Introduction
Math significantly aids the criminal-justice system in catching criminals and “cracking down” on crime. In Patterns, Prevention, and Geometry of Crime by Martin Andresen and J. Bryan Kinney addresses how math does so in ten different studies, with each one focusing on using either patterns or geometry to prevent crime. The studies address the geometry of crime, crime patterns, and “crime generators” and “crime attractors.” Using math, criminal-justice professionals can take the patterns and geometry of crimes committed to create preventative techniques, to understand why criminals pick certain places and what led to those decisions, which includes six different methods, and how all that information fits together.
Mobility Polygons
One way to investigate the geometry of co-offending is by utilizing mobility polygons. Mobility polygons take all locations in a crime incident into account, including the where the crime occurred, the residence(s) of the offender(s), and the residence of the victim (Felson 8). It also includes the journey to crime, which is “a measure of the distance between the offender’s residence and the location of his criminal action” (Felson 3). By plotting out these points, one can get an idea of where the offender lives in relation to the victim and where he chooses to commit crimes in the area. The distance shows how much he travels in a direction for crime. Mobility polygons can also account for co-offending, meaning that police can compare movements of a single criminal to multiple ones. One strength of mobility polygons is that they depict changing crime patterns as “youths age, or societies develop, or as transit systems are extended” so law enforcement can see the effect these factors have on crime (Felson 9). Using mobility polygons, law enforcement can track the changes to see what areas need more patrols or target hardening, a process which makes the target less desirable for crime, such as installing street lights or security systems. Mobility polygons would not be possible without distance calculations and graphing, both of which are mathematical.
Crime Paths and Spatial Dynamics
By looking into the spatial dynamics associated with crime paths, the movements of criminals can be analyzed. Rossmo et al. write, “Crime patterns are also shaped by victim’s routine activities, and a useful perspective is gained by considering how the spatial and temporal patterns … of both offenders and victims bring them into contact” (17). Many studies of crime in the past failed to consider the role of the victim in how and why crime occurs. The victim is very crucial to understanding crime because such knowledge “informs the core functioning of geographic profiling models” (Rossmo et al. 16). If a criminal never comes across a person or place that he wishes to commit a crime against, then no crime will be committed. He is not in the same geographic area as a suitable target. Therefore, if a criminal is looking for a specific kind of target, he may have to travel a little or travel a lot (Rossmo et al. 18). The discussion moves on to looking at travel paths of those on parole and their movements before and during re-offense. Here the crime path knowledge is applied because “the pre-offense movements of some parolees differed significantly from their offense day movements” and “combining these measurements with time and location information” provides insight into what parolees are doing (Rossmo et al. 27). This information is useful to the people monitoring parolees because if the person’s pattern changes, then they may be able to identify that a crime is about to happen. The ability to monitor time and location could also be extended to criminals and could prove effective in catching them at the scene or preventing the crime. Law enforcement knows the geometry of their movements and can tell when a new point is added. The crime location the parolee chooses obviously has a target, a victim that is in the area where the person is searching. The selection process is why the movements of the victims help criminologists better understand how crime happens because it helps explain criminal patterns and deviance from routines.
Location Quotients
Location quotients are very handy when investigating vehicles stolen for export in states, counties, and cities. It is a formula that uses area and amount of crime, and because population is not needed, it is more accurate since pinpointing an exact number is hard and population counts do not account for commuters and visitors (Block et al. 56). The study identified areas that had the highest amount of vehicle thefts. For example, border states and states with ports such as California, Arizona, and Washington were on the list even when different mathematical formulas (count, rate, location quotient, and overage) were used to determine the amount of thefts. The math shows that, no matter how the crime is broken down, a crime-ridden area is a crime-ridden area. Breaking the crime areas down into counties, and then cities, it becomes evident where the hot spots for vehicle theft are located. The city breakdown is especially important because law enforcement there can then be on high alert for motor vehicle theft. However, as the authors expound, “when location quotients are calculated, accounting for overall crime levels, it becomes clear that these cities have larger crime problems that are general rather than specific to vehicle theft” (Block et al. 54). Math shows that vehicle theft is a major crime in places that already have high crime rates. This finding is significant because it shows that these areas struggle with crime and, therefore, need a plan to help with all of it, not just vehicle theft for export. Perhaps by examining what factors make the places desirable for that crime, like being close to a border, and strengthening law enforcement and educating the populace to reduce their pull, the others will decrease as a result. This principle is called diffusion of benefits, and it states that efforts to prevent one crime prevent another. “Cracking down” on one major crime may decrease overall crime rates. Through the use of different formulas, the number of vehicles stolen for export can be found, which is an indicator of a larger crime problem and can help solve the larger issue at hand by increasing efforts to stop the theft of vehicles.
Crime Patterns
Prolific offending is when a small group of criminals commits most of the crime, and so crime patterns allow law enforcement to see commonalities between the offenses. Most crimes are planned out and have a pattern to them that becomes evident when examining crime hot spots. Prolific offenders are crucial to understanding crime patterns because of how much they contribute to the creation of them, but also because “prolific offenders will create patterns that are less random and therefore more concentrated than overall offending patterns” (Croisdale 70). A person who frequently commits crime will have a cadence to his movements and spots where he likes to strike. Someone who is just starting out will plan out his crime, but he has yet to develop his own pattern and is less likely to have frequented spots. It is important to keep in mind that “opportunities, motivation, activity spaces, and crime templates affect offending to create dynamic patterns” (Croisdale 70). All of those elements affect the spatial layout of crime patterns as well as when crime occurs. The researcher theorizes that, if a prolific offender were to move, he would have “an initial attachment to the previous template until the offender became more aware of new spaces, and, thus, over time the crime template would evolve to adapt to opportunities in the new spaces” (Croisdale 71). Criminals adapt their methods and patterns to an area, and this process applies to if they discover new places for crime, too. Through percentile analysis, which is where a group is broken up based on a factor (like the number of crimes committed, as with this study), research showed that criminals in the percentiles of the low 90s committed at least two crimes a year (Croisdale 74). This analysis proves that a very small portion of the criminal population commits most of the crimes. The examination of previous offender data combined with how criminals adapt to an area “could, or are beginning to, converge and create new patterns; that is, predict crime” (Croisdale 76). Thus, without the aid of percentile analyses and data tables, the ability to predict crime would not be able to improve. Additionally, computational analysis could allow the criminal-justice system to find those who are on the way to becoming persistent offenders (ten or more charges in a five-year period) and intervene so that they will desist from crime and turn their lives around. The movements of prolific offenders assist the criminal-justice system in being able to predict crime since they are responsible for a majority of it and create traceable patterns.
Crime Generators and Crime Attractors
Another set of research revolves around hotels and motels as “crime generators” and “crime attractors”. Since hotels and motels must attract business, the question was, do they also attract crime because of location and the fact that strangers are constantly passing through? LeBeau broke down hotels/motels into different categories based on their features in order to determine if there were independent variables that produced crime and to see if it was possible to distinguish between those that were “crime attractors” and “crime generators” (80). The research used Charlotte-Mecklenburg, North Carolina. The crimes investigated were prostitution, drug, domestic violence, robbery, and property crimes. Each category of hotels/motels had similar frequencies for each crime recorded. For example, those that are independently owned have a “higher rate of arrests, crimes, and calls'' than the chains (LeBeau 83). Also of note is that the crimes were clustered around certain areas with varying intensities despite the nature of them. Crimes typically took place around the interstate, the college, the mall, and the two coliseums. Criminals chose locations for crime that would be accessible, like with the interstate, or have features that would complement the act. For example, if a criminal wanted to commit a property crime, he would look for a hotel that had lax security measures. So, features of the hotels themselves in addition to nearby businesses and venues play a role. Some features include price, number of rooms, and number of parking spaces (LeBeau 90). If a hotel/motel has all the necessary factors that line up with what criminals are seeking, a lot of them will be attracted to that place, creating a pattern. The breakdown into subgroups based on these different factors, or independent variables, allowed the researchers to see where the numbers fell or who was going where (LeBeau 84-85). If there was a large percentage, then it shows that preventative measures need to be taken and that the staff should be aware of what crimes their establishment is attracting. Plotting out data of where crimes commonly occur and breaking down the variables that attract the criminals allows the hotels/motels and law enforcement to better prevent crime.
Regional Mobility Patterns
Researchers have utilized urban backcloth and regional mobility patterns to investigate juvenile crime. The study looked into how communities fared with crime based on how well the youth were controlled and where they tended to frequent. It was found that “in general, cities that push youth out in search of recreational activities tend to have lower levels of juvenile crime” (Bichler et al. 129). This phenomenon happens because if a city does not have ample places for youth activity, they are likely to go to another to find it (Bichler et. al 129). Therefore, juveniles end up in roughly the same area in large groups, so juvenile crime will all happen in the same vicinity, making them “crime generators”. These findings were supported by statistics and mathematical models. In order to measure crime levels in several California cities, they “were logged to normalize the distributions. To account for the juvenile population, a control variable measuring the percent of the residential population under 18 years old was included in the model” (Bichler et al. 126). Without a way to effectively measure what one is trying to study, there can be no study. Normalizing the distributions was necessary so that all values from the different regions could be measured on the same scale since making comparisons of measurements on different scales would prove difficult. The control variable is necessary to have something to measure against. Otherwise, the findings do not have as much value. The researchers were able to determine because of the distributions that “[a]s individual’s activity space grows, so do their search patterns and/or their victimization areas,” which corresponds to the movements of juveniles (Bichler et al. 131). The study shows that accounting for the flow of people and how a region operates are very important to understanding crime patterns, for without this knowledge, criminologists would be hard-pressed to fully understand criminality.
Connections
Though each of the methods touch on different mathematical techniques and their application to various areas of criminality, they all share commonality. Many factors must be considered when analyzing criminal patterns, and despite the differing nature of crimes, the same factors affect all of them. Distance plays a huge role in crime, as seen with mobility polygons and motor vehicle theft. A criminal will travel as little or as much as he thinks necessary to commit the crime and avoid detection. The time also plays a role, for criminals pick when to offend based on the crime selected and when the elements line up to successfully get away with it. For example, burglars are not going to break into homes when families are there; they will wait until the house will be empty for a long enough period of time. Additionally, the text explains, “Flow or movement between communities is also demonstrated to be an important factor in predicting crime patterns” (Bichler et al. 120). Criminals have the opportunity to move locations, and so understanding that fact, as well as being able to utilize mathematical models to predict where crime will occur based on past offenses, aids in prevention. All patterns have a “criminal event, crime characteristics, and offender motivation” (Croisdale 70). By examining these factors and comparing them with formulas and statistics, an understanding emerges of how criminals are moving, enabling police to prevent crime. Even though math cannot deal directly with the psychology behind crime, it helps law enforcement determine why people pick certain places for certain crimes and how people move, which is an advantage to understanding the criminal mind because of the patterns involved. So, math plays an integral role in catching criminals and controlling crime. No matter what section of crime is being researched, the patterns that criminals demonstrate make mathematics applicable to all of them.
Conclusion
Whether it be mobility polygons, crime paths, or motor vehicle thefts, mathematics plays an important role in enforcing the law and preventing crime. Methods like plots, percent analysis, and scales make it possible for law enforcement to see where criminals frequent, for what reasons, and when. They can then take this information and improve the effectiveness of patrols to target hot spots since they know the patterns of criminals and what places are “crime generators” and “attractors”. They can take the patterns and geometry of high-trafficked areas in order to increase crime prevention. While the research involved differed based on the subject, the application of the mathematical procedures is similar in many ways, such as through the use of independent variables and locations. If it were not for math, research to further an understanding of criminals, their motivations, and their movements would not have been possible.
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