The SPOTLITE Anomaly Detector
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The SPOTLITE Anomaly Detector
SPOTLITE includes any incident where police use firearms—including those with non-fatal outcomes—as well as pursuits or any other uses of force that result in a civilian death. The SPOTLITE anomaly detector focuses attention on places in the United States that are worth paying closer attention to because they have more or fewer SPOTLITE incidents than would be predicted for them by a statistical model. Counties with higher than predicted numbers of lethal force incidents involving law enforcement are highlighted in orange, while counties with lower than predicted numbers of such incidents are highlighted in blue. Counties with about as many incidents as predicted for them are shown in white.
Anomalies Are Deviations from Predictions
The map above shows whether a county has unusually higher or lower numbers of lethal force incidents involving law enforcement than would be predicted knowing only its population size, population density (urban vs. rural), and levels of civilian firearm violence. Since these three factors should be important reasons why some counties have higher and some have lower numbers of SPOTLITE incidents, the anomaly detector reveals when other unobserved factors beyond these three are contributing to the number of observed SPOTLITE incidents. However, it doesn’t tell us what those other unobserved factors might be. Counties that fall within predicted incident levels are also worth examining. These are places where incident counts align with those in similar counties, regardless of whether existing policing practices could be improved. The baseline category of “about as predicted” simply indicates a county with incident-rates that are typical given recent policing practices in the United States.
Anomalies Aren’t Good or Bad, Just Different
The presence of an anomaly indicates only that something is different about a particular county relative to others that have the same population size, population density, and levels of civilian firearm violence. Counties with higher than predicted numbers of SPOTLITE incidents might be places where officers could benefit from better training. Counties with lower than predicted numbers of SPOTLITE incidents might be places where novel policies or training practices are already being effective at reducing unnecessary uses of lethal force. Or these might be counties where local patterns of crime or policing are just different. The anomaly detector can’t tell us what the difference means, or how it should be understood.
Anomalies Raise Questions without Providing Answers
Anomalies are clues, not answers. Anomalous counties are different from other counties that share the same population size, population density, and levels of civilian firearm violence. Once an anomaly is detected, the next step is to start asking why it is different. Understanding why counties are anomalous requires asking questions that the anomaly detector itself doesn’t answer. For example, because anomalies are detected at the level of entire counties, we might look more closely at which agencies are contributing to the observed incident counts. We might ask why a county’s anomaly levels have changed (or not changed) over time. What is it about an anomalous county that is different from others that have the same population, population density, or levels of civilian firearm violence? These are the questions that the anomaly detector was designed to prompt.
Anomalies Focus Attention
The SPOTLITE anomaly detector works best as an attention-directing tool. It tells us which counties in the country stand out for having unusual numbers of police uses of lethal force. It is also useful for tracking anomaly levels over longer periods of time. Is a county becoming more anomalous than it used to be? Has it gone from being highly anomalous to being more consistent with the prediction model? Such changes over time can be useful for understanding whether policy changes are having intended effects, and whether the factors that give rise to police uses of lethal force might be shifting over time.
To download the data or learn more about the anomaly detection methodology, click HERE .
The anomaly detector was constructed by building a statistical model that took into consideration the amount of civilian firearm violence in a county, the number of people living in the county, and the density of the county’s population. This model produced an estimated number of SPOTLITE incidents for each county-year with a corresponding standard deviation specific to each county-year. These estimates provide the predicted number of SPOTLITE incidents for a particular county in a given year. The standard deviations of these estimates were used to calculate a rate of difference between the number of actually observed SPOTLITE incidents and what was predicted by the statistical model for a particular county in a given year. The size of this difference relative to the size of the standard deviation for the predicted number of SPOTLITE incidents in a given county-year yields the anomaly rate. The anomaly rate identifies counties with unusually more or fewer police uses of lethal force than predicted based on SPOTLITE’s simple four-variable predictive model. For more details about how the anomaly detector was created, please see this white paper.
Key to this assessment is converting incident counts that are difficult to compare across counties to anomaly rates that can be compared. The anomaly rate for any county is a number that indicates the rate of difference between the observed number of SPOTLITE incidents in a given year and the estimated number of such incidents predicted for that county from a statistical model created by the SPOTLITE team. Creating an anomaly rate for a county begins with calculating the difference between the expected and observed number of SPOTLITE incidents within a given year. This number is then converted into a rate by dividing the difference by the standard deviation for that county-year’s expected number of incidents (the standard deviation measures the normal amount of variation for this county and similar counties year to year). An anomaly rate of 2 means that the observed number of police uses of lethal force in a given county-year is 2 standard deviations away from the expected number for that county-year. For example, if the predicted number of SPOTLITE incidents was 14 with a standard deviation of 2 and the observed number was 8 SPOTLITE incidents, the anomaly rate would be 3 standard deviations from what was expected (14 - 8 = 6 and 6 ÷ 2 = 3). The reason why this anomaly rate is more informative than a simple difference between observed and expected incidents is that a difference of 6 incidents might be very large in smaller counties that normally have few of these incidents in a given year (therefore, a large positive anomaly), but might fall within normal year to year variation for a county that normally has 50 or more of these incidents in a year (therefore, not an anomaly at all).
Anomaly categories for counties with very small populations and predicted incident counts of less than 1 were assessed differently than other counties. First, when the observed number of SPOTLITE incidents was 1 and the predicted number was less than 1, the anomaly rate was automatically set to 0. This adjustment was made because, in counties with very small populations, the predicted number of incidents can be extremely low. Under the standard calculation, a single observed incident in these counties could be flagged as anomalous simply because of the small predicted value. We determined that, in such cases, a single incident was insufficiently informative to be considered an anomaly, and therefore assigned these cases an anomaly rate of 0. Second, for the same reason, cases where the observed number of SPOTLITE incidents was 0 and the predicted number was less than 1 were also assigned an anomaly rate of 0. In these situations, the difference between observed and predicted values was not considered meaningful enough to warrant an anomaly designation.
Once an anomaly rate is calculated, each county-year is classified in a seven-category scheme as having either more incidents than predicted, fewer incidents than predicted, or about as many incidents as predicted relative to national benchmarks for similar counties. The table below details the breakdown of this categorization.
Many fewer than predicted | Anomaly rate less than -2.0 | Dark Blue |
Somewhat fewer than predicted | Anomaly rate between -2.0 and -1.0 | Blue |
Slightly fewer than predicted | Anomaly rate between -1.0 and -0.5 | Light Blue |
About as predicted | Anomaly rate between -0.5 and 0.5 | White |
Slightly more than predicted | Anomaly rate between 0.5 and 1.0 | Light Orange |
Somewhat more than predicted | Anomaly rate between 1.0 and 2.0 | Orange |
Many more than predicted | Anomaly rate greater than 2.0 | Dark Orange |
Comparing Maricopa County, AZ (population 4,492,261) and Lee County, FL (population 772,268) in 2019. The estimated number of SPOTLITE incidents for Maricopa County in 2019 was 48.3 and the observed number was 45 incidents. In contrast, Lee County was predicted to have 6.6 incidents based on national benchmarks but only 3 incidents were observed. Even though the difference between observed and predicted incident counts is similar in both counties (about 3), Lee County’s standard deviation of predicted incidents was much smaller at 2.6 whereas Maricopa County’s standard deviation was 6.9. This means that Lee County’s difference of 3 incidents between observed and predicted is considered more anomalous (scoring an anomaly rate of -1.4), which places Lee County in the category of “somewhat fewer than predicted” for 2019, while Maricopa County had an anomaly rate of -0.47, which places it in the category of “about as predicted.”
Comparing Baltimore City County, MD (population 576,498) and Spartanburg County, SC (population 335,864) in 2021. The predicted number of incidents for Baltimore was 9.8 with a standard deviation of 3.1, but the observed number of incidents was 16. For Spartanburg, the predicted number of incidents was 4.0 with a standard deviation of 2.0, but 10 incidents were observed. The difference between predicted and observed (about 6) is considered more anomalous for Spartanburg than for Baltimore, due largely to Baltimore’s higher standard deviation. The anomaly rate for Baltimore is 1.98, classified as “somewhat more than predicted”, while the anomaly rate for Spartanburg is 3.0, classified as “many more than predicted”.
Comparing Sandoval County, NM (population 155,943) and Fort Bend County, TX (population 927,120) in 2023. The predicted number of incidents for Sandoval was 1.5 with a standard deviation of 1.2, and 1 observed incident. The predicted number of incidents for Fort Bend was 5.0 with a standard deviation of 2.2, and 4 observed incidents. While the differences between predicted and observed are not the same nor are the standard deviations, the anomaly rate for both Sandoval and Fort Bend is -0.4, and therefore they are both classified as “about as predicted”.