Abstract

In his Sutherland address and associated Criminology article, Weisburd (2015) argued for the existence of a “law of crime concentration” based on empirical findings from a number of studies that indicated that the majority of crime tends to consistently concentrate in a very small proportion of places. This study expands on previous efforts by examining the law of crime concentration across all jurisdictions within the United Kingdom, multiple levels of crime concentration, and for different types of crime. Analyses confirm that crime indeed concentrates in a small proportion of street segments. However, this study also finds that the level of crime concentration can vary across different types of places and crime types. Further, two specific aspects of small places—population density and the length of street segments—significantly explains the variation of these concentrations. Finally, limitations with the data used are discussed.

Introduction

Scholars in both the environmental criminology and crime and place traditions have continued to build strong theoretical and empirical support for a simple but powerful generalization: crime concentrates geographically at very specific locations (see Eck et al., 2007; Groff et al., 2009; Groff et al., 2010; Johnson and Bowers, 2004; Madensen and Eck, 2008; Sherman et al., 1989; Smith et al., 2000; Weisburd et al., 2004; Weisburd et al., 2012; Wikström et al., 2012). Additionally, substantial evaluation research continues to find that when communities and law enforcement target these crime concentrations with particular interventions, they can reduce and prevent crime at those places (National Research Council, 2014; National Academies of Sciences, 2018). This body of research led Weisburd (2015) to assert, in his Sutherland Address for the American Society of Criminology published in Criminology, the existence of a “Law of Crime Concentration.” He noted that study after study showed that crime tends to concentrate “within a narrow bandwidth of percentages for a defined cumulative proportion of crime” (p. 132). Weisburd supported his assertion by calculating crime concentrations across eight cities1 using the same type of data (crime incidents), the same measure of crime (incident reports), the same geographic unit of analysis (street segment), and the same time frame (one year), at aggregations of 25% and 50% of all crime events. He found that when reverse ranking street segments from those with the most to the least crime, about 50% of crime was concentrated in just 4.2 to 6 percent of larger cities’ highest crime street segments. He also confirmed the preliminary finding by Hibdon (2013) that crime might be even more concentrated in less populated cities; between 2.1 and 3.5 percent of street segments held 50% of crime at street segments.

A natural inquiry follows the proposal of such a law: How universal or generalizable is it? Weisburd (2015) argued that prior research consistently showed that a large proportion of crime is concentrated in a very small proportion of places, especially microgeographic places (i.e., street addresses and street segments) (see Pierce et al., 1988; Sherman et al., 1989; Weisburd and Amram, 2014; Weisburd and Green, 1995; Weisburd et al., 2004; Weisburd et al., 2009; Weisburd et al., 2012; Wheeler et al., 2016). While most of these studies have been conducted in large urban cities, a few have also focused on suburban areas or smaller towns (e.g., Dario et al., 2015; Gill et al., 2017; Hibdon, 2013). These findings of crime concentrations have also not been limited to the United States. Curman et al. (2015) found that less than 10% of street segments housed 60% of crime in Vancouver, Canada. Weisburd and Amram (2014) noticed that 50% of crime incidents in Tel Aviv-Jaffa were located in 5.6% of street segments. Jaitman and Ajzenman (2016) also discovered in five Latin America cities (Belo Horizonte in Brazil, Bogota in Colombia, Montevideo in Uruguay, Sucre in Venezuela, and Zapopan in Mexico) that 3 to 7.5 percent of street segments produce 50% of crime, and 0.5 to 2.9 percent of street segments generate 25% of crime. Further, studies have also shown that this geographic concentration of crime is likely stable over many years (Andresen et al., 2017; Curman et al., 2015; Groff et al., 2010; Weisburd et al., 2004).

Some have questioned the law, and a special issue of this journal was dedicated to this topic (Volume 33, Issue 3). Most notably, Hipp and Kim (2017) examined crime concentrations in forty-two cities in Southern California and found variations in crime concentrations across those cities. They argued that variations (or the lack thereof) may be explained by how concentrations were calculated, particularly the temporal parameters of that calculation. Using both historically and temporally adjusted crime concentration measures, they argued that crime concentrations varied much more than Weisburd’s narrow bandwidth, and especially in the top 5% of street segments. In another study, Oliveira et al. (2017) found that while crime concentrates across numerous cities regardless of size, different types of crime concentrate differently. They argued that crime patterns may be too complex a system to be reduced to a general law. In total, these studies seem to indicate some support for, but also challenges to Weisburd’s law.

This study continues to examine the salience of Weisburd’s law of concentration by being the first to analyze crime concentrations across all jurisdictions in an entire country outside of the U.S. Rather than look at distinct cities or towns across varying political (and policing) landscapes as others have done, we hold country and general policing approach constant but examine crime concentrations across various sizes and types of jurisdictions and also various type of crime. Unlike Hipp and Kim (2016) and for purposes of fair comparison, we use the same approach as Weisburd (2015) to calculate crime concentrations for two geographic areas of analysis in England and Wales: all police force jurisdictions, as well as all “local authority districts,” which are smaller locales within each of these jurisdictions. Through this expanded analysis, we find some similarities but also important variations of crime concentration compared to Weisburd’s findings. We also add to the debate by exploring the role that street segment length plays in explaining variations of crime concentration found within locales.

Calculating Crime Concentrations Across all Jurisdictions in a Country

Examining crime concentrations across heterogeneous jurisdictions within an entire country or nation allows us to see if Weisburd’s law holds up in suburban, urban, rural, and mixed-use communities with varying crime levels, but that fall under (generally) similar policing and political mandates. To accomplish this, this study uses publicly available crime data from England and Wales from the Open Government Website for Public Information2 to analyze crime concentrations across 42 of its 44 police jurisdictions that cover England and Wales.3 Using police jurisdictions allows us to capitalize on the consistency of crime data reporting within jurisdictions. However, many of these 42 police jurisdictions also include multiple cities and towns (UK Cities, 2017) of varying physical sizes and levels of urbanity and population density. Thus, in addition to calculating crime concentration in these larger police jurisdictions, we also analyze crime concentrations for all 336 local authority districts within these 42 jurisdictions and included the City of London in this specific analysis (see note 2) to explore the salience of Weisburd’s law in these individual cities and towns.

The data from the Open Government Website for Public Information have both benefits and limitations. The dataset is advantageous because it is the only publicly available comprehensive crime dataset in England and Wales that is standardized across all police jurisdictions.4 This data also includes geographic location data for each crime event. Such standardized and specific crime data is not publicly available across all police jurisdictions in the United States, or even within one U.S. state, given the decentralized nature of police services and reporting in the U.S. and the lack of specific location information in nationally available crime data.5 Using this standardized data allows us to see if Weisburd’s law holds for very different types of places (e.g., urban, suburban, and rural) located within a single political jurisdiction and policing organizational mandate. The data also provide information for us to calculate crime concentrations for all crime, specifically for violence, property crime, and disorder and drug crimes.

However, the data is limited because of rules governing its open-source nature.6 To protect the privacy of victims, data.police.uk replaces crime coordinates with a master list of “snap points.” The master lists of “snap points” were created by the police.uk according to the following rule: Any snap point, which had fewer than eight addresses associated with it, were discarded to protect the privacy of victims (see discussions of this by Tompson et al., 2015, p.102). Tompson et al. (2015) argue that this modification underestimates crime locations, especially in more rural places. Because “snap points” appear over the center point of a street, a commercial premise, or above a public place, there may be fewer snap points due to a smaller number of street segments and commercial premises in rural areas relative to urban areas. This may result in increased crime concentration. Additionally, there are no crime incidents at intersections in the data because data.police.uk uses a master list of anonymous map points to anonymize locations over the center point of a street or above a public space or commercial premise. Unfortunately, compared to the U.S., this is the only publicly available dataset that can be used to examine all jurisdictions in a nation and is therefore employed here. However, because of the nature of these data, this study may overestimate the level of crime concentrations for more rural locations because low population density may lead to fewer addresses and snap points resulting in either removing or relocating crime locations to the next closest catchment point.

To provide a fair comparison with Weisburd’s concentration calculations, this study also uses a single year of data—2016—provided at the crime event level, which includes the location of the event (as expressed as an XY coordinate) and the type of crime.7 Crimes were aggregated into four categories for this study: “all crime,” “property crime,” “violent crime,” and “disorder/drug crime.” Property crime includes bicycle theft, burglary, criminal damage and arson, other theft, shoplifting, theft from the person, and vehicle crime. Violent crime contains robbery, violence and sexual offenses. Disorder and drug offenses include all antisocial behavior and drug-related offense. Appendix 1 displays the heterogeneity across the 42 police jurisdictions in the U.K. as to numbers of crime by types, numbers of street segments, the size of the jurisdiction, population, population density, and median length of street segments. There are approximately 2.8 million street segments in England and Wales. The median length of these street segments is 85.8 meters, but vary greatly across police jurisdictions. Like Weisburd, we used a geographic information system to assign each crime location to its closest street segment (identified by the Open Roads data from Ordinance Survey8) and then summed the number of events at each segment to create a base measurement for our crime concentration calculations. Only a very small amount of the crime—1.2 percent—could not be geocoded for this analysis.

Once crimes were geocoded to street segments, four types of crime concentrations were calculated using the same method Weisburd (2015) employed at street segments and Sherman et al. (1989) used at the address level. These included calculating the percentage of street segments (ranked from most to least crime) that houses 25%, 50%, 75%, and 100% of all crime within the 42 police jurisdictions. We also repeat these calculations for property crime, violence, and disorder/drug crime. The crime concentrations were calculated by generating a frequency count of crime for each street segment, then sorting segments in descending order by crime counts. The proportion of total crime (or type of crime) for each segment was calculated, along with a cumulative proportion of crime from segments with the most to the least crime. For each of the 336 local authority districts within the 42 jurisdictions and the City of London, we calculate 50% crime concentration only.9

After calculating crime concentrations for both larger police jurisdictions and smaller local authority districts, we then explore whether the level of urbanity (as measured by population density) for each of the 42 jurisdictions and the 336 local authority districts might explain variations of crime concentrations (if found). In particular, preliminary research by Weisburd (2015), Gill et al. (2017), and Hibdon (2013) shows that smaller cities and towns tend to have higher crime concentration than larger cities (i.e., the same proportions of crime are concentrated in even smaller proportions of street segments). To explore this hypothesis further, we also create a proxy measure for urbanity—street segment length. Knowledge from environmental and place-based criminology indicates that physical layouts of places likely influence crime patterns. Although obtaining street-level physical data information for every street in England and Wales would be monumental task, this analysis uniquely adds to this area of inquiry by exploring street segment lengths within each jurisdiction and the relationship between these lengths and crime concentrations. Rural areas, for example, may have relatively fewer opportunities for criminal activities that are spatially dispersed over longer street segments. More urban places may have shorter street segments and, therefore, more opportunities for crime across different segments. Such variations could explain why rural and suburban cities appear to have much more intense crime concentrations in a smaller number of street segments.

Results: Consistency and Variation in Concentrations

Overall Crime Concentration for All Crime

Table 1 shows, for all crime, the average percentage of street segments in which each proportion of crime is concentrated using Weisburd’s calculation for the 42 jurisdictions examined in England and Wales. Specific crime concentration calculations for each jurisdiction are displayed in Appendix 2, organized by ascending population density of the jurisdictions. Overall, these results show that a significant amount of crime occurs at a very small percentage of street segments, which generally supports Weisburd’s law. The range of crime concentration for 50% of crime is 1.01 to 4.09 percent of street segments, with a mean of 2.4 percent of segments. This bandwidth is similar to Weisburd’s bandwidth of 2.1% to 6% when including smaller and larger cities.

Table 1 Average crime concentration calculations for 25%, 50%, 75% and 100% of all crime at street segments across 42 police jurisdictions in England and Wales

Whether our (or Weisburd’s) range could be described as “narrow” is up for debate. Note that on average, 75% of crime already falls within only 6.3% of all street segments on average (and all crime in 20.3% of all street segments). This suggests that relatively, our range of crime concentration may be interpreted as wider than its values appear (given that the maximum thresholds are already low). In other words, a range of 1-4% may reflect a great deal of variability across jurisdictions if 75 percent of crime is concentrated within 6% of all street segments.

One challenge in comparing our findings with Weisburd’s is that Weisburd (2015) describes “small cities” as those with 108,511 population or less, and large cities as about 300,000 population or more (Weisburd, 2015, p. 141, Table 2). Weisburd (2015, p. 143) argues that for larger cities, an even tighter bandwidth of 4.2% to 6% of segments housing 50% of crime is discovered, while for smaller and more suburban locales, 50% of the crime is housed in 2.1% and 3.5% of street segments. In this jurisdiction-level analysis, the jurisdictions all have populations of approximately 500,000 or more (see Appendix 1). But our jurisdictions also encompass diverse geography and many multiple cities and towns. Weisburd’s sample also does not include rural areas, which our sample does. For example, while Weisburd’s three “smaller” cities are smaller in population, they would not likely be considered rural, and some would even be considered suburban or even urban locales. For example, Ventura, California, and Brooklyn Park, Minnesota have population densities of about 1,200 per square kilometer, which is closer to West Yorkshire’s population density.

Some might argue that the 42 jurisdictions are too physically large to be comparable to other calculations of crime concentrations, because these jurisdictions also include cities and towns. Thus, we also examined all 336 “local authority districts” (LADs) within each of the 42 jurisdictions and also the City of London. Theoretically, the law of crime concentration should hold whether one examines larger jurisdictions (or regions) or smaller towns within those regions, especially if the law seems to work for large metropolises and smaller cities. Given that concentration calculations must be done for each jurisdiction separately, we only calculated the percentage of street segments (in descending order) that includes 50% of crime here. Interestingly, when calculating crime concentrations for these 336 smaller towns and cities within these larger police jurisdictions, we discovered that crime concentrations was similar to that of the 42 jurisdictions: 50% of crime, on average, fell within 2.54% of the street segments in each jurisdiction. However, the standard deviation was larger (0.95), and the min-max range was 0.72 to 6.52%, suggesting a larger bandwidth than the 1-4% for the 42 jurisdictions. Thus, while theoretically the law of crime concentration might hold at larger jurisdictions, when those jurisdictions are further divided into smaller places, the bandwidth of crime concentration may be greater. The range indicates that crime may concentrate even more than in smaller, less crime-prone areas.

Crime Concentrations by Crime Type

Table 2 shows the average crime concentrations across the 42 jurisdictions by crime type, for each proportion of crime. When examining specific types of crime, a more complex picture emerges. For example, while 25% of all crime appears to occur, on average, in 0.60% (s.d. = 0.18) of street segments, when examining violence, property crime, or disorder/drug crime separately, these percentages are smaller, and the difference between these concentrations and the concentrations of all crime is for the most part statistically significant (except for disorder/drug crimes which seem to have similar levels of concentration as violent crime). For example, 25% of violent crime occurs in 0.52% (s.d. = 0.18); 25% of property crime is concentrated in 0.40% (s.d. = 0.12) of street segments; and 25% of disorder/drug crimes are concentrated in 0.51% (s.d. = 0.15) of street segments, on average across the 42 jurisdictions. This pattern (specific crime categories being more concentrated than all crime generally) is repeated at 50%, 75%, and 100% of crime. Additionally, the range (or bandwidth) of crime concentration for each crime type can be quite different compared to all crime. Fifty percent of drug and disorder crimes in each jurisdiction, on average, seem much more concentrated (.86 to 2.85%) than all crime more generally (1.01 to 4.09%). These findings support Oliveira et al. (2017)’s assertion that crime concentrations can vary by crime type, potentially signaling a more complex system of crime concentration (and patterning) at places. Given our findings for all crime in the 336 LADs, we would also anticipate that specific crime types in these smaller locales would also be even more tightly concentrated.

Table 2 Average crime concentrations calculations for different categories of crime across the 42 police jurisdictions

Street Segment Length, Population Density, and Crime Concentrations

We next examine the relationship between street segment lengths in these jurisdictions and variations in crime concentration. As Gudmundsson and Mohajeri (2013) note, street networks tend to be denser and street lengths are shorter in inner parts of cities than outer parts. Longer street segments are more common in suburban and rural locations. Hacar (2020) also found that urban and suburban areas tend to have relatively shorter streets. Additionally, both the median and mean street segment lengths for each jurisdiction are highly and negatively correlated with a jurisdiction’s population density, another measure of urbanity (Spearman’s Rho = -.79 and -.93, respectively). Together, shorter street lengths and greater population density suggest that jurisdictions with shorter streets segments have more people living, working, and operating on those segments, resulting in a greater spread of crime opportunities across street segments (and therefore less crime concentration). Longer street segments are more common in suburban and rural locations and could have fewer opportunities for crime across the street segment. Variations in street segment lengths—and thus crime opportunities from the physical and social environments—may help to explain variations in crime concentrations across jurisdictions.

We use median street segment length for our analysis, which is less likely to be influenced by data outliers. Figure 1 shows scatter plots of our crime concentrations for property and violent crime at 25, 50, 75, and 100 percent of crime across the median street segment length for each of the 42 jurisdictions in our study. Overall, these figures indicate that when jurisdictions have, on average, shorter street segments, these types of crime are less concentrated no matter the proportion of crime included in the concentration calculation. In other words, jurisdictions with shorter street segments (which tend to be more population-dense places) have greater proportions of street segments with violence and property crime than jurisdictions with longer street segments.

Fig. 1 Crime concentrations of property and violent crime plotted against length of street segments

However, a closer comparison of violent and property crimes shows an interesting nuance to these findings. Figure 1a shows the crime concentration levels by the median length of street segment only when 25% of crime is included in the concentration calculation. Given the way we calculate crime concentrations, the segments that include 25% of the crime are those within a jurisdiction with the highest amounts of crime. One can see that no matter the median segment length in the jurisdiction, property crime is comparatively more highly concentrated than violence when only examining these very high crime places. However, this pattern does not hold when including larger proportions of crime in the calculation. Figures 1b, 1c, and 1d progressively show that the greater proportion of crime that is included in the concentration calculation (e.g., 50, 75, and 100%), the more likely we see that violent crime is much more concentrated than property crime.

This phenomenon seen in Figure 1 does not repeat itself when comparing violence with disorder/drug crime. Figure 2 shows the crime concentration calculations for 25, 50, 75, and 100 percent of crime across different median street segment lengths for violence and disorder/drug crime. When crime concentration is calculated for 25% and 50% of crime, violence appears less concentrated than disorder/drug crime in places with short street segments, but more concentrated in streets with longer segments. This pattern occurs when 75% of crime is used to calculate concentration levels. At that proportion of crime, violence appears less concentrated than drug and disorder crimes only at the most urban places (shortest street segments). However, when the entire field of crime is used to calculate crime concentrations, violence appears to be more concentrated than drug and disorder crimes. Thus, although the statistical difference of mean values for crime concentration between violent and disorder/drug crime is not significant (see Table 2), Figure 2 illustrates a higher violent crime concentration at 100 percent concentrations and stronger violent crime concentration in jurisdictions with longer street segments. We note that violent crime may be more highly concentrated than property and disorder/drug crimes at 100 percent concentrations because the total number of violent crime (about 1.2 million) is much smaller than property crime (about 2,3 million) and disorder/drug crime (about 2 million). In other words, the high violent crime concentration could result from using a much smaller number of crimes to calculate crime concentrations compared to the other crime types.10

Fig. 2 Crime concentrations of violent and disorder/drug crime plotted against length of street segments

Again, this same nuance appears when comparing property and disorder/drug crime. Figure 3a shows that property crime is more highly concentrated in smaller places than disorder/drug crime at 25 percent concentration, and this pattern reverses at higher percent concentration (Figures 3b, 3c, and 3d). The levels of property crime concentration tend to noticeably decrease at 100 percent crime concentration compared to disorder/drug crime (Figure 3d). The high property crime concentration at 25% concentration (Figure 3a) is also seen in Figure 1a, which suggests that property crime appears to be much more concentrated when only examining the highest crime segments, than when including all segments that have crime.

Fig. 3 Crime concentrations of property and disorder/drug crime plotted against length of street segments

Figures 1, 2, and 3 collectively provide a more telling story than the correlations between street segment length and crime concentrations alone. These findings seem to reaffirm Oliveira et al.’s (2017) suggestion that crime concentration levels for specific types of crime reveal a more complex picture of crime. For example, the findings in Figures 1 and 3 suggest that when just considering the highest crime places in jurisdictions as represented by the 25% analysis, property crime appears much more concentrated, but this is not the case when including greater proportions of crimes in the concentration calculation. This may indicate, for example, that routine activities and opportunities for property crime are likely hyper-concentrated on streets with businesses, causing this effect. Figure 2 also raises a hypothesis about the nature of crime patterns of drugs and violence. The somewhat consistent higher concentration of violence at shorter street segments indicates that in larger cities, violence may be less location-specific than in suburban and rural places as compared to drugs and disorder. Yet, as the levels of violence likely decline in suburban and rural areas, it becomes much more highly concentrated in very specific places compared to drugs and disorder.

To further explore the relationship between street segment length and crime concentrations, Table 3 shows the percentage of specific numbers of crime incidents that occurred in various ranges of street lengths in England and Wales. The ranges of street segment lengths follow a set percentile of length of street segments for each of the 42 jurisdictions (i.e., 1 to 30 meters for 10^th percentile of length of street segments; 31 to 60 for 25^th percentile; 61 to 120 for 50^th percentile; 121 to 240 for 75^th percentile; 241 to 480 for 90^th percentile; and 481 and above for the rest of street segments. The ranges of the number of crime incidents per street segment (for those segments with at least 1 crime event) are also set to roughly the same percentiles (i.e., 1 incident is the 5^th percentile; 2 incidents for the 10^th percentile; 3 to 5 incidents for the 25^th percentile; and so on for the 50^th, 75^th, and 90^th percentiles).11 Table 3 shows that the largest proportion of crime incidents occurred on street lengths between 61 and 120 meters (about 37%). The second-largest proportion of crime incidents occurred on lengths between 121 and 240 meters (30%). The third-largest proportion of crime incidents occurred on street lengths between 31 and 60 meters (17%). In total, these three street length ranges house 84% of all crime in the data. The remaining 16% of crime occurred between 241 and 480 meters (about 11%), 481 meters and above (about 4%), and 1 to 30 meters (about 3%).

Table 3 Percentages of crime concentrations for different ranges of street segment lengths, by numbers of incidents, for 42 jurisdictions in England and Wales.

Table 3 demonstrates that longer street segments do not necessarily have more crime because of their size. More likely is that crime occurs on street segments within a particular length (e.g., between 31 and 240 meters). Thus, jurisdictions with long street segments (longer than 240 meters) are likely to have higher crime concentrations not because more crime occurs on longer street segments, but because the crime in these places tends to be concentrated on the small number of shorter street segments.12 At the same time, this finding does not mean that very small street segments will have high levels of crime. In our jurisdictions, streets ranging between 1 to 30 meters also appear to have a smaller proportion of crimes (2.5% of all crime) than street segments of 31 to 60 meters (17%). Perhaps very short and long street segments are too short or too long to be “activity spaces” (Brantingham et al., 2009; Felson and Boba, 2010) or “behavior settings” (Felson and Boba, 2010; Taylor, 1997; Weisburd et al., 2016).

Not only are the findings of crime concentrations at specific lengths of streets significant, but population density can further explain the variation of crime concentrations across these jurisdictions. As Figure 4 shows, population density and median street segment length are strongly correlated but in a non-linear way. In other words, jurisdictions with high population density have lower levels of crime concentrations, and lower population density jurisdictions have higher levels of crime concentrations, again confirming the urban-suburban-rural differences in crime concentrations. It is likely the case that the combination of population density and street segment length is what drives the activity spaces for crime and the resulting crime concentration calculations. Figure 4 shows a noticeable negative exponential relationship between the length of street segment and the population density.

Fig. 4 Non-linear relationship between length of street segments and population density for the 42 jurisdictions

Figure 4 also shows that the length of street segments quickly decreases (from 310 to 100 meters) as population density increases (from 50 to 1,000 km²), but that the length of street segments becomes more stable (around 100 meters) as population density increases from 1,000 to 5,500 km². The stability of the length of street segments above a population density over 1,000 km² may explain the tight bandwidth of crime concentrations. For instance, if we look at jurisdictions with a population density of over 1,000 km², we observe a very tight bandwidth of crime concentration (see Figure 5) because of the diminishing exponential decay of length of street segments, while increasing population density. Our findings are also reinforced by Weisburd’s. The large cities that he examines (Cincinnati, Seattle, Tel Aviv-Yafo, New York, and Sacramento) all have very high population densities (average 4,743 km²)13 also have tight bandwidths of crime concentrations (4.2 to 6% of streets hold 50% of crime). This finding can be further explained by the relationship between population density, street segment length, and the levels of crime concentration.

Figure 5 shows the relationship between the population density of the 42 jurisdictions and the percentage of street segments with 50% of all crime, which can further support the tight bandwidths of crime concentration. Here, one sees a negative exponential increase in the number of street segments with 50% of the crime, but with gradual decreases in magnitude as population density increases, especially after 1,000 people per square kilometer. Especially when population density reaches 1,000 people per square kilometer, the increases in the percentage of street segments get smaller and results in the tighter bandwidth. As Figure 5 shows, for example, Metropolitan London has only one percent more street segments (about 4%) compared to Cleveland (about 3%) even though population density of Metropolitan (5,523 km²) is about six times greater than Cleveland (942 km²). In contrast, Cleveland's percentage of street segments (about 3%) is three times more than Dyfed-Powys (about 1%). In this regard, even if we measure crime concentration in a place with a much higher population density, we would have relatively small increases in the percentage of street segments. Thus, the negative exponential relationship between the length of street segments and the population density could explain both the significant variations of crime concentration and the narrow bandwidth across the 42 jurisdictions depending on urbanization likely contributes to the spatial dispersion of crime.

Fig. 5 Non-linear relationship between 50% of crime concentration and population density for the 42 jurisdictions

The strong relationship between population density and the level of crime concentrations also applies to the 336 Local Authority Districts (LAD).14 Figure 6 shows the level of all crime concentrations at 50% concentration from LADs within the 42 police jurisdictions and the City of London. As aforementioned, the bandwidth of crime concentration for these areas is 0.72 to 6.52, which is larger than the bandwidth for the 50% concentration calculations for the 42 police jurisdictions. This density analysis indicates this may be because we are essentially increasing the variability of population density across geographic areas of interest when examining subdivisions of the 42 jurisdictions.

Fig. 6 Non-linear relationship between 50% of crime concentration and population density for 336 LADs

Discussion and Conclusion

Our analysis reveals that crime is highly concentrated, whether one calculates it across the 42 police-defined jurisdictions or the 336 Local Authority Districts within those jurisdictions in England and Wales. However, it also reveals variations in crime concentrations and therefore bandwidths that are not always as narrow as those found by Weisburd (especially when examining the 336 LADs). By examining crime concentration at the jurisdiction level and for smaller cities and towns, we also mimicked crime concentration analysis in big metropolitan areas and smaller rural and suburban places. It may be the case, given Weisburd’s analysis of mostly large and urban cities, that the law of crime concentration may be most salient when examining more populated and larger cities (in particular those with over 1,000 km²). Our street segment analysis also suggests that variations in crime concentrations may be further explained by street segment length (and also population density). Perhaps Weisburd’s law might be considered less of a “law” and more an “equation” that needs further specification.

We also find noticeable variations in crime concentrations for specific types of crime. For example, property crime is more spatially concentrated than violent and disorder/drug crime at 25% concentration. Violent crime is more spatially concentrated at 75% and 100% of crime than property and disorder/drug incidents, but this may be due to a smaller number of incidents used in the calculation. Disorder/drug crime concentrations are somewhere in between property and violent crime. This may be the case that highly clustered commercial business districts and shopping malls generate significant amounts of spatially-concentrated property crime (e.g., shoplifting), while the rest of the property crimes (e.g., burglary, vehicle crime, criminal damage, and arson) are less concentrated.

These findings further support the idea of conceptualizing Weisburd’s law as an equation and are also aligned with prior empirical and theoretical work. Perhaps opportunities for criminal activities are greater and more geographically distributed in urbanized residential settlements because these places have more short street segments that have greater population density and that provides more “behavior settings” (Barker, 1968; Wicker, 1987) and “activity spaces” (Felson and Boba, 2010) for crime. Because there are likely more convergences of motivated offenders, a suitable target, and a lack of guardianship (Cohen and Felson, 1979) in urbanized spaces, urbanization likely contributes to the spatial dispersion of crime (and therefore less crime concentration across a jurisdiction).

There are limitations to this study, similar to those already raised by Hipp and Kim for this journal and Oliveira et al. (2017). The calculations of crime concentrations could be sensitive to both temporal fluctuations and the temporal unit of analysis used. A longitudinal study of crime concentrations would be needed to fully explore this limitation and consider the spatial and temporal variations of crime concentration with low criminal events (see Eck et al., 2007; Mohler et al., 2018). And, as already discussed, the data is yet another limitation to this study—spatial accuracy. The anonymization of crime data could possibility underestimate the level of crime concentrations of certain crime types with victims and jurisdiction with low population density (see Tompson et al., 2015). If this is the case, then we would expect even greater bandwidths of crime concentration that we found in our analysis, further questioning the idea of a narrow bandwidth of crime concentration. If and when specific location data becomes available in NIBRS, this will allow for more precise analysis of crime concentration. However, given the totality of the findings here, and what we have learned from environmental criminology more generally, it would not be surprising to find that while crime generally concentrates at places, the variations in the levels of crime concentrations may vary, depending on the jurisdiction or the type of crime analyzed.

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