 2.3% Hispanic racial
composition. The Pittsburgh Bureau of Police (PBP) has approximately 900 sworn
officers distributed across six police zones, each with a police station,
commander, and officers. Prior to our field study, PBP maintained a policy
that uniformed patrol officers conduct proactive patrols informed by
experience and recent crime events to prevent crimes and protect citizens. For
such patrols, officers used discretionary time when not responding to 911
calls for service or other official duties. PBP policy for proactive patrols
required community-oriented policing methods such as engaging with local
citizens, avoiding enhanced enforcement actions such as zero-tolerance
policing (37). Officers were free to choose between car and foot patrol. Foot
patrol used “park and walk” so that parked marked police cars provided
additional police presence.

PBP set the goal that each officer assigned a hot spot spend an average of 15
minutes per shift on proactive patrol at the hot spot, with officers assigned
to hot spots across all three shifts and seven days per week (45 minutes of
patrol per hot spot per day). The result was a small-scale program with 36 hot
spots for the city consisting of six hot spots (three chronic and three
temporary) for each of Pittsburgh’s six police zones with 0.5 percent of the
area of the city under treatment at any given time. During the study year,
actual treatment duration averaged 35.5 minutes per day for both chronic and
temporary hot spots, less than the targeted 45 minutes.

We evaluated the hot spot program through a controlled field study motivated
by crossover trials from the field of public health. Using historical data on
serious violent crime frequency, we divided each of the six police zones into
two halves of roughly equal area and counts of historical violent crimes to
minimize spillover contamination of control hot spots by proactive patrols at
treatment hot spots. Residual crime-deterrence effects after patrols leave an
area are typically only one or two hours (38, 21), thus temporal spillover
effects from treatment in previous weeks to control hot spots were expected to
be negligible. The areas exposed to treatment were initially randomized and
then alternated on a weekly basis between the halves of each police zone, so
that no grid cell was selected for treatment two weeks in a row. Predicted hot
spots in the “control” partitions for a given week were not provided to PBP;
thus, control hot spots had policing as usual, including reactive policing in
response to 911 emergency calls for service and a limited number of police-
designed proactive patrols that existed before and during the experiment.

February through October 2017 included first a pilot implementation in one of
the six zones, followed by sequential rollout of the hot spot program in the
remaining five zones, with a burn-in period to increase patrol numbers to
impactful levels. The field study ran for 12 months from November 6, 2017
through November 4, 2018. During the study year, there were a total of 37
homicides, 56 rapes, 686 robberies, 682 aggravated assaults, 1230 burglaries,
6394 larcenies, and 772 motor vehicle thefts (exclusive of domestic violence
and retail crimes).

## Results

### Per-cell reductions in crime volume from proactive patrols

Policing-as-usual for patrol officers in Pittsburgh, while mainly consisting
of responding to 911 calls for emergency services, also included a number of
police-generated proactive patrols. We therefore expected that control hot
spots, known to the researchers but not provided to PBP, would have some
police-generated proactive patrols. Overall, control hot spots had proactive
patrols in numbers equal to 14.8 percent of patrols conducted in treatment hot
spots (1.9 vs. 12.9 patrols per hot spot per week), with 18.8 percent for
chronic hot spots (2.6 vs. 13.8 patrols per hot spot per week) and 10.1
percent (1.2 vs. 12.1 patrols per hot spot per week) for temporary hot spots.
Thus, the observed differences between P1V crimes in treatment and control hot
spots represent the impact of targeting predicted (chronic or temporary) hot
spots on a given week of the experiment, resulting in an additional 11
proactive patrols to targeted cells on average.

We employ a fixed-effects regression model to evaluate statistical
significance of per-cell P1V crime reductions from the hot spot program in
Pittsburgh. The units of analysis are cell-weeks, and outcomes $Y$ are Part 1
Violent (P1V) crime counts per cell. We defined a regression model (Equation
1) with a binary variable $T_{p,w}$ indicating whether partition $p$ was
selected for treatment in week $w$, $HS_{c,w}$ indicating whether cell $c$ was
selected as a hot spot in week $w$, and $D_{c,w}$ indicating the number of
proactive patrols in cell $c$ during week $w$. $HS_{c,w}\times D_{c,w}\times
T_{p,w}$ is then an interaction term between hot spot selection and treatment
dose. Fixed effect terms for partitions and weeks are $\alpha_{p}$ and
$\delta_{w}$ respectively, and $\epsilon_{c,p,w}$ terms are cell-specific
errors. Model coefficients are estimated through ordinary least squares
regression.

$\displaystyle\begin{split}Y_{c,p,w}&=\beta_{0}+\beta_{1}[HS_{c,w}\times
D_{c,w}\times T_{p,w}]\\\
&+\beta_{2}HS_{c,w}+\alpha_{p}+\delta_{w}+\epsilon_{c,p,w}\end{split}$ (1)

To minimize spillover of deterrence effects across treatment and control
boundaries, cells in the control partition but directly adjacent to treatment
hot spots were dropped from the analysis. Similarly, cells in the treatment
partition that were directly adjacent to control hot spots were dropped. The
primary coefficient of interest is $\beta_{1}$, which represents the per-cell
reduction in target crimes within treatment hot spots associated with each
additional proactive patrol. We report results for four model variants: Model
1 examines the dose-dependent treatment effect of patrols to hot spot cells
and includes week and zone-partition fixed effects. Model 2 also examines
possible changes in crime volume in cells adjacent to hot spots and in non-
adjacent cells. Model 3 estimates separate dose-dependent treatment effects
for chronic and temporary hot spots. Finally, Model 4 estimates separate dose-
dependent treatment effects for car patrols and foot patrols at chronic and
temporary hot spots. We expected car patrols to be 1/3 the duration of foot
patrols (5 minutes vs. 15 minutes per patrol), and therefore we compute
combined patrol dose as (number of foot patrols) + (number of car patrols/3)
for Models 1-3.

A concern in estimating dose-dependent treatment effects is that dose was not
randomized across hot spots. It is possible that officers may direct proactive
patrols either toward or away from cells with high incidence of P1V, thereby
affecting the dose-dependent treatment effect coefficient. We refute this
possibility by computing the correlation between average number of proactive
patrols when treated and average P1V when control for the 464 cells that are
selected as both treatment and control at least once in the study period, and
find null correlations for all patrol types (foot patrols vs. P1V: r=0.017;
car patrols vs. P1V: r=-0.009; foot + car patrols vs. P1V: r=-0.000). See SI
Table S6 for the full table of dose-dependent regression results with P1V
outcomes. We report non-dose-dependent results in SI Table S7, and also
provide results in SI Table S8 on Part 1 Property crimes, to demonstrate that
crime prevention was not limited to the targeted P1V crimes.

#### Model 1

The coefficient on Hotspot × Treatment Dose is negative and statistically
significant ($\beta$=-0.0009, 95% CI=[-0.001, -0.000], p<0.001), while the
coefficient on the Hotspot indicator variable is positive and statistically
significant ($\beta$= 0.0431, 95% CI=[0.040, 0.046], p<0.001). Taken together,
these results indicate that cells selected as a hot spot experience higher
crime volume on average, but treating these areas with additional proactive
patrols tends to decrease crime relative to hot spots that do not receive
patrols.

#### Model 2

We find a weakly statistically significant reduction in P1V crimes in cells
adjacent to hot spots ($\beta$=-0.0014, 95% CI=[-0.003, 0.000], p=0.082),
providing some evidence for a small degree of spatial diffusion of crime
deterrence benefits to areas surrounding predicted hot spots, and no evidence
for crime displacement. Note that this result represents the effect of being
adjacent to a treatment hot spot regardless of treatment dose at that hot
spot. We find no statistically significant change in P1V crime in cells not
adjacent to hot spots ($\beta$=-0.0001, 95% CI=[-0.001, 0.000], p=0.895).

#### Model 3

The coefficients on Hotspot × Treatment Dose for both chronic and temporary
hot spots are negative (indicating a reduction in crime volume from treatment)
and statistically significant (chronic hot spots: $\beta$=-0.0015, 95%
CI=[-0.002, -0.001], p<0.001; temporary hot spots: $\beta$=-0.0008, 95%
CI=[-0.001, 0.000], p=0.024). Differences in the estimated treatment effects
in chronic and temporary hot spots provide evidence that equivalent patrol
protocols to chronic versus temporary hot spots may result in differing crime
deterrence benefits.

#### Model 4

For foot patrols, the coefficients on Hotspot × Treatment Dose for both hot
spot types are negative (indicating a reduction in crime volume from
treatment) and statistically significant (chronic hot spots: $\beta$=-0.0031,
95% CI=[-0.005, -0.002], p<0.001; temporary hot spots: $\beta$=-0.0025, 95%
CI=[-0.004, -0.001], p=0.001). In contrast, car patrols do not appear to
provide P1V crime prevention (chronic hot spots: $\beta$=0.0002, 95%
CI=[0.000, 0.001], p=0.47); temporary hot spots: $\beta$=0.0006, 95%
CI=[0.000, 0.001], p=0.094). Since car patrols and foot patrols are positively
correlated (r=0.49), dropping car patrols from Model 4 reduces the estimated
dose-dependent effect size of foot patrols on P1V crime to $\beta$=-0.0027
(p<0.001) and $\beta$=-0.0016 (p=0.003) for chronic and temporary hot spots
respectively.

### Overall reduction in crime volume from proactive patrols

The observed differences in P1V crimes between control and treatment hot spots
are reported in Table 1. Within all hot spots, we measured 24 fewer P1V crimes
in treatment hot spots relative to control hot spots, or a 25.3% reduction in
P1V crimes per hot spot cell ($n_{treatment}$ = $n_{control}$ = 1872 cell-
weeks). We see a larger percentage reduction in temporary hot spots for P1V
crimes, with a reduction of 33.3% in temporary hot spots (n=936) and 23.8% in
chronic hot spots (n=936). In cells adjacent to hot spots (queen’s case), we
measured an 8.6% decrease in P1V crimes per cell in treatment areas. While the
numbers of crimes reduced are small, their impact in terms of cost avoidance
to society and victims is large compared to the cost of proactive police
patrols. In Table 1, we compute that overall there were $3,411,328 in crime
costs avoided, while the cost of patrols was less than $300 thousand (see SI:
Evaluation of Program Impacts). Counts and standard deviations of P1V crimes
in treatment and control cells are reported in SI Table S5. We observe a
statistically significant reduction in the number of African American and
other non-white victims of P1V crime, with 25 (39.7%) fewer victims in
treatment vs. control cells over the study. Prevention of P1V crimes with
multiple victims accounts for a higher proportional reduction in minority
victims than the 25.3% reduction in overall P1V.

Table 1: Observed differences in Part 1 violent (P1V) crime counts between
control areas and treatment areas over 12 months of proactive hot spot patrols
(November 6, 2017 – November 4, 2018).

2* | Part 1 violent crimes
---|---
| % Change | # of Crimes |  Est. Costs Avoided*
Chronic Hot Spots | -23.8% | -19 | $2,701,891
Temporary Hot Spots | -33.3% | -5 | $709,437
All Hot Spots | -25.3% | -24 | $3,411,328

*Costs per P1V crime computed based on costs to individuals and society from individual component crimes reported in (39) and inflated to 2018 dollars. Note that the cost of the proactive police patrols was less than $300 thousand. See SI Table S9 for costs of individual component crimes.

Figure 1: Hot spot footprint in Pittsburgh over 12 months for two types of hot
spots, chronic hot spots predicted using a long-term moving average (left),
and temporary hot spots predicted using a multilayer perceptron (right). Cells
are highlighted if they were selected as a hot spot at least once in the study
period. Boundaries indicate the six police zones.

### Spatial dispersion of chronic and temporary hot spots

As discussed in SI: Evaluation of Prediction Models on Historical Data, the
temporary hot spot model was selected to increase spatial dispersion of top-
selected hot spots as measured by a selection entropy index. Figure 1 shows
the hot spot footprints for chronic and temporary hot spots across the
12-month period of evaluation. Cells are flagged in red if they were included
as a hot spot at least once in the study period. As expected, the chronic hot
spots selected using a one-year moving average remained fairly static, only
occurring in a small fraction of the city over 12 months (recall that there
were an equal number of chronic and temporary hot spots during the study
year). By contrast, temporary hot spots were spread over five times the area
of chronic spots over the same period (9.0% vs. 1.8% of the city area).

### Arrests during hot spot patrols

Over-policing is unnecessarily large amounts of police control and arrests,
particularly for racial minority or economically disadvantaged communities
(40). Over-policing is especially a concern for “broken window” crimes that do
not threaten public safety and can involve officer discretion in enforcement,
such as consumption of alcohol on streets, possession of small amounts of
marijuana, disorderly conduct, loitering, disturbing the peace, and
jaywalking. Over-policing results from racial profiling, institutional biases
ingrained in the culture or policies of a police department, or personal
biases of officers. In contrast, Pittsburgh police policy for proactive
patrols is to engage with the local residents and employ community-oriented
policing (for example, warning of possible violent crimes and gathering
information on potentially dangerous locations). To assess the impacts of the
hot spot program on potential harms from over-policing, PBP crime analysts
(41) tabulated the number of arrests occurring during hot spot patrols. In the
time window during and 30 minutes after the over 24,000 hot spot patrols in
treatment hot spots conducted during the study year, only four arrests
occurred while on patrol. Two of these were on-view arrests for minor drug
offenses, and the remaining two were for 911 calls for service to domestic
disturbances.

## Discussion

The results from this field study provide statistically significant evidence
that a small-scale hot spot program based on proactive patrols, targeting only
0.5% of Pittsburgh, leads to measurable reductions in serious violent crime in
those areas, while avoiding over-policing arrests of racial minorities. These
results contribute to the ongoing debate around proactive policing, showing
both benefits and mitigation of certain potential harms when community-
oriented policing practices are employed. However, determining whether to
conduct hot spot policing in a given jurisdiction requires additional studies
to assess the impact of proactive patrols on police-community relations and to
rule out other potential harms to individuals related to more frequent
interactions with police. If policy-makers assess that the benefits of such a
program outweigh the risks, adequate oversight procedures should be created to
ensure that proactive patrols follow best practices, avoiding aggressive and
harmful policing practices, and to evaluate whether the program continues to
achieve crime prevention benefits while avoiding unintended harms.

A reduction of 24 P1V crimes is 1.6% of observed citywide violent crime during
this period, corresponding to an estimated $3.4 million in avoided crime costs
to citizens and society. While the crime reduction is small with respect to
citywide crime volume, it results from a relatively small amount of effort per
patrol shift (an average of 35.5 minutes of hot spot patrol per day). It is
reasonable to expect that hot spot-based policing would experience diminishing
marginal benefits as the number of patrolled hot spots grows, but the small
dosage of hot spot patrolling evaluated in this study and the steepness of the
prediction tradeoff curve beyond 0.5 percent area on the horizontal axis
nonetheless leave considerable capacity for scaling up the patrol program, as
would eliminating car patrols and using foot patrols only. Additional studies
are needed to evaluate the effects on crime volume of programs with different
scales and to ensure that potential undesirable impacts related to over-
policing are avoided as programs scale.

Chronic and temporary crime hot spots exhibit fundamental differences
affecting the mechanisms by which proactive patrols deter crime. Chronic hot
spots may experience elevated rates of crime for years or decades at a time.
These highest-crime areas are typically known to police, but crime volume can
remain high even in the presence of regular police patrols. By contrast,
residential areas tend to experience low baseline rates of crime, but may
represent areas where the fear of crime is highest (42, 43). Patrolling of
temporary hot spots results in a spreading out of police resources to
residential areas away from commercial zones where crime is chronically high.
Results from this study indicate that patrols to temporary hot spots provide a
meaningful reduction in crime counts, despite having significantly less
overall crime volume than chronic hot spots.

This study provides evidence that hot-spot-based predictive policing has
potential for substantial societal benefits through the prevention of serious
violent crimes. However, predictive policing systems also present non-trivial
risks of harms resulting from over-policing or under-policing, or potential
exacerbation of societal inequalities. In SI: Best Practices for Hot Spot
Prediction and Prevention, we discuss a set of best practices for assessing
and mitigating risks of bias and over-policing in predictive policing systems.
These best practices include but are not limited to (1) using beneficial,
community-oriented patrol protocols rather than aggressive enforcement, (2)
appropriately choosing minimally-biased target variables and predictor
variables for prediction models, (3) regularly vetting prediction models
across multiple evaluation criteria, (4) ensuring geographic dispersion of
targeted patrols with a dynamic prediction model, (5) considering impacts of
the scale and intensity of a targeted intervention, and (6) designing a
predictive policing system around place-based rather than person-based
predictions. We encourage future researchers and users of predictive policing
systems to carefully consider not only the potential impacts of a program on
crime reduction, but also the other consequences, intended and unintended.

More empirical studies are needed to understand the potential impacts on crime
volume and other citizen outcomes from hot spot programs of different scales
and across cities. This study focuses on hot spot models that rely on reported
crime data, and additional work is needed to understand the impacts of
specific areas and communities being overrepresented or underrepresented in
reported crime data. Further research is also needed to identify what patrol
activities and strategies are most effective at fostering goodwill among the
communities being policed in addition to providing crime reduction benefits.
Ultimately, designing a predictive policing system that is both transparent
and equitable is essential for long-term support from the general public.

### Data

For the purpose of evaluating alternative crime forecast models and simulating
a setting in which police command staff and crime analysts make weekly
decisions about where to distribute proactive patrols, we relied only on data
sources readily available to PBP for one-week ahead crime forecasts.
Specifically, we obtained two data sets spanning five years of historical data
from June 1, 2011 through June 1, 2016. The first data set is compiled from
the City of Pittsburgh’s Automated Police Reporting System (APRS) and contains
data on all 206,150 crime incidents recorded by the PBP within the five-year
period of analysis. For each incident, the data set contains an associated
crime code corresponding to the FBI Uniform Crime Reports (UCR) hierarchy.
Criminal offenses are divided into two primary groups in the UCR hierarchy;
Part I offenses represent the most serious categories of crime that are likely
to be reported to police, and Part II crimes include less serious offenses.
Part I crimes are further divided into two categories: violent crimes (P1V)
and property crimes (P1P). SI Table S1 reports crime counts for the seven
component crime types which make up all Part 1 offenses in the APRS data.
(Though arson is also categorized by the FBI as a Part 1 offense, data on
arson were not provided by PBP.)

Historical biases in policing activity disproportionately affect minority
communities, and relying on historical crime reports could therefore result in
a further entrenchment of these biases. Brantingham et al. (44) examine
whether biases in algorithmic place-based policing result in discriminatory
consequences for minority groups and find no significant difference in arrest
rates across racial-ethnic groups between treatment and control areas. Still,
feedback loops are possible when relying on victimless crime data, such as
drug arrests, for hot spot selection, in which case police have more
discretion on enforcement than with crimes with victims (45). Areas may be
initially selected for increased patrols due to high volume of historical
victimless crime reports; these areas subsequently generate additional reports
of crime due to increased police presence, then the same areas are again
selected as hot spots, and so on. To mitigate this issue, we selected hot
spots based on predictions of P1V crimes, which consist of serious violent
offenses including homicide, rape, robbery, and aggravated assault. Reporting
of these offenses is less likely than other crime types to depend on presence
or absence of police in an area. Predictions of these crimes are therefore
less prone to feedback loops resulting from increased patrols.

The second data set provided by PBP includes information on 911 calls for
service to the Pittsburgh police, totaling approximately one million calls
over the five-year period of analysis. This data includes the time and place
that a call was made, as well as a code indicating the reason the call was
made and a descriptive field indicating the outcome of the call. Taken
together, the APRS data and CAD data provide a comprehensive picture of when
and where crimes are being reported in Pittsburgh. An important caveat is that
crimes that go unreported to police are not represented in these data. This
analysis therefore evaluates prediction methods at forecasting crimes as they
are reported to police, with the purpose of simulating one-week-ahead
forecasts of reported crime made by police analysts.

### Selection of Prediction Methods

To understand the tradeoffs between various prediction methods and model
specifications and to design an appropriate process for weekly hot spot
selection, we evaluated the performance of a set of ten prediction models on
the five years of historical crime data obtained from the PBP. Results from
this analysis directly informed the choice and design of prediction models
used in the field study of a hot-spot-based predictive policing program in
Pittsburgh.

We divided historical APRS and CAD observations into a two-year model
calibration period (June 1, 2011 through June 2, 2013) and a three-year
evaluation period (June 3, 2013 through June 1, 2016). We conducted rolling
one-week-ahead forecasts of P1V crime counts over the entire evaluation period
to simulate crime analysts making weekly forecasts for hot spot selection.
Input features provided to the models varied by model, but can include lagged
counts of the target variable, and lagged counts of various “leading
indicator” events which may be predictive of the outcome variable, namely
other crime types or categories of 911 calls. Models were retrained throughout
the evaluation period using a moving window of two years of training data,
allowing models to adapt to changes in crime patterns to make optimal
predictions. We compared ten prediction methods that have demonstrated success
on forecasting crime counts or other types of spatiotemporal count data in
previous studies: within-cell moving averages, kernel density estimation,
L1-regularized logistic regression with lagged count features, L1-regularized
logistic regression with crime cluster features, Gaussian process regression,
univariate self-exciting point process modeling, self-exciting point process
modeling with spatial covariates, multilayer perceptrons with lagged count
features, multilayer perceptrons with lagged count and local neighborhood
features, and convolutional neural networks. Models were evaluated on the
prediction performance as well as equity in crime deterrence benefits, as
measured by the spatial dispersion of top-predicted areas. A full discussion
of the comparison of prediction methods is provided in SI: Evaluation of
Prediction Methods on Historical Data.

Based on the outcomes of the empirical comparison of prediction methods, we
determined that using a single prediction model for hot spot selection would
not perform well on the competing objectives of (1) prediction accuracy and
(2) equitable distribution of hot spots throughout the city. A hot spot
program with the sole aim of capturing the most crime within hot spots would
likely be very static, with the same small set of chronic hot spots being
selected for patrols each week. Based on the empirical results, we therefore
chose separate prediction models for selecting weekly chronic and temporary
hot spots for the field experiment. Chronic hot spot cells were selected using
a cell-specific one-year moving average of crime counts. Temporary hot spot
cells were selected using a fully connected feedforward neural network which
predicts a difference from the long-term moving average within each cell. The
temporary hot spot model includes time lags of target crimes, leading
indicator crimes, and 911 call types (see SI Table S2 for a full list of
leading indicator variables). Inputs to the hot spot models relied on the APRS
and CAD data sets provided by PBP, refreshed on a weekly basis.

We acknowledge the generosity of the Richard King Mellon Foundation for
funding this study. We also acknowledge Chief Scott Schubert and Deputy Chief
Thomas Stangrecki for their leadership in developing the hot spot program.

## Supplemental Information Appendix

## Evaluation of prediction methods on historical data

Table 2 reports crime counts for the seven component crime types which make up
all Part 1 offenses in data provided by the Pittsburgh Bureau of Police (PBP)
from June 1, 2011 through June 1, 2016. Part 1 Violent (P1V) crimes were
chosen as the target variable for prediction and model selection.

We compared ten prediction models that have demonstrated high performance on
forecasting crime counts or other types of spatio-temporal count data in the
literature. The training and prediction framework was standardized across the
ten models, with model parameters tuned in a two-year calibration period from
June 1, 2011 through June 2, 2013, and model performance for one-week-ahead
predictions assessed in a three-year evaluation window from June 3, 2013
though May 29, 2016. Leading indicator variables for multivariate models are
reported in Table 3. The models considered were:

  * •

Within-Cell Moving Average (MAVG). A window length of fixed size was selected
to optimize prediction accuracy for the calibration period. At prediction
time, target crimes are tabulated for each spatial unit over the entire time
window ending at the present time period.

  * •

Kernel Density Estimation (KDE). A density surface of target crimes was
estimated from spatial occurrences of the target variable over a fixed time
window using a Gaussian kernel. Kernel bandwidth and time window size were
chosen to optimize prediction accuracy for the calibration period.

  * •

Logistic regression with lagged count features and $L1$-regularization (LASSO-
LC). A logistic regression model with $L1$-regularization was trained using
lagged count features from leading indicator variables made up of individual
crime types and 911 call categories. Counts were converted to binary class
labels indicating presence or absence of crime, and the regularization
parameter was selected to optimize prediction performance for the calibration
period.

  * •

Logistic regression with crime cluster features and $L1$-regularization
(LASSO-CC). Spatiotemporal clusters of leading indicator crimes were detected
using the Fast Subset Scan approach of Neill (46). Cluster characteristics
(size, duration, and intensity) were used as features for a sparse logistic
regression model trained and tuned identically to LASSO-LC.

  * •

Gaussian Process Regression (GP). A Gaussian process regression model was
trained assuming separable covariance across time and the two spatial
dimensions. The isotropic squared exponential covariance function was applied
for all three dimensions, and counts for leading indicators were included as
linear terms in the mean function (47, 48). GP hyperparameters were tuned to
optimize prediction performance for the calibration period.

  * •

Univariate Self-Exciting Point Process (SEPP-UNI). As presented by Mohler (7),
a univariate self-exciting point process model was trained in which a set of
background crimes of the target type are assumed to occur independently across
time and space according to a stationary Poisson process, and subsequently
result in elevated predicted risk for offspring events in the spatial
vicinity. Background and offspring event rates are estimated iteratively
through variable-bandwidth kernel density estimation.

  * •

Self-Exciting Point Process with spatial covariates (SEPP-MULTI). An extension
of the SEPP-UNI model was trained to allow counts from leading indicator
crimes to contribute to the overall intensity function of the target crime,
following the training procedure described by Reinhart (49).

  * •

Multilayer Perceptron (MLP) with cell-specific lagged count features (MLP-LC).
A densely-connected feedforward network was trained to predict target crime
counts from 52 weeks of lagged crime data for a set of leading indicator crime
types (50). Model architecture was selected based on prediction accuracy in
the calibration period, with a single hidden layer and ten hidden units
outperforming other variants under consideration.

  * •

MLP with lagged count and local neighborhood features (MLP-NH) Additional
neighborhood features were added to the MLP-LC model, consisting of lagged
crime counts for leading indicators within the eight cells (queen’s case)
adjacent to the target cell for each observation.

  * •

Convolutional Neural Network (CNN). A convolutional neural network was adapted
to predict target crime counts from a rectangular grid overlay of the city and
lagged target crime counts within each cell. The CNN is designed to identify
spatial patterns of target crimes which appear throughout the city and are
predictive of future crime, rather than learning spatial structure
individually within neighborhoods or other micro-areas.

A variety of evaluation metrics are available for measuring the relative and
absolute performance of different prediction methods. For this analysis, the
evaluation framework was designed to align closely with police goals for a
hot-spot-based predictive policing program. In the place-based forecasting
setting, a natural approach to assessing performance of crime prediction
methods is to measure the prediction accuracy as the percent of crime volume
predicted across a range of forecasted areas (28, 51, 34). A prediction
tradeoff curve plots the crime volume captured versus percentage area of a
police jurisdiction forecasted over a range of area percentages from zero up
to an upper limit determined by patrol resource constraints. The curve
provides a visual depiction of the benefit/cost tradeoff faced by police when
allocating resources to proactive patrols. If a single model outperforms
others everywhere along the tradeoff curve (i.e., is the highest curve), then
that model is likely to perform best regardless of how much area is ultimately
selected for crime prevention.

We define a new measure, hot spot selection entropy, to evaluate the spatial
dispersion of top-predicted areas from each prediction model. For a given
prediction model, let $n_{i}$ be the number of times grid cell $i$ appears in
the top-predicted 1% of all $N$ cells across all forecast periods, and define
$p_{i}$ as the proportion of total hot spot selections occupied by cell $i$:

$p_{i}=\frac{n_{i}}{\sum_{j=1}^{N}n_{j}}$

Then hot spot selection entropy $H$ is calculated as the entropy of this hot
spot distribution across grid cells:

$H=-\sum_{i=1}^{N}p_{i}\log_{2}p_{i}$

Hot spot selection entropy is highest for predictions that lead to a uniform
distribution of hot spots across the city, and lowest for prediction methods
that choose the same hot spots in every time period. This statistic therefore
provides a useful point of comparison relating to the geographic dispersion of
hot spots selected by crime forecasting models.

Prediction tradeoff curves for all ten forecasting models on predicting P1V
crimes are presented in Figure 2. All models under consideration demonstrate
some effectiveness at predicting crime, with all curves showing similar
performance at the smallest levels of area forecasted within the city. As more
area is forecasted, the relative performance of the models becomes clearer,
with all models experiencing diminishing marginal rates of crime predicted as
more area is forecasted. The MAVG model shows the best prediction performance
in the top-predicted areas, from zero up to 3% of the city area forecasted.
Police departments are typically only able to effectively patrol 1-3% of a
city in a hot spot policing program, thus these results indicate the
relatively simple MAVG method is likely the best candidate for selecting hot
spots that capture the maximum amount of crime on average. With the exception
of the relative poor performance of the SEPP-UNI and LASSO-CC models, most of
the prediction models performed fairly similarly within the 0-3% range of
feasible areas shown in Figure 2. Although some of the models evaluated here
are considerably more difficult to design, tune, and train than the MAVG
model, it seems that the additional complexity of these models does not
improve prediction performance within these feasible levels of patrol.

Table 4 reports summary statistics from the comparison of prediction methods
using prediction curves of Figure 2. The partial area under the tradeoff curve
(pAUC), analogous to the pAUC of receiver operating characteristic (ROC)
curves, reports the area under the tradeoff curve up to 1% of the city area
forecasted. The pAUC results are a measure of predictive accuracy which relate
directly to feasible levels of patrols that may be dispatched to the top 1% of
hot spots selected by these models. As depicted visually by the prediction
tradeoff curves, predictions from the MAVG model give the highest pAUC at the
1% level compared with all other models. This high level of prediction
accuracy comes at the expense of decreased hot spot selection entropy (H)
values. The MAVG model has among the lowest entropy values across models,
indicating that the same cells are selected repeatedly in the top 1% of
predictions for this model. This lack of spatial dispersion of predictions is
unsurprising given the design of the MAVG model, which leverages only long-
term trends in crime to make predictions. The MLP-LC model provided the
greatest variance in top-predicted cells, with hot spot selection entropy of
8.42 over the evaluation period. These results indicate that for a hot spot
program where prediction accuracy and equity of proactive patrols are both key
objectives, an approach that leverages multiple models is necessary to achieve
good performance on both metrics simultaneously.

Table 5 reports the percent of hot spot selections occupied by frequently-
selected locations for a hot spot program targeting 1% of a city’s total area,
which provides an intuitive basis for understanding how frequently the top-
selected hot spots change over time across models. Even the MLP-LC model,
which had a high hot spot selection entropy relative to other methods, results
in predicted hot spots that persist for long periods of time, with 43.6% of
hot spot selections occupied by locations that remain hot spots for greater
than 75% of the study period.

Through discussion with PBP command staff, we identified an objective to
predict temporary hot spots, which represent short-term flare-ups over
baseline levels of crime. In order to predict temporary flare-ups in target
crimes throughout the city, we modified the MLP-LC model by tweaking the
target variable for prediction. MLP-DIFF is identical to MLP-LC in structure
and inputs, but the outcome variable for prediction is changed from total
observed crime counts to the difference between observed counts and a one-year
moving average of target counts within each cell. The target variable is
clipped at zero to prevent negative observed outcomes and predictions. The
predictions from MLP-DIFF no longer represent the predicted number of target
crime counts at each location, but instead represent the predicted positive
difference from baseline levels of crime. Although the MLP-DIFF model results
in lower prediction accuracy with respect to total crime captured, the hot
spot selection entropy for this model is 10.53, much higher than the highest-
entropy model considered in the previous section. Further, Table 5 indicates
that the MLP-DIFF model results in top-predicted areas persisting for much
shorter periods of time than the MLP-LC and MAVG models.

Based on this evidence that the within-cell moving average (MAVG) and MLP-DIFF
model address different police objectives for a proactive patrol program, we
selected these two models for separate identification of chronic and temporary
hot spots respectively. Despite the change in prediction interpretations for
the MLP-DIFF model, we can still examine the prediction tradeoff curve and hot
spot selection entropy from the temporary hot spot model to compare it with
models predicting raw counts. In Figure 3, we show the tradeoff curves for the
MAVG and MLP-DIFF models, as well as a composite curve that represents a
combined chronic-temporary hot spots program with equal numbers of chronic
(MAVG) and temporary (MLP-DIFF) hot spots. The composite curve is constructed
to provide the tradeoff between the overall most accurate model, MAVG, and the
composite model at any percentage area on the horizontal axis. From about 0.5%
to 1% area, the vertical distance between the MAVG and composite curve is
approximately constant, 1.5% prediction accuracy, representing the prediction
accuracy lost by adopting the composite curve instead of MAVG. Of course, the
benefit from this loss is a substantial increase in spatial dispersion of
crime prevention services by police.

## Evaluation of hot spot program impacts

We report number of cell-weeks and counts and standard deviations of P1V
crimes in treatment and control cells for chronic and temporary hot spots in
Table 6. Table 7 shows full regression results estimating dose-dependent
treatment effects on P1V crimes in hot spots. We report results for four model
variants: Model 1 examines the dose-dependent treatment effect of patrols to
hot spot cells and includes week and zone-partition fixed effects. Model 2
additionally examines possible changes in crime volume in cells adjacent to
hot spots and in all other cells (cells not selected as a hot spot and not
adjacent to a hot spot). Model 3 estimates separate dose-dependent treatment
effects for chronic and temporary hot spots. Finally, Model 4 estimates
separate dose-dependent treatment effects for car patrols and foot patrols on
chronic and temporary hot spots. The interaction terms with Dose variables
represent the estimated dose-dependent treatment effect to hot spots, while
the interaction terms with the Treatment variable represent the treatment
effect of being in a treatment partition (either adjacent to or not adjacent
to a hot spot).

We additionally provide non-dose-dependent regression results in Table 8
estimating treatment effect of a cell being displayed to patrol officers as a
hot spot, regardless of the observed number of proactive patrols to the
location while selected as treatment. The interaction terms with the Treatment
variable represent the treatment effect of being selected as a hot spot for
hot spot cells, and the effect of being in a treatment partition for cells
adjacent to or not adjacent to a hot spot. While P1V crimes represent the
primary target for proactive patrols, we additionally provide P1P results in
Table 9 as evidence that crime prevention benefits are not limited to the
targeted P1V crimes. Model 3 indicates that although proactive patrols
targeted violent crime hot spots, patrols to chronic hot spots resulted in a
statistically significant reduction in property crime in those areas. This
effect on property crime was not observed in temporary hot spots, as these
areas are less likely than chronic hot spots to be located in highly
trafficked commercial areas where high levels of property crime tend to occur.

Table 10 shows estimates of per-offense costs to society as reported by
McCollister et al. (39). Costs were inflated from 2008 dollars to 2018 dollars
using the CPI inflation rate reported by the U.S. Bureau of Labor Statistics.
We estimate the cost of proactive patrols overall to be less than $300
thousand, as follows. The 2018 PBP budget for uniformed officers below the
rank of sergeant was $48.5 million for 755 officers with an average cost per
officer of $64,218, which we scale up by 20% (to $77,062) to additionally
account for employment benefits provided to officers. Assuming 2,080 hours per
officer per year, the cost per hour and officer was $37.05. The hot spot
program had 7,744 hours of patrol during the experimental year and thus cost
$286,906. The benefit/cost ratio was 11.9 ($3,411,328 in benefits generated
from $286,906 in costs).

## Equity in the allocation of crime prevention services by police

The field of analytical ethics addresses what governmental programs should do
in regard to equitably allocating scare resources. This section applies
analytical ethics, as espoused by Anthony Culyer (32) in regard to
governmental health care programs, to the case of crime prevention by
municipal police.

Culyer provides two preconditions for a governmental program to be considered
for adoption. First, the program must be instrumental, a necessary condition
if a more ultimate need is to be met. We argue that public safety, including
crime prevention, is essential for the pursuit of happiness in other aspects
of life as is health care. The field experiment of this paper provides
statistical and practical evidence that the Pittsburgh hot spot program
reduced serious violent crime. Second, only programs that are cost effective
should be considered. The Pittsburgh program meets this requirement with a
benefit/cost ratio of 11.9.

Culyer argues that need for a service is the most relevant factor for
equitable allocation of scarce resources in a program. He provides two
principles for meeting needs: “…that like needs should receive like attention
and resources (horizontal equity) and greater needs should receive greater
attention and resources (vertical equity).” Together these principles provide
guidelines for the design of equitable programs given resource limitations.
For example, in a crime hot spot program, some locations may need large
allocations of patrol resources while other locations need only small
allocations, and yet others may need none at all. A program that only targets
some areas, or targets some areas substantially more often than others, could
be considered “equitable” if its allocation of resources meets these needs.
Nevertheless, two critical questions are left unanswered: how do we define
need, and how should resources be allocated as a monotonically increasing
function of need?

In the case of the hot spot program, a community’s need for proactive patrols
refers primarily to reducing future instances of serious violent crime, yet
should also consider the other potential impacts of policing on the well-being
of the individuals being policed. While precisely quantifying need is
challenging, it is clear that areas which would have a large number of serious
violent crimes in the absence of crime prevention services are in greater need
of such services. Thus we employ predictive models, estimating the expected
number or probability of serious violent crimes that will occur in the next
forecast period. To provide equitable crime prevention, we must first have
models that are as accurate and unbiased as possible, necessitating our
rigorous evaluation of multiple alternative models on historical data. We also
quantified, through a field experiment, to what extent serious violent crimes
would be reduced (and thus, needs met) through proactive patrols, showing that
the proportional reduction is greater for temporary hot spots. Temporary hot
spots also tend to target different (more residential and less commercial) and
more dispersed areas than chronic hot spots, and thus might be preferred by
policy makers for other reasons. This motivated us to provide two separate and
largely independent forecast models for chronic and temporary hot spots as
policy levers, allowing city policy makers to decide the number of chronic
versus temporary hot spots when allocating crime prevention services.

Given the prediction scores as an estimate of need, we must still consider how
resources can be best allocated to achieve horizontal and vertical equity. In
regard to horizontal equity, all areas of a city should be able to receive
prevention resources whenever serious violent crimes are likely to occur in
the near future, thus reducing the likelihood that such crimes will take
place. In regard to vertical equity, more resources should be allocated to
areas with higher prediction scores (i.e., higher estimated probability of
future crimes), but it is clear that some such allocations are preferable to
others. For example, at the small scale of the Pittsburgh program (0.5% of the
city with crime prevention services at a time), chronic hot spots are most
effective in crime prevention. However, an all-chronic hot spot program
concentrates police resources at the same few locations each week, leaving
needs for the rest of the city unmet. Such an allocation is suboptimal with
respect to horizontal equity, since there are many other areas which have
nearly as high scores yet receive few or no crime prevention resources.
Similarly, it is suboptimal with respect to vertical equity, in that only the
few very highest-scoring areas are differentiated from other areas in their
resource allocations. Our combined chronic and temporary hot spot program,
while still focusing resources on areas with higher prediction scores,
allocates resources to a much greater number of areas, as measured by the
footprint map which shows all hot spots that received one week or more of
crime prevention by police in a year. It also spreads resources more evenly
between these areas, as shown by our entropy measure, thus improving both
vertical and horizontal equity as compared to the all-chronic hot spot
program.

Finally, we note that for large intervention doses such as saturation patrols,
prediction scores might be insufficient to measure a community’s need for
proactive policing: we must also consider the diminishing marginal returns of
extremely frequent patrolling, as well as potential negative impacts due to
over-policing. Given the much smaller intervention doses considered here, as
well as the use of community policing to mitigate potential harms, we believe
that allocating resources separately to chronic and temporary hot spots, as a
monotonically increasing function of the prediction scores, is broadly
consistent with Culyer’s definition of equity.

## Best Practices for Crime Hot Spot Prediction and Prevention: Assessing and
Mitigating Risks of Bias and Over-Policing

The authors of this paper have listed below a number of recommended best
practices based on our more than four decades of combined experience working
with law enforcement and city leaders to develop and implement predictive hot-
spot policing systems. These recommendations are supported by scientific
evidence gathered from the field trial of predictive policing in Pittsburgh
presented in the main text, as well as our expertise and understanding of the
literature on policing and algorithmic fairness.

We believe that predictive policing has potential for substantial societal
benefits through the prevention of serious violent crimes, but also presents
non-trivial risks including the potential for (1) harms resulting from over-
policing or under-policing of minority or low income areas, and (2)
exacerbation of societal biases and inequalities, such as racial disparities
in arrest rates. Considering these risks and benefits, we believe that the
goals of predictive policing should be threefold: (1) reducing serious crimes,
especially serious violent crimes as a first priority, that have the most
substantial impacts on society; (2) improving equity in the distribution of
policing resources; and (3) minimizing harms due to over-policing. Systems
that only focus on the first goal run the risk of causing societal harms that
outweigh their benefits, as well as negatively impacting already-disadvantaged
neighborhoods and subpopulations.

We strongly encourage future researchers and users of predictive policing
systems to adopt this broader view of what a predictive policing system should
be designed to achieve, carefully considering not only the potential impacts
of a program on crime reduction, but also the other consequences, both
intended and unintended, of such systems. Such consideration should have two
aspects: (1) incorporation of best practices for system design,
implementation, and deployment, and (2) continued measurement of societal
impacts as a system operates, with iterative improvement of both the system
and corresponding policing practices to maximize benefits, minimize harms, and
improve equity.

###  0.1 Use beneficial rather than aggressive policing interventions

Perhaps the most critical factor influencing the societal impacts of a
predictive policing program is the policing intervention itself: when an area
is targeted for a hot-spot patrol, how do the patrolling officers interact
with citizens in that area? Aggressive policing practices such as broken-
windows policing, which includes strict enforcement of low-level crimes
(leading to increased arrests for minor offenses such as marijuana possession
and loitering) and frequent use of pedestrian stops, has been shown to cause
substantial harms to disadvantaged and minority communities, including adverse
impacts on health and educational outcomes (52). In our field trial of
predictive policing in Pittsburgh, we reaffirmed the Pittsburgh Bureau of
Police’s policy that officers use community-oriented policing while on
proactive patrol. In community-oriented policing, officers focus on problem
solving and citizen engagement (via foot patrols), for example, warning of
possible violent crimes and gathering information. The result was that, during
our study, very few arrests were made by hot spot officers while on patrol,
nor were arrests increased for commonly over-policed crimes.

We strongly encourage future users of predictive policing systems to think
carefully about the way in which they intervene, to avoid aggressive policing
approaches that cause detrimental outcomes to already vulnerable communities,
and to ensure that all hot-spot patrol officers are properly trained in
community-oriented policing techniques.

###  0.2 Appropriately choose the target variable for prediction

In our field trial of predictive policing in Pittsburgh, we focused on
predicting and preventing Part 1 Violent crimes: the serious crimes of
homicide, rape, robbery, and aggravated assault. In addition to representing
the types of crime which were of greatest interest to Pittsburgh law
enforcement officials and city leaders, and those with the greatest costs to
society (as estimated by McCollister et al. (39)), the choice of serious
violent crimes as the target variable also mitigates potential biases in
several ways. With the exception of domestic crimes (not considered in our
study), serious violent crimes tend to be reported to the police (53), as
opposed to victimless crimes such as drug offenses, which tend to be
discovered only if officers are looking for them.

The results of this are twofold: first, arrests for minor crimes, and
particularly victimless crimes, tend to exhibit strong racial biases, for
example, from 2001-2010, African-Americans were arrested 3.73 times as often
as whites for marijuana possession despite approximately equal rates of use
(54). Thus targeting of such crimes for prevention, in addition to being an
inefficient use of police resources, exacerbates existing societal biases
including disparities induced by current policing practices. Second, as argued
by Lum and Isaac (45), targeting victimless crimes has high potential to lead
to undesirable feedback loops, where policing in an area discovers the
presence of victimless crimes, which are then used to justify sending
additional patrols to that area, resulting in rapid amplification of
disparities. Thus, we strongly recommend targeting serious violent crimes, or
a similar quantity, rather than minor and victimless crimes.

###  0.3 Appropriately choose predictor variables to minimize bias

A number of variables commonly used as predictors in hot-spot policing have
the potential to induce biases into the predictive model, and should be
avoided. As noted above, crime offense data for victimless crimes such as drug
possession have the potential to be racially biased because of racial
disparities in arrest rates. We advise against using arrest data, which is
likewise biased by policing practices. Furthermore, using demographic data
(such as race), socio-economic data (such as poverty level), or neighborhood-
level proxies for race and socio-economic status as predictors should be
avoided; we recommend using demographic data only to evaluate systems and to
determine whether they have had disparate impacts on poor and minority
communities. In our randomized field trial of predictive policing in
Pittsburgh, our hot spot prediction models do not include socio-economic,
racial, individual person, drug possession or dealing offense, or arrest data;
they only use selected crime offense and 911 emergency call data. Crime
offenses include all incidents in which a crime is reported, whether or not
there was an associated arrest. The chosen sources of data are likely to be
less biased than those for arrests and victimless crimes, but are not
necessarily unbiased; thus, whenever possible, additional sources of bias
(such as reporting biases in 911 call data) should be assessed and mitigated.

###  0.4 Regularly vet prediction models on multiple evaluation criteria

Selecting a prediction model for identification of hot spots requires
evaluating candidate models on each of the multiple objectives of a predictive
policing program. First and foremost, predictions should reflect actual
underlying crime patterns, with selected hot spots capturing meaningful
proportions of total crime. Prediction tradeoff curves show the full tradeoff
between crime volume captured by predicted hot spots and area treated by a
hot-spot policing program, enabling comparison of models on predicted crime
volume across hot-spot programs of varying scales. Candidate models may vary
considerably in their mechanism of prediction, with some capturing long-term
crime trends and others responding to short-term shifts in crime patterns.
Measuring the geographic dispersion of predicted hot spots across forecast
periods indicates how dynamic a hot-spot policing program will be, and whether
a given prediction model can equitably distribute police effort across areas
that could benefit from additional community-oriented policing. Finally, the
demographic and neighborhood characteristics of hot spots from candidate
prediction models indicate which models might contribute to over-policing and
provide critical context for designing beneficial policing interventions.

Crime patterns shift over time and in response to police interventions. Any
operational prediction model(s) underlying a hot-spot policing program should
be periodically reevaluated on the full set of objectives outlined above, to
ensure that predicted hot spots are continuing to provide intended benefits.
Ideally, regular vetting of operational models is conducted by both (1)
analysts with technical proficiency in predictive modeling, and (2) law
enforcement officers with awareness of local crime and neighborhood
characteristics. Leveraging expertise in both the technical underpinnings of
hot-spot prediction and local crime patterns enables periodic course
correction to improve and maintain effectiveness of operational models over
time.

###  0.5 Ensure the geographic dispersion of targeted patrols; use chronic and
temporary hot spots to balance efficacy and equity

We believe that geographic dispersion of patrols, spreading police presence
more equitably according to need throughout the city, is a necessary component
of equity in policing. Placing too many police resources in a given area has
the potential to harm both that area (due to risks of over-policing) as well
as other areas (which are not receiving sufficient resources for prevention of
serious violent crimes).

For our field study of predictive policing in Pittsburgh, conscious of the
need to balance crime prevention with equitable resource distribution while
avoiding over-policing, we assessed the impacts of patrolling two different
types of crime hot spots, chronic and temporary. As compared to chronic hot
spots, temporary hot spot policing improved simple measures of equity and
avoidance of over-policing: we observed much greater dispersion of patrols
across the city, and each temporary hot spot was treated no more than 15% of
the time over the 52-week study period. Dispersion of patrols was
substantially lower for chronic hot spots, and some areas would be targeted
essentially every week by an operational chronic hot spot program without
randomization. (In our cross-over experimental design, chronic hot spots had
the maximum potential of being targeted for patrols half the time.)

The desired trade-off between temporary and chronic hot spots is not entirely
clear: temporary hot spots increase equity, but their effectiveness may not
scale to larger predictive policing programs. More generally, both temporary
and chronic hot spots seem to be potentially useful targets for predictive
policing, for small-scale programs with attention paid to equity. In addition
to the use of temporary hot spots to spread prevention benefits across the
city, we encourage randomization of patrols among chronic hot spots with
similar predicted probabilities, to reduce disparities between communities
with similar policing needs.

###  0.6 Consider impacts of the intensity and scale of the targeted
intervention

Our randomized field trial of predictive policing in Pittsburgh demonstrates
the potential to achieve small but significant crime reductions through a
small-scale, targeted policing program. So one might consider trying to gain
more crime reduction through a larger-scale program (intervening on more hot
spots) and/or through higher patrol intensities (targeting more patrols per
hot spot). However, there are several reasons to carefully assess societal
costs and benefits before scaling up. First, a larger-scale program may simply
be infeasible given police resources. In our Pittsburgh study, which targeted
patrols using roughly half of patrol officers’ discretionary time, our desired
intensity of treatment was to average one additional 15-minute community-
oriented patrol per 8-hour police shift, but patrol intensity averaged 79% of
target patrol duration (and 62% of target patrol counts) over the study
period. In this setting, increasing the number of hot spots would spread
resources too thinly to achieve the desired prevention effect. Second, even
given sufficient police resources, increasing the number of hot spots will
likely require targeting areas with lower predicted crime rates than the
“hottest” hot spots, resulting in fewer crimes prevented per hot spot. We note
that the tradeoff curves of Figures 2 and 3 are still fairly steep beyond 0.5%
area, both for the MAVG model for chronic hot spots and for the combined
model, indicating some capacity to scale up the program. Furthermore, given
that the field study showed that only foot patrols (not car patrols)
significantly reduce P1V, the possibility exists of increasing effectiveness
with the same level of patrols by using only foot patrols. Third, increasing
the number of hot spots may decrease the accuracy of crime prediction,
particularly for temporary hot spots. Fourth, increasing the number of hot
spots without explicitly considering geographic dispersion increases the
likelihood that any given area will be repeatedly targeted with patrols, thus
increasing the risk of negative impacts due to over-policing. Similarly,
increasing patrol intensities in a given area would be expected to have
diminishing marginal returns (the impact of adding an extra unit decreases as
more crime is prevented) as well as increasing marginal costs (both due to
risks of over-policing as well as increased disparities between targeted and
non-targeted areas).

###  0.7 Avoid introducing inequalities via experimental design

When conducting controlled experiments to assess the impacts of new policing
practices, including predictive policing, inequality could arise from the
long-term, arbitrary assignment of some areas to a treatment group and some
areas to a control group, including but not limited to over-policing of the
treatment group and/or under-policing of the control group. Thus we recommend
the use of cross-over experimental designs whenever possible to balance the
total amount of targeted policing effort across the entire study area. In this
study design, each zone is divided into subareas assigned to, say, group A and
B, of roughly equal crime levels for the crimes being prevented. The subareas
can number more than two and should be bounded by locations with low crime
rates to protect against spatial contamination of control hot spots by nearby
treatment hot spots. Then in subsequent periods, or selected randomly, A and B
alternate being treatment versus control areas for locations of hot spots.
Generally, the effect of treatment on a hot spot has a residual period on the
order of hours after patrol, so that temporal contamination is not an issue
between time periods. If, however, there is a general treatment effect lasting
more than a period of treatment, the cross-over design fails. We believe that
a general effect will not take place during an experimental period, but could
be possible for extended periods of treatment.

###  0.8 Systematically measure impacts, both intended and unintended

For operational deployment of predictive policing systems, continued
measurement of impacts on the policed communities is essential to assess and
mitigate any unintended consequences of targeted patrolling. Ideally, this
assessment should be conducted by an organization that is impartial and
independent of the law enforcement agency conducting predictive policing, with
results supplied both to the Mayor’s Office and the public (at regular
intervals, to improve transparency) and to law enforcement (for continuous
performance improvement).

Quantities to measure could include arrests (particularly those for commonly
over-policed crimes and minor drug offenses), police use of force, citizen
contacts, and crime victimization, and should be broken down both by
neighborhood and by demographics (e.g., to assess racial disparities in
policing). Both arrests made by hot-spot officers while on targeted patrols,
as well as overall arrests, should be measured, to assess both direct and
indirect impacts of the program. In addition to measuring the number of
observed crimes in the targeted areas, crime displacement to nearby areas
should also be assessed, though we did not observe any displacement of crime
in our Pittsburgh study. Finally, we encourage continued measurement of the
number of patrols each hot spot receives each week, both to keep track of
treatment intensity (and assess its potential impacts on both crime reduction
and arrests) and to ensure that an adequate number of patrols are conducted to
achieve crime prevention benefits.

###  0.9 Predict where, not who

While the focus of this discussion is on best practices for geographically
targeted prediction and prevention of crime, some cities have instead focused
on crime prediction at the individual level. For example, the City of
Chicago’s Strategic Subjects List predicts individuals’ probability of being
involved in a shooting, either as perpetrator or victim. We believe that, in
addition to sharing the numerous challenges of place-based crime forecasting,
person-based forecasting creates substantial privacy concerns as well as
presenting increased risk of harm to individuals and communities, for example,
due to false positives. As we have argued in (55), “Person-based forecasting
identifies specific individuals as posing a high risk for crime, some of whom
may have never committed a crime in the past. Place-based predictions offer
less opportunity for officers to make biased judgments about an individual’s
propensity for crime or violence prior to engagement. Such biases can lead to
poor decision-making and improper use of force.”

Figure 2: Prediction tradeoff curves for 10 forecasting models on one-week-ahead predictions for Part 1 violent (P1V) crimes across a three year evaluation window. Figure 3: Composite tradeoff curve representing a combined chronic-temporary hot spot program. Table 2: Counts of Automated Police Reporting System crime incidents for all Part 1 offenses from June 1, 2011 through June 1, 2016 in Pittsburgh, PA. Uniform Crime Reports (UCR) codes correspond to a hierarchy of crime types employed by the Federal Bureau of Investigation. | UCR Code | Crime Type | Frequency
---|---|---|---
4*  Part 1 Violent (P1V) Offenses | 1 | Criminal Homicide | 296
| 2 | Forcible Rape | 991
| 3 | Robbery | 5822
| 4 | Aggravated Assault | 5856
3*  Part 1 Property (P1P) Offenses | 5 | Burglary | 11665
| 6 | Larceny/Theft | 37230
| 7 | Vehicle Theft | 3870
Table 3: Leading indicator variables provided as inputs to multivariate prediction models. Data Source | Leading Indicator Variable
---|---
14*  Automated Police Reporting System (APRS) | Criminal Homicide
| Forcible Rape
| Robbery
| Aggravated Assault
| Burglary
| Larceny/Theft
| Vehicle Theft
| Simple Assault
| Vandalism
| Liquor Law Violations
| Public Drunkenness
| Disorderly Conduct
| Criminal Mischief
| Trespass
11*  Computer-Aided Dispatch (CAD) | Assault
| Burglary
| Criminal Mischief
| Disorderly Person
| Disturbance
| Drug-related Complaint
| Harassment
| Larceny
| Suspicious Activity
| Vehicle Theft
| Weapons or Gunshot Complaint
Table 4: Partial area under the tradeoff curve ($pAUC$) and hot spot selection
entropy ($H$) for a 1% target area from 10 forecasting models across a three
year evaluation window. Best-performing model for each column denoted in bold
face.

| Part 1 violent crimes
---|---
| $pAUC\times 10^{2}$ | $H$
MAVG | 1.31 | 6.38
MLP-LC | 1.23 | 8.42
MLP-NH | 1.23 | 8.21
CNN | 1.23 | 7.43
LASSO-LC | 1.14 | 7.06
SEPP-MULTI | 1.10 | 7.58
KDE | 1.06 | 6.83
GP | 1.05 | 6.30
LASSO-CC | 0.94 | 8.31
SEPP-UNI | 0.87 | 6.34

Table 5: Percent of hot spot selections occupied by frequently-selected locations (1% target area). | % of Total Hot Spot Selections Occupied by Locations Persisting For:
---|---
|  $>$ 25% of All Weeks |  $>$ 50% of All Weeks |  $>$ 75% of All Weeks | 100% of All Weeks
MAVG | 96.2% | 91.0% | 82.6% | 69.6%
MLP-LC | 74.2% | 55.5% | 43.6% | 0.0%
MLP-DIFF | 3.5% | 1.7% | 0.0% | 0.0%
Table 6: Counts and standard deviations of P1V crimes in treatment and control hot spots across cell-weeks. | Control | Treatment | % Reduction
---|---|---|---
| Sum of P1V | Std. Dev. | N (cell-weeks) | Sum of P1V | Std. Dev. | N (cell-weeks) | in P1V
All Hot Spots | 95 | 0.22 | 1872 | 71 | 0.20 | 1872 | 25.3%
Chronic Hot Spots | 80 | 0.29 | 936 | 61 | 0.26 | 936 | 23.8%
Temp. Hot Spots | 15 | 0.13 | 936 | 10 | 0.10 | 936 | 33.3%
Adjacent Cells | 163 | 0.12 | 11869 | 149 | 0.11 | 12135 | 8.6%

Table 7: Ordinary least squares (OLS) regression results estimating dose-
dependent treatment effect of proactive patrols on P1V crime counts. Units of
analysis are cell-weeks. Reference group for Model 1 is non-hot spot cells.
Reference group for Models 2-4 is control cells not selected as hot spots or
adjacent to hot spots.

| (1) | (2) | (3) | (4)
---|---|---|---|---
Hot Spot | 0.0431*** | 0.0437*** |  |
| (0.040, 0.046) | (0.041,0.046) |  |
Hot Spot $\times$ Dose (Combined) | -0.0009*** | -0.0009*** |  |
| (-0.001, 0.000) | (-0.001, 0.000) |  |
Chronic Hot Spot |  |  | 0.0772*** | 0.0768***
|  |  | (0.074, 0.081) | (0.073, 0.080)
Chronic Hot Spot $\times$ Dose (Combined) |  |  | -0.0015*** |
|  |  | (-0.002, -0.001) |
Chronic Hot Spot $\times$ Dose (Car) |  |  |  | 0.0002
|  |  |  | (0.000, 0.001)
Chronic Hot Spot $\times$ Dose (Foot) |  |  |  | -0.0031***
|  |  |  | (-0.005, -0.002)
Temp. Hot Spot |  |  | 0.0122*** | 0.0116***
|  |  | (0.009, 0.016) | (0.008, 0.015)
Temp. Hot Spot $\times$ Dose (Combined) |  |  | -0.0008** |
|  |  | (-0.001, 0.000) |
Temp. Hot Spot $\times$ Dose (Car) |  |  |  | 0.0006*
|  |  |  | (0.000, 0.001)
Temp. Hot Spot $\times$ Dose (Foot) |  |  |  | -0.0025***
|  |  |  | (-0.004, -0.001)
Adj. to Hot Spot |  | 0.0102*** | 0.0102*** | 0.0102***
|  | (0.009, 0.011) | (0.009, 0.011) | (0.009, 0.011)
(Adj. to Hot Spot) $\times$ Treatment |  | -0.0014* | -0.0014* | -0.0014*
|  | (-0.003, 0.000) | (-0.003, 0.000) | (-0.003, 0.000)
(Not Adj. to Hot Spot) $\times$ Treatment |  | -0.0001 | -0.0001 | -0.0001
|  | (-0.001, 0.000) | (-0.001, 0.000) | (-0.001, 0.000)
Constant | 0.0041*** | 0.0035*** | 0.0035*** | 0.0035***
| (0.002, 0.006) | (0.002, 0.005) | (0.002, 0.005) | (0.002, 0.005)
Week FE | Included | Included | Included | Included
Zone-Partition FE | Included | Included | Included | Included
Adj. $R^{2}$ | 0.005 | 0.007 | 0.009 | 0.009
No. Observations | 361719 | 361719 | 361719 | 361719

Notes: 95% confidence intervals shown in parentheses. Significance at the 1%
level is denoted by ***; ** denotes significance at the 5% level; and *
significance at the 10% level.

Table 8: Ordinary least squares (OLS) regression estimating non-dose-dependent
treatment effect on Part 1 Violent crime counts. Units of analysis are cell-
weeks. Reference group for Model 1 is non-hot spot cells. Reference group for
Models 2 and 3 is control cells not selected as hot spots or adjacent to hot
spots.

| (1) | (2) | (3)
---|---|---|---
Hot Spot | 0.0465*** | 0.0472*** |
| (0.044, 0.049) | (0.044, 0.050) |
Hot Spot $\times$ Treatment | -0.0128*** | -0.0128*** |
| (-0.017, -0.009) | (-0.017, -0.009) |
Chronic Hot Spot |  |  | 0.0818***
|  |  | (0.078, 0.086)
Chronic Hot Spot $\times$ Treatment |  |  | -0.0203***
|  |  | (-0.026, -0.014)
Temp. Hot Spot |  |  | 0.0125***
|  |  | (0.008, 0.017)
Temp. Hot Spot $\times$ Treatment |  |  | -0.0053*
|  |  | (-0.011, 0.000)
Adj. to Hot Spot |  | 0.0102*** | 0.0102***
|  | (0.009, 0.011) | (0.009, 0.011)
(Adj. to Hot Spot) $\times$ Treatment |  | -0.0014* | -0.0014*
|  | (-0.003, 0.000) | (-0.003, 0.000)
(Not Adj. to Hot Spot) $\times$ Treatment |  | -0.0001 | -0.0001
|  | (-0.001, 0.000) | (-0.001, 0.000)
Constant | 0.0041*** | 0.0035*** | 0.0035***
| (0.002, 0.006) | (0.002, 0.005) | (0.002, 0.005)
Week FE | Included | Included | Included
Zone-Partition FE | Included | Included | Included
Adj. $R^{2}$ | 0.005 | 0.007 | 0.009
No. Observations | 361719 | 361719 | 361719

Notes: 95% confidence intervals shown in parentheses. Significance at the 1%
level is denoted by ***; ** denotes significance at the 5% level; and *
significance at the 10% level.

Table 9: Ordinary least squares (OLS) regression estimating non-dose-dependent
treatment effect on Part 1 Property crime counts. Units of analysis are cell-
weeks. Reference group for Model 1 is non-hot spot cells. Reference group for
Models 2 and 3 is control cells not selected as hot spots or adjacent to hot
spots.

| (1) | (2) | (3)
---|---|---|---
Hot Spot | 0.1501*** | 0.1525*** |
| (0.142, 0.158) | (0.145, 0.160) |
Hot Spot $\times$ Treatment | -0.0093* | -0.0093* |
| (-0.020, 0.001) | (-0.020, 0.001) |
Chronic Hot Spot |  |  | 0.2356***
|  |  | (0.225, 0.246)
Chronic Hot Spot $\times$ Treatment |  |  | -0.0157**
|  |  | (-0.031, -0.000)
Temp. Hot Spot |  |  | 0.0693***
|  |  | (0.058, 0.080)
Temp. Hot Spot $\times$ Treatment |  |  | -0.0029
|  |  | (-0.018, 0.012)
Adj. to Hot Spot |  | 0.0342*** | 0.0342***
|  | (0.031, 0.037) | (0.031, 0.037)
(Adj. to Hot Spot) $\times$ Treatment |  | -0.0034 | -0.0034
|  | (-0.008, 0.001) | (-0.008, 0.001)
(Not Adj. to Hot Spot) $\times$ Treatment |  | 0.0001 | 0.0001
|  | (-0.001, 0.001) | (-0.001, 0.001)
Constant | 0.0171*** | 0.0150*** | 0.0150***
| (0.013, 0.021) | (0.011, 0.019) | (0.011, 0.019)
Week FE | Included | Included | Included
Zone-Partition FE | Included | Included | Included
Adj. $R^{2}$ | 0.012 | 0.014 | 0.016
No. Observations | 361719 | 361719 | 361719

Notes: 95% confidence intervals shown in parentheses. Significance at the 1%
level is denoted by ***; ** denotes significance at the 5% level; and *
significance at the 10% level.

Table 10: Per-offense estimates of costs to society from Part 1 crime types.

| Cost* ($2008) | Cost** ($2018)
---|---|---
4*Part 1 Violent | Murder/Manslaughter | $8,982,907 | $10,548,448
| Forcible Rape | $240,776 | $282,738
| Aggravated Assault | $107,020 | $125,671
| Robbery | $42,310 | $49,684
3*Part 1 Property | Burglary | $6,462 | $7,588
| Larceny | $3,532 | $4,148
| Vehicle Theft | $10,772 | $12,649

*Reported in McCollister et al. (39).

**Costs in 2008 dollars were inflated to 2018 dollars using
https://www.bls.gov/data/inflation_calculator.htm.

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