Redrawing Hot Spots of Crime in Dallas, Texas

Abstract

In this work we evaluate the predictive capability of identifying long term, micro place hot spots in Dallas, Texas. We create hot spots using a clustering algorithm, using law enforcement cost of responding to crime estimates as weights. Relative to the much larger current hot spot areas defined by the Dallas Police Department, our identified hot spots are much smaller (under 3 square miles), and capture crime cost at a higher density. We also show that the clustering algorithm captures a wide array of hot spot types; some one or two addresses, some street segments, and others an agglomeration of larger areas. This suggests identifying hot spots based on a specific unit of aggregation (e.g. addresses, street segments), may be less efficient than using a clustering technique in practice.

While targeting police resources at micro place hot spots has been one of the most successful policing interventions to reduce crime (Braga et al., 2019), it is still an open question as to how to construct those hot spots. Using open crime data from Dallas, Texas, this article provides an example of constructing long term micro place hot spots. Using historical data to identify hot spots of crime, we show how our identified clusters capture a higher density of crime costs than current Dallas hot spot areas on future crimes.

While there are a plethora of prior articles examining the predictive ability of different hot spot methods (Chainey et al., 2008; Drawve, 2016; Levine, 2008; Van Patten et al., 2009), there are three novel contributions of this work. First, we illustrate the use of a hierarchical clustering technique, DBSCAN (Campello et al., 2013), to formulate different contiguous hot spot areas. A point of contention in prior work is the correct spatial unit of analysis to conduct analysis on. For example, several scholars often suggest street segments (Rosser et al., 2017; Weisburd et al., 2004), some suggest street segments and intersections (Braga et al., 2010; Wheeler et al., 2016), and others have suggested targeting specific addresses (Eck et al., 2007; Lee & Eck, 2019; Sherman et al., 1989). Using a hierarchical clustering technique allows one to avoid needing to specify such a spatial unit of analysis up front, and can be used on address based crime data to identify a reasonable resolution for a particular hot spot. In the micro place hot spots we identify, we subsequently show some are one or two addresses clustered together, others are a street segment, and others are an agglomeration of several nearby street segments.

The second novel contribution of this work is to construct hot spots using law enforcement cost of responding to crime estimates, which is related to prior research creating hot spots using crime harm scores (Macbeth & Ariel, 2019; Ignatans & Pease, 2016; Ratcliffe, 2015; Sherman et al., 2016). Crime harm has been characterized in prior research by either asking survey respondents to rank different crimes (Wolfgang, 1985), or by translating sentencing decisions to create harm weights (Ratcliffe, 2015), with the ultimate goal that policing resources are better allocated relative to the harm a particular crime impacts on the community, as opposed to counting all crime equal (Sherman & Cambridge University Associates, 2020).

In place of crime harm scores however, here we use average Uniform Crime Report (UCR) cost of crime estimates (per law enforcement) for Texas as weights in the DBSCAN algorithm (Hunt et al., 2019). This provides more interpretable hot spot summaries in terms of direct cost of crime estimates relevant to police departments. These cost of crime estimates can be used to provide more actionable information in terms of cost-benefit analysis for police departments when planning a hot spots policing strategy.

The third novel contribution of the study is to evaluate the predictive accuracy of our identified cost of crime weighted hot spots using historical data to predict future crimes. While prior work has mapped harm spots (Curtis-Ham & Walton, 2017; Fenimore, 2019; Norton et al., 2018; Weinborn et al., 2017), the majority of that work has simply focused on crime concentration, and has not assessed the predictive accuracy of a technique to create such harmspots (for an exception, see Macbeth & Ariel, 2019). Additionally, most of that work has mapped harm spots at a specific pre-chosen unit of analysis (Curtis-Ham & Walton, 2017; Mitchell, 2019; Norton et al., 2018; Weinborn et al., 2018, for an exception see Fenimore, 2019 who used weighted kernel density estimates). We show here in our constructed hot spot areas there is no single spatial unit of analysis that would consistently cover the same areas we identified.

The study area of Dallas was chosen for one main reason. They have historically identified long term hot spot areas, Target Area Action Grids (TAAG) (Ferguson, 2017; Worrall & Wheeler, 2019). These hot spot areas on their face do not conform with contemporary advice on targeting micro place hot spots of crime. TAAG areas cover 64 square miles of Dallas, around 20% of the city. We show that TAAG areas capture around 60% of the total crime cost in the city. Weisburd’s law of crime concentration states that approximately 5% of the places within a city typically capture around 50% of the total amount of crime (Weisburd, 2015). Thus it suggests one can identify a much smaller subset of the city and capture crime at a much higher density.

A common statistic used to evaluate crime forecasts is the Predictive Accuracy Index (PAI) (Chainey et al., 2008). The PAI is simply the ratio of the proportion of crime captured for the numerator and the percent of the area covered by the prediction in the denominator. A simple extension this statistic is to consider not just the proportion of total crimes captured, but the total cost of crime captured. We show that current TAAG areas in Dallas have cost-of-crime PAI's of around 3 (60% crime cost/20% of area of city), while Weisburd's law of crime concentration suggests a reasonable baseline for PAI statistics should be 10 (50% of crime cost/5% of the area). Our identified hot spot areas are much smaller, cover less than 1% of the area of the city (around 2.5 square miles), capture 12% of the total cost of crime in the city, and subsequently have a combined PAI of 16.

Data used for the analysis all come from open data sources. Address level geocoded crime data is available from dallasopendata.com. For this analysis we use crime data from June 2014 through December 2016 as the training dataset to draw historical hot spots, and then compare to test data from January 2017 through June 2018. While additional crime data was available at the time of writing, Dallas PD underwent a transition to NIBRS reporting, which subsequently caused various anomalies in the open data (such as a dramatic drop in thefts). The Dallas open data does not contain reported rapes, so the analysis here only examines the other Part 1 UCR index crimes; murder, aggravated assault, robbery, burglary, theft, and motor-vehicle-theft. Crimes that were given the address of a Dallas PD station (or sub-station) were removed from the analysis.

For GIS files, we obtained 2017 TAAG hot spot areas from the same dallasopendata.com website. We obtained an outline of the city, as well as street centerlines, from https://gis.dallascityhall.com/shapefileDownload.aspx. There are a total of 54 TAAG areas. All geographic analysis was conducted using a local projection relevant for Dallas, a Lambert conformal conic projection centered in Texas.

Although the main analysis uses area as the denominator for PAI calculations, street centerlines are used as an alternative denominator in place of area for PAI calculations in supplementary analysis (Drawve & Wooditch, 2019). This supplementary analysis is available in the appendix, and largely mimics the same findings using area for PAI calculations that we focus on in the main analysis.

We eliminated several lochs from the city outline of Dallas proper, as including these areas would artificially increase PAI statistics, although they cannot reasonably have geocoded crime incidents occur within them (Wheeler & Steenbeek, 2020). Figure 1 displays a map of Dallas proper, along with the 2017 Dallas PD identified TAAG areas. While these are 2017 areas, many are historically consistent, and are the same as those reported in Worrall and Wheeler (2019).

Figure 1. Historical Hot Spots Used by the Dallas Police Department, Target Area Action Grid (TAAG) Areas.

For cost of crime estimates, we use the Texas specific estimates presented in Hunt et al. (2019). Table 1 lists the descriptive statistics, as well as those cost of crime estimates per UCR offense. As the testing period is shorter (1.5 years vs. 2.5 years), the total numbers of crimes are smaller. But on a per unit time scale, the overall crime counts between periods are largely comparable, so estimates based on the pre-data should be reasonable to forecast in time. This is especially the case since others have found micro place hot spots tend to be very stagnant over long periods of time (Andresen et al., 2017; Curman et al., 2015; Weisburd et al., 2004; Wheeler et al., 2016).

Table 1. Cost of Crime and Crime Totals.

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There are two main methodological advances presented in the paper. One is the use of the DBSCAN (Density Based SCAN) clustering technique to create hotspots of crime (Campello et al., 2013). Being a hierarchical clustering technique, it is well suited to identify irregular shaped hotspots, such as runs along a street (Brantingham & Brantingham, 1993; Grubesic, 2006).

While the contribution of illustrating DBSCAN is a minor change compared to other common hierarchical clustering techniques (Haberman, 2017), the main reason it was chosen is because it can easily incorporate weights into the clustering algorithm.1 Here we use cost of crime estimates as those weights when constructing hot spots. This is similar to past work that has used crime harm estimates to construct and evaluate hot spots (Macbeth & Ariel, 2019; Ratcliffe, 2015).

For a brief description of how the clustering algorithm works, DBSCAN has two parameters that need to be chosen by the analysts; epsilon (the radius to which two points can ultimately be connected), and the minimum number of points (or here weighted points) to establish a cluster. These parameters are chosen here as 400 feet for epsilon, and $400,000 for the total costs of crime within a hotspot. Four hundred feet was chosen as this is slightly less than the average street segment size in Dallas (Wheeler & Steenbeek, 2020). For an average length street segment in Dallas, if there were only crimes reported at either end, this technique would not link them together. We believe approximating a street segment length in epsilon is a reasonable distance parameter, given the large literature specifying crime hot spots as particular high crime street segments (MacBeth & Ariel, 2019; Weisburd et al., 2004; Weisburd, 2015). If a street segment only has crimes reported at two polar ends, with no crimes in between, we believe it is more likely they should be connected to other potential hot spots, not with each other.

Four hundred thousand dollars (in 2010 dollars) (Hunt et al., 2019) was chosen as a baseline cost of crime hot spot value for the ad-hoc reason it tended to produce a total number of hot spots similar to the total number of TAAG areas. $400,000 is the minimum weight needed for the technique to return an identified cluster, it will ultimately identify areas with even more crime cost than that baseline.

For a simplified example of how DBSCAN works, imagine you have two locations, A and B, that are 300 feet apart, and each have a total of $200,000 in crime cost. Even though each location by itself does not meet the $400,000 threshold, combined they do. The epsilon parameter is what defines the threshold as to whether two points can be combined to consider their joint weight. Points A and B then form a core cluster. Points additionally within 400 feet from either A or B will additionally be considered inside the cluster, but unless all points within a particular radius of 400 feet exceed the $400,000 in crime cost, those points will not be considered a core point for the cluster.

Thus the epsilon distance parameter and the minimum weight parameter are two details that need to be chosen by the analyst, they are not automatically chosen in an algorithmic way. This is both a strength and a weakness – there are likely no universal solutions for what those values should be to produce the ‘best’ hot spots, but that choice also allows the analyst to adjust the parameters for their own particular circumstance. So cities that are more spread out an analyst may choose a larger distance parameter, or for hot spot interventions that are more costly the analyst may make the threshold for hot spot identification larger as well. Ultimately all hot spot creation procedures involve some arbitrary decisions, e.g. choosing a bandwidth for a kernel density map, and the necessary decisions to use DBSCAN is no more onerous than other common hot spot techniques.

We use the open source R statistical package to conduct the analysis, in particular the dbscan library, with cost estimates for crime as the weights (Hahsler et al., 2019). We create DBSCAN clusters based on the training dataset, and then buffer the core points within the clusters 400 feet to generate hot spot areas. We additionally merge any two clusters that this procedure results in overlaps, as well as remove any holes (areas in which it is entirely surrounded by a cluster). We then count the testing set number of crimes and their cost that fall within those hot spots, which provides an example of how such hot spots are used prospectively by police in practice (Berk, 2008). This procedure results in a total of 61 micro place clusters.

To evaluate the clusters, we then use the predictive accuracy index (PAI) to assess the accuracy of the hot spots. This common technique to measure accuracy (Chainey et al., 2008; Levine, 2008), and was used in the recent National Institute of Justice Forecasting challenge (Flaxman et al., 2019; Lee & Eck, 2019; Mohler & Porter, 2018).

The PAI statistic is typically defined as the proportion of crimes captured in a hot spot area, divided by the proportion of the city the hot spot covers. For an example, if a particular set of identified hot spots covers 2% of the city, and the hot spots capture 10% of the total crime, that would result in a PAI of 20. Here we make a simple modification to the PAI to accommodate cost of crime estimates, for the numerator we consider the total cost of crime captured, instead of simply the proportion of crime. So in our prior example, if there is a total of $1 million dollars in crime cost in a city, and the same hot spot captures $200,000 in crime cost (20% of the total cost), using the same 2% of the area denominator, the PAI statistic would then be 40. We evaluate both the total cumulative PAI identified by our DBSCAN clusters vs. Dallas PD defined TAAG areas, as well as provide graphs and maps of individual identified hot spots.

Table 2 displays the resulting citywide aggregate statistics, accumulating the entire TAAG and our identified DBSCAN hot spot areas. The total crime cost captured in the DBSCAN areas is just under $20 million dollars, which is 12% of the cost of crime in the city (over $169 million dollars). Given that the DBSCAN areas cover less than 3 square miles (1% of the city), this results in a PAI statistic of 16. Although the clusters were only fit on the cumulative proportions of each crime, overall they result in very similar PAI statistics when doing the (non-cost weighted) breakdowns for individual crime types, thus the results do not appear to be driven by a particular crime type.

Table 2. Cumulative PAI Statistics for DBSCAN Areas vs. TAAG Areas.

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While the TAAG hot spots capture a much larger proportion of crime and crime cost, they also cover a much larger area of the city. TAAG areas cover 65 square miles, 19% of the city. Overall TAAG’s capture 54% of the costs of crime in Dallas (over $92 million dollars), resulting in a PAI of 2.9. Again the statistics only vary slightly when considering non-weighted crime counts, and are typically around a PAI of 3.

Figure 2 displays PAI statistics for individual TAAG and DBSCAN hot spot areas. The majority of the TAAG areas hover under a PAI of 5, whereas the DBSCAN areas have a much broader distribution. While the left tail of the DBSCAN hot spots falls short of the PAI over 10 ideal laid out in the introduction, 50 of the 61 DBSCAN clusters have a PAI of over 10. It happens that only three of the DBSCAN areas have a lower PAI (based on the cost of crime) than the highest PAI for TAAG areas.

Figure 2. PAI Statistics for Individual DBSCAN Crime Harm Weighted Hotspots vs. Current TAAG Areas.

Figure 3 displays a screenshot of an interactive map we created to explore the areas, https://apwheele.github.io/MathPosts/HotSpotMap.html. The blue DBSCAN areas are all smaller than 0.2 square miles, whereas the red TAAG areas tend to be around 1 to 2 square miles. Like other work on hot spots at micro places (Weisburd et al., 2004), the DBSCAN clusters are spread throughout the city, although have several sub-clusters in different areas of the city. The majority (but not all) of DBSCAN areas are covered by TAAGs. This suggests many of the TAAG hot spots currently in place can simply be adjusted to focus on more specific places.

Figure 3. Screenshot of Interactive Map Showing Superimposed TAAG Areas (Red) With the Constructed DBSCAN Hot Spot Areas (Blue). Map available at https://apwheele.github.io/MathPosts/HotSpotMap.html.

Another way to consider the size of a hot spot is to consider the length of the streets in the area, since that will more naturally define the area in which officers will be patrolling (Drawve & Wooditch, 2019; Ratcliffe & Sorg, 2017). For reference hot spot areas in terms of street length, in the Philadelphia policing tactics experiment, the hot spot areas tended to cover around 3 miles of streets (Groff et al., 2015). For the Philadelphia foot patrol experiment, the areas covered a total of 1.3 miles of street on average (Ratcliffe et al., 2011). The DBSCAN hot spots here on average cover just under 1 mile of street. Of the 61 DBSCAN hot spots, only 11 cover more than 1.3 miles of street length, and only one covers more than 3 miles of street length. For comparison the current TAAG areas cover on average 24 miles of streets. The smallest TAAG area in terms of street length coverage is 12 miles.

Figure 4 illustrates a more zoomed in focused screen shot of the same interactive map. The map provides tooltips when clicking on a blue DBSCAN area, and this provides a breakdown of the total crimes and the cost of crime captured in a particular DBSCAN area. The particular example shown, a cluster that runs along Scyene road and expands onto Saint Augustine road illustrates the utility of a hierarchical clustering technique. Clusters that rely on identifying elliptical shaped clusters would have a difficult time approximating that shape. This particular hot spot contains a Family Dollar store, a gas station, an elementary school, and several apartment complexes, each likely an individual high risk crime generator (Eck et al., 2007), that all in toto contribute various crimes to this hotspot. One can see from the tool tip that the hot spot contains a variety of violent (26 aggravated assaults, 13 robberies), as well as non-violent crimes (15 burglaries, 58 thefts, and 26 thefts of motor-vehicles).

Figure 4. Zoomed in Screenshot of Interactive Map Showing Superimposed TAAG Areas (Red) With the Constructed DBSCAN Hot Spot Areas (Blue). Blue DBSCAN areas have a textual description showing crime totals and harms totals for the individual area. Map available at https://apwheele.github.io/MathPosts/HotSpotMap.html.

In terms of the question do hot spots tend to be a single address or a street segment, one can find examples to support either. Many of the clusters are 1 to 2 addresses, although this may in part be a function of the nature of the clustering algorithm. It can return a single address as a cluster if it happens to have more than $400,000 dollars in cost in the training dataset. But if there are any addresses within 400 feet, even with a single crime, they will also be within the core cluster. One can also find examples that more closely approximate street segments, or several street segments nearby one another, which are a function of multiple addresses accumulating to reach that $400,000 threshold.

Other exploratory data analysis did not reveal any obvious patterns to the identified hot spots. In particular we examined whether specific crime types tended to dominate the identified clusters. It could be since violent crimes have larger costs, the hot spots tend to be more violent on average. Or the opposite, since property crimes are much more prevalent, the hot spots are all dominated by thefts. Neither of these appeared to be the case – the majority of hot spots tended to have a wide distribution of crimes (although one could find some counter-examples dominated by violent or property crimes). To quantify this, we have estimated the Shannon entropy statistic for each of our DBSCAN clusters (Lee & Eck, 2019).2 For this statistic, if a hot spot only contained one crime type, the entropy would be 0. Higher values signify more entropy, so it is harder to predict what type of crime may fall within that hot spot. The average entropy for each area is 1.38, with a maximum entropy given six potential crime types under examination here is 1.79. Thus areas are much closer to max entropy than they are encompassing a predictable set of crime types.

This is contra to the work by Haberman (2017), who found hot spots of different crime types did not tend to overlap. This difference is perhaps a result of clustering on the combined crimes, instead of clustering crimes individually. Although the difference in results may also be the case that Dallas has substantively different crime patterns than Philadelphia.

The results of the analysis demonstrated what we believed at the onset – that Dallas PD could identify much smaller hot spots than the current TAAG areas in place and capture a much larger density of cost of crime per area. Like prior analysis of concentration of crime harm (Curtis-Ham & Walton, 2017; Fenimore, 2019; Norton et al., 2018; Weinborn et al., 2018), we find micro places that have high values of crime cost in clusters. Additionally, we show that such micro places have long term stability in the cost of crime, by showing that hot spots generated with historical data also capture high values of crime cost in the future (Norton et al., 2018). As such, our work is complimentary to many past analyses, and builds on a long standing literature of constructing and evaluating the predictive capability of hot spots clustering.

An additional finding of the work is that we identify a heterogenous set of areas that qualify as hot spots in our clustering algorithm. While much past work has either conducted analysis at a pre-specified unit of analysis, such as census areas (Curtis-Ham & Walton, 2017), street segments (Norton et al., 2018), or specific addresses (O’Brien & Winship, 2017), our approach identifies hot spots that do not nicely conform to any of those pre-specified units of analysis. Thus there is likely a potential to be more efficient in hot spot identification when using a solution that does not presume a specific structure for hot spots at the start. Although we note that any of these ranking approaches is likely better to the status quo of constructing hot spot areas based on personal intelligence (MacBeth & Ariel, 2019).

That being said, ultimately the nature of hot spot identification will always come with some arbitrariness, given that hot spots themselves have no well agreed upon definition (Taylor, 2015). Subsequently a limitation of this work is that we do not consider here other methods used to identify hot spots and test their accuracy. Many exist, in addition to the traditional clustering techniques mentioned in the literature review, there are a variety of model based approaches (Drawve, 2016; Mohler et al., 2018; Wheeler & Steenbeek, 2020) we have not touched on here. Thus while we cannot say that our DBSCAN analysis is dispositive that it is better than these other approaches, we believe it is likely the case one can use many of these different approaches to improve upon the current Dallas TAAGs, even simply just counting up street segments with the highest crimes is likely much more accurate (MacBeth & Ariel, 2019; Wheeler & Steenbeek, 2020).

One strong limitation of the current analysis is that the definition of the cost of crime is not well agreed upon. While here we use the work of Hunt et al. (2019) that is mostly based on costs associated with police response to particular crimes, there is a wide array of ways to calculate the cost of crime (Domínguez & Raphael, 2015). For example, a murder in this analysis is valuated at $124 thousand dollars, whereas the value of a statistical life is often pegged at over one million dollars (Domínguez & Raphael, 2015). This difference has to do with who bears the cost of the murder – for police it is mostly in terms of investigative time, whereas the cost is much more severe for the victims family (and infinite for the victim themselves). It may also be that crime prevented for individuals accumulate over a lifetime (Cohen & Piquero, 2009), with failing to prevent crime resulting in long term negative externalities for various individuals. Finally, this does not consider additional considerations on allocating police resources, such as equity or preventing disproportionate minority contact with a hot spots policing approach (Wheeler, 2020). So while these cost of crimes estimates are relevant to police departments themselves, they may not be reasonable to the greater public when constructing a hot spots policing strategy.

Additionally, this work relying on public data does not include rapes, and we also do not include Part 2 crimes, which are often considered public disorder crimes and additionally contribute to quality of life (Boggess & Maskaly, 2014; Chappell et al., 2011; Ratcliffe, 2015). This is not a limitation for a police department applying such estimates internally, where they have access to all of the reported crime data, but even then non-reporting will cause such estimated cost of crime hot spots to be an underestimate of the cost of crime at particular places. Ultimately how to appropriately value crime harm is as much an ethical question as it is an empirical. This work shows one way to do so, using labor costs directly relevant to police departments, but this is not to say other ways, such as via sentencing severity or public surveys are inherently inferior. But it is likely the case that many of these different schemes will produce similar rankings in crime (e.g. all would likely identify homicide as a higher harm than theft), so we believe using any crime harm ranking scheme is likely better than the defacto standard of treating such crimes equally when creating hot spots.

So we believe that both of these biases likely underestimate the cost of crime that is occurring the hot spots we identify here. Given that the ultimate goal of identifying such hot spots is to prevent crime, these estimates may then be gross underestimates of the potential return on investment if Dallas PD targets crime in those identified areas. But that is also conditional on a hot spots policing strategy to be effective (Mitchell, 2019) – just placing hot spots on the map and not doing anything with that information will ultimately not reduce crime at those locations.

Related to this is that in the DBSCAN algorithm itself we need to define an agreed upon minimal threshold at which to identify a location as a hot spot. Here we arbitrarily choose $400,000 dollars. Ultimately this minimum threshold would be better determined by considering the nature of the intervention police departments wish to engage in that hot spot area. So for example if the particular intervention was more cost intensive (e.g. overtime patrols), this would likely only be justified in hot spot areas with higher cost thresholds. In that case, a $400,000 hot spot over a year may not be sufficient, and the department may wish to raise this threshold. Cheaper interventions, such as nudging officers to do more patrols in high crime areas (Mohler et al., 2015), may however justify lowering the threshold to lower dollar amounts.

It may also be that a police department wishes to focus on a particular set of crimes for a hot spots policing strategy, e.g. just focus on gun violence. Given our identified hot spots here tend to have a variety of different crimes, it may still make sense to generate general cost of crime hot spots, and then filter for those areas that contain certain levels of specific crime types, as it is likely the case an intervention focused on one crime type is likely to have positive spillovers to reducing other crime types.

While this work focuses on long term crime forecasting, the application of using DBSCAN can potentially be extended to short term crime forecasting (Flaxman et al., 2019; Garnier et al., 2018; Lee et al., 2020; Mohler et al. 2015; Ratcliffe et al., 2020). One approach that we believe may be fruitful is to use DBSCAN on the output of a predictive policing application applied at the address and intersection level to create homogenous areas to assign subsequent patrols (Deryol et al., 2016). Although raster based approaches to predictive policing are popular (Caplan et al., 2011), these raster grids do not conform to the actual micro places and the street network that heavily influence crime (Groff, 2014; Rosser et al., 2017). While prior work has used the creation of the raster grid orientation and size of the grid cells as a hyperparameter when tuning machine learning models (Flaxman et al., 2019; Mohler & Porter, 2018), one could similarly use the DBSCAN parameters of epsilon and minimum weight in the same capacity to avoid relying on grid cells entirely. Such results are likely to result in more natural, contiguous hot spot areas to target. Such contiguous areas would not only require fewer resources to target (relative to separate hot spots not in the same area), but also would likely result in better police adherence when targeting those hot spots boundaries (Sorg et al., 2017).

Given that errors associated with geocoding tend to be around 100 feet on average for crimes occurring outdoors (Wheeler et al., 2020), it likely does not make sense to cluster crimes within a smaller distance than that shown here, but it may be the case that one would identify more agglomerated areas if the epsilon clustering criteria was slightly larger, as one can see sub-clusters of the individual clustered hot spot areas in the resulting map in this analysis. It is likely the case that idiosyncratic characteristics of different jurisdictions will likely change what distance parameter captures the most weighted crime cost, so future research may be warranted about how to best tune this value given a similar test and validation data set.

The policy implications of constructing hot spots based on cost-of-crime estimates, as opposed to either direct counts of crime or weights based on sentencing severity are rather straightforward. They provide a much more direct cost-benefit analysis of the potential return on investment directly relevant to police departments.

For a direct estimate, let us take an example from the hot spot that captured the largest cost of crime, a hot spot in the center of Dallas that captured around 1.5 million dollars of crime within 1.5 years. The average crime reduction in the Braga et al. (2019)meta-analysis is around 20%. As such, the expected return to partaking in a hot spots policing strategy at this one location is around $200,000 per year. Such a return on investment would justify assigning additional resources to target this hot spot. For locations with smaller overall costs of crime, while it likely does not justify allocating additional resources, it certainly may justify reallocating existing resources to target crime in those particular micro places.

While this analysis is illustrative of how one might create cost-of-crime weighted hot spots, ultimately the optimal strategy to construct hot spots needs to entail what actions the police department is going to take within those hot spots (as well as functional constraints in the resources the police department can allocate). Historically Dallas PD has only generically stated TAAG area hot spots were formulated to predict areas of high crime (Ferguson, 2017). They have not articulated specific strategies they would undertake at said hot spots.

Take for example if Dallas PD knew they wanted to create foot or bike patrols for identified hot spots, and budgeted enough to assign 4 different officers on some regular basis. It is likely the case that only four officers cannot cover all 61 micro place hot spots identified in this analysis, but it would be easily possible for those officers to cover at least one of the micro place hot spots identified here, which are all under 0.2 square miles (Haberman & Stiver, 2019; Ratcliffe & Sorg, 2017). Given that such areas have a specific cost attached to them, it also provides more straightforward cost-benefit analysis if the Dallas PD wishes to advocate for more resources to be able to cover such hot spots, or to justify reallocating existing resources to cover such hot spots.

While those same officers could cover the existing TAAG areas, expanding the size of such hot spots will result in a more diffused intervention by the police, no matter what the intervention is (Larson, 1975). As such it is likely in Dallas PD’s best interest to take a more vested approach to identify micro places, even if they do not have a specific plan for what to do in the current hot spots at the current time. It may be a police department wishes to generate such hot spots first, and then take a problem oriented approach to solving crimes in those areas (Braga et al., 1999). Given that targeted police interventions at large areas tend to be less successful than micro placed focused interventions (Lum et al., 2011), weighted cost-of-crime DBSCAN identified hot spots are a tool crime analysts for any police department should consider in formulating a hot spots policing strategy.

The feasibility of such an approach should be within the capabilities of Dallas PD to implement. This analysis comes with a set of replication materials using open source data and open source code, thus Dallas PD (or any other interested police department) can replicate the analysis using more current data for free if they so wish. Given the consistency of other papers identifying hot spots of crime, it is likely the case such work can generate areas of hot spots which show promise of generating significant returns on investment for many police departments. Hot spots weighted by cost of crime estimates can then be used as an upfront tool to justify either new investments in police departments to allocate resources to hot spots or to shift current resources to hot spots. This provides a direct cost-benefit calculation to justify to police departments to shift resources from reactive to proactive policies (Nagin et al., 2015).

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

The authors received no financial support for the research, authorship, and/or publication of this article.

Notes

References