Analysis of Fatal Police Shootings

On August 29, 2014, Michael Brown, an 18-year old black male, was fatally shot by Darren Wilson, a 28-year old white male police officer, in Ferguson, Missouri, after an altercation stemming from a pedestrian stop relative to a recent robbery in the vicinity. The shooting, mixed with contradictory testimony from several onlookers, ignited civil unrest with focus on the relationship (or lack thereof) between predominantly white police forces and predominantly black communities. The ensuing unrest and national reach of the protests in Missouri helped legitimize the 2013 Black Lives Matter movement as a national movement in an effort to speak out against police killings of African American citizens, racial profiling, and racial inequality in the United States criminal justice system.

Since the incident in Ferguson, there have been numerous deaths of African Americans at the hands of police. Most notably after the Ferguson shooting, the shootings of Tony Robinson in Madison, WI (March 6, 2015); Eric Harris in Tulsa, OK (April 2, 2015),  and Walter Scott in North Charleston, SC (April 4, 2015).

But have the rates of shooting African American citizens change? Are these protests well-founded? Has anything really changed since? In this article, we take a look…

Data Collection: Washington Post’s “Fatal Force”

Since the Michael Brown shooting, the Washington Post has devoted resources into the valiant effort to catalogue all fatal shootings during police confrontations since January 1, 2015. The Post began tracking several elements associated with each reported police shooting/fatality, such as Name of Person, Date, Manner of Death, Person Armed, Age, Gender, Race, City/State of Fatality, Signs of Mental Illness, Threat Level Detailed in Incident, Suspect Fleeing, Body Camera in Use. To track an example, let’s take a look at Tony Robinson’s entry:

Name: Tony Robinson

Date: March 6, 2015

Manner of Death: Shot

Armed: Unarmed

Age: 19

Gender: Male

Race: Black

City: Madison

State: Wisconsin

Signs of Mental Illness: False

Threat Level: Attack

Suspect Fleeing: Foot

Use of Body Camera: False

The Washington Post obtains this information through a series of efforts: culling local news reports, law enforcement websites and releases, social media, and monitoring of independent databases such as Killed by Police and Fatal Encounters. The Post has also filed open-records requests with departments associated with the shootings.

The records obtained by the Washington Post (available on their website) document only shootings in which a police officer, in the line of duty, shot and killed a civilian; situations that closely resemble the situation experienced in the Michael Brown case noted above. Due to this, situations such as the Freddy Gray case in Baltimore, MD or the Sandra Bland case in Hempstead, TX are not tallied in these efforts. Therefore, we cannot analyze “in police custody” situations; nor can we analyze shootings by off-duty police officers or non-shooting deaths.

Case Study: Tony Robinson (2015 – Madison, WI)

Let’s start with a case study that is in the Washington Post catalogue. According to the Wisconsin State Journal, in the Friday evening of March 6, 2015, police officer Matt Kenney was dispatched to intervene in a domestic incident at 1125 Williamson Street. With Kenney on his way, dispatch describes Robinson’s name, age, apparel, and actions in the community; which included hitting and attempting to strangle people but was unarmed. Within 150 seconds of the call, Kenney entered into the apartment where the calls were made. Within 18 seconds of entry, a struggle ensued and Kenney shot Robinson.

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In a March 14, 2015 article from The Guardian, Robinson lived in a portion of the 1125 Williamson Street residence as an apartment and shared the apartment with two other individuals: Javier Limon (18) and Anthony Limon (19). According to the Guardian, Robinson had spent the earlier part of the afternoon consuming hallucinogenic mushrooms and spending time on Governor’s Island. The Guardian then notes that after returning home, the drugs kicked in, prompting Robinson to violently attack people on Williamson street, including punching a friend in head and chasing his roommate, Javier, down the street in the car. The car chase allegedly prompted Javier to call the police in an attempt to calm down his roommate.

At that point, according to the Guardian, Kenney forced entry into the residence to confront Robinson. This prompted Robinson in knocking down Kenney, who opened fire on Robinson in response. Immediately afterwards, Kenney attempted CPR on Robinson before both being taken for medical care.

As a background on Robinson: Robinson was born to a 17-year old mother with a largely non-present father due to incarceration. Robinson moved to a small town of Stoughton, Wisconsin when he was 5-years old. Robinson’s uncle, Turin Carter, noted that the family faced intense racism and ultimately moved away from Stoughton to more racially diverse areas of Madison such as Allied Drive. Robinson ultimately grew to be the man of the house in the family and completed high school at nearby Sun Prairie early. However, shortly after graduation in 2014, Robinson participated in a home invasion that resulted in a felony armed-robbery conviction in December 2014. Hit with three years probation, Robinson planned on going to community college the following fall with the hopes of moving to be with his uncle, Turin, in hopes of turning his life around.

The reason for such a case study in this article is two-fold. The first reason is to articulate a singular story that is vital to the Black Lives Matter movement. Without explicitly stating justification or mis-justification, we only wish to show that the people involved in these incidents are not egregiously bad persons; but rather two individuals (possibly more) finding themselves in a situation that ultimately neither want to find themselves in. The second reason, a personal reason to the writer, is that coming from Stoughton, Wisconsin after spending the majority of his life in Los Angeles, California; can attest to the large polarization in race within the small community outside of Madison. While the city on a whole is for diversity and is against racism; this writer has personally witnessed several incidents of racism that he had never even witnessed in the Rodney King era of Los Angeles living. Incidents that the writer had personally witnessed between 1997 and 1999 (high school) included Confederate flags begin thrown in the faces of Vietnamese students by white students with the latter students telling them “get used to it” interlacing in racial slurs, slashing of tires of African-American students by white students because students like that “didn’t deserve good things” and police officers boasting that they knew all the names of the black kids in town and could find them at a moments’ notice. To be fair, however, these incidents involved approximately twenty individuals in a town of 12,000. To emphasize, this small minority of twenty; while twenty too many, is not a make-up of the entire town.

Let’s Look At The Numbers…

 In 2015, there were a total of 991 fatal shootings by police in the United States. By November 22nd, 2016, there have been a total of 860 fatal shootings. If no change in the rate of shootings have occurred, we should have expected 887 shootings to date. So, we can claim immediately that fatal shootings are down compared to last year! But that’s just a raw number. Let’s take a look at the trend in police shootings.

Result #1: Fatal police shootings are NOT down from last year.

Despite seeing that at this point last year, we have 27 less fatal shootings by police, the difference is not significant. To test this, let’s consider the shootings over the course of a year as a counting process. In order to determine if shootings are down, we form the hypothesis that shootings are the same as last year and attempt to find evidence that suggests otherwise. For a counting process, we can simply take a look at the daily totals and show that the rates are not much different.


Distribution of daily fatal police shootings for 2015 (blue) and the first 327 days of 2016 (red).

From the distribution of daily fatal shootings by police, we see that the distributions are not different between the two years. Here, we see that despite having 36 less days of the year than in 2015, there are more three-fatal shootings per day in 2016 (72) than in 2015 (69). All other categories are dominated by 2015, including less days of zero fatal shootings.

So let’s take a test that compares two distributions of unequal sizes and identify the test statistics. A common one is the non-parametric Wilcoxon-Mann-Whitney test for comparing two distributions. With the hypothesis that the distribution of shootings are the same between 2015 and 2016, we test that the number of shootings is actually down in 2016 using a one-tailed test. To do this, we note the distributions as follows:


No. Shootings 2015 2016 Ranks
0 24 23 24
1 73 66 117
2 88 75 268
3 69 72 420
4 55 52 544
5 33 25 626.5
6 13 11 667.5
7 8 3 685
8 2 1 692

The column of ‘Ranks’ are just the average ranking for all ties between days that have the same number of shootings. In this case, we have a 2015 score of 61022 and a 2016 score of 58698. Check: 61022 + 58698 = 119720, 365*328 = 119720 (split accordingly to ranking distribution).

Using the tie-correlated normal approximation, we end up with a test statistics of 0.434277; which has a p-value of 0.332035. This is a strong non-rejection of the hypothesis that the distributions are the same! 

As a further illustration, let’s take a look at the rate of fatal shootings by police:


Number of fatal police shootings over 2015 (blue) and 2016 (red).

As we can see, not only are the distributions of shootings per day nearly identical over the days, the distribution of the count process is nearly identical over the course of the year.

We do note that a counter-argument to this presentation is that there are approximately 2 million more people in the United States between 2015 and 2016; therefore same counts are technically less. However, by making this argument, we are making the assumption that these 2-million individuals are all suspect to random inspection (including newborns and immigration under the age of 18); which account for the largest population increase. In fact, the CDC states that there were roughly four million births in the United States in the previous year. Combined with the roughly 2.5-million deaths in the United States; and we have the vast majority of new eligible fatal shootings to be less than a year old. These counts are effectively negligible.

VERDICT: Fatal Shootings by Police have not changed. 

Result #2: Fatal police shootings broken down by race…

Now that we see that, despite the public outcry of fatal police shootings, the rate of fatal police shootings have not changed, we can now take a look at the central theme of race and shootings are related. Let’s start by looking at fatal shootings of white persons between 2015 and 2016. During this time, of the 1851 fatal police shootings, 878 (47.43%) where caucasian. The Census Bureau reports that 61.6% of the United States is white, of non-Hispanic origin; the same race in the fatal shootings reporting. This may suggest that the distribution of fatal shootings by police under-represent the white population of the United States.

Speaking of Hispanics: A total of 307 of the 1851 fatal shootings were non-white Hispanic, or 16.59% of all fatal police shootings. Compare this to the Census Bureau’s reported 17.6% of the United States population being Hispanic, we find that the rate is representative of the shootings. This suggests that Hispanics are not targeted aggressively.

Let’s compare this to the African-American community. Of the 1851 fatal police shootings, 457 (24.69%) were African American. Compare this  to the Census Bureau’s reported 13.3% of the United States population being African American, we find that the rate over-represents the black community. This suggests that African-Americans are targeted aggressively.

But wait…

There is a race category in the Washington Post data: UNKNOWN. This race exists because the reporting arm of the fatal police shooting has either not determined the race of the person shot or that the information is not available for release to the public. So let’s make an adjustment and remove these persons from the 1851 total. To note, there are 141 of these cases. So let’s adjust the numbers and report them:

  Census Fatally Shot
Black 13.3 26.73
Hispanic 17.6 17.95
White 61.6 51.35
Asian 5.6 1.4
Other 1.9 2.57
Total 100 100


In order to perform a test whether we can decidedly state that “the African-American community is targeted” through these numbers, we realistically have to obtain dispatch rates of officers to persons of each race. Otherwise, performing a test states that every race is uniform in dispatch calls. And we cannot verify that.

So let’s try to use supplemental numbers to help us. For instance, the Uniform Crime Reporting (UCR) from the Federal Bureau of Investigation (FBI) reports statistics reported to them directly from police municipalities across the United States, in an effort to determine crime rates across America. These number in effect help inform consumers of the types of crimes that are prevalent in their areas and help Congress identify how to distribute resources to police forces. It does not, however, identify how effective a police force is, as the only appropriate way to test this is to remove a police force for over a decade and write down what police would have done for arrests after the fact. This would be quite ill-fated…

So let’s use these numbers to approximate the number of police interactions. Using Table 43 for the 2015 UCR, we see that:

  Census Fatally Shot FS % UCR-43 UCR %
Asian 5.6 24 1.40 101064 1.23
Black 13.3 457 26.73 2197140 26.64
Hispanic 17.6 307 17.95 1278492 15.50
White 61.6 878 51.35 4474720 54.25
Other 1.9 44 2.57 197293 2.39
Total 100 1710 100 8248709 100

Before we begin our analysis, what does this table show us? First off, on the raw number level, every minority has a higher fatal shooting percentage than they do relative to an arrest. The only racial group with that relationship inverted…? Caucasians. 

But let’s perform the test instead of jumping to conclusions. Let’s either confirm or deny that minorities tend to be fatally shot at a higher rate in a police encounter through the use of a statistical test. For this test, we make the assumption that the UCR provides us a reasonable (at least at a rate consistent) estimate of the number of police interactions with minorities over a particular period. Then we provide a sequence of two tests…

Result 2A: Fatal Police Shootings are SOMEWHAT racially biased. And it’s NOT who you think it is being targeted…

The controversial case is that fatal police shootings are racially biased in the direction of African American communities. To test this, we take a look at the number of police interactions and identify the number of fatal police shootings. Our hypothesis in this case is that the rate of arrests across races are consistent with the rate of fatal police shootings across races. A failed test will suggest then that a particular group is more likely to be fatally shot, while another group is less likely to be fatally shot.

This is a simple test, actually: the Chi-Square goodness-of-fit test. Given the arrest rates as an indicator of confrontational interactions between police and civilians, the test merely asks is the proportions of fatal shootings differ. Since there are 1710 fatal shootings over 2015 and 2016, we then expect there to be 927 fatal shootings of white persons, 455 fatal shootings of black persons, 266 fatal shootings of Hispanics, 20 fatal shootings of Asian persons, and 40 fatal shootings of other races. Performing the Chi-Square goodness-of-fit test, we obtain a test statistic of 9.98 with four degrees of freedom. This gives us a p-value of 0.040766.

Unfortunately, this p-value puts us in a sticky situation as it’s neither very large or very small. We’d like to see something larger than .20 or much less than .01. At the .01 level, we would say, fatal police shootings are not racially biased; but at the .05 level we would that fatal police shootings are indeed racially biased. Who’s to blame for this stickiness? Hispanic shootings. 

Of the 9.98 test statistic, roughly two-thirds of the weight comes from Hispanic persons being fatally shot at a rate much higher than expected. In fact, if Hispanics are removed from the analysis, the test statistic drops to 2.18 and the p-value inflates to 0.535898; indicating that there are no racial biases in shootings.

Note that Hispanics are only separated due to the Washington Post data.

VERDICT: Hispanics are more likely to be fatally shot in a police confrontation; and this is considered to be nonrandom. African Americans, Asians, and Whites are at random and are therefore not racially discriminated in fatal shootings. 

Result 2B: Fatal Police Shootings of African-Americans are not racially biased; but African-Americans ARE more likely to be targeted…

So while we show that given a police confrontation, an African American is not more likely to be fatally shot, we take a look at the given in that statement. Specifically, we identify the rate at which African-Americans are being subjected to police interactions.

This is another difficult test to piece together. Let’s remove race from the example and focus on a scenario that explains the difficulty of testing in a cartoonish way. Consider two populations of actors: 20 Pirates and 80 Not Pirates. Suppose that all Pirates are bad and that all Not Pirates usually nice. Suppose further we have two classrooms where two unfortunate teachers must teach their class rooms and hand out detentions whenever someone is bad. One teacher obtains 18 Pirates and the other teacher obtains 2 Pirates. We then find out that one teacher’s class has a significant portion in prison. How are we able to identify who the Pirates are? How do we allocate resources to crack down on Pirates?

This cartoon is the exact problem with answering the racial profiling question. Are police profiling African-Americans at a higher and more aggressive rate than any other race? Is the African-American community more prone to commit crime and therefore are being arrested at a rate equal to their actual crime rate? The roots of these questions are best explained by experts like Roland Fryer . In his analysis, he valiantly attempts to understand the cartoonish Pirate problem by identifying a micro-economics of a police interaction that results in a fatal shooting. Something that the Washington Post, the FBI UCR, nor even sites like SpotCrime are able to report.

So let’s give it our best try here and note where we make approximations to allow us to test for racial profiling. According to the CDC, there are approximately 15800 homicides each year. Since the most recent published tables are from 2014, we will use these numbers. Here we find that 7362 homicides are of Caucasians, 7876 homicides are of African-Americans, 308 are of Asians, and approximately 400 are of other races. In the CDC study, Hispanics are not separated. For 2014, the FBI UCR notes that 8,230 persons were arrested for murder; but of these 8230 persons, only 5703 homicides occurred. So this data may not be helpful without extra context (multiple charges for a single murder; single person with multiple murders; etc.).

So let’s look at some dispatch data. The website  actually gives insight to police calls in cities. Through the use of dispatch data, we can identify where folks are calling in and where police officers are relaying calls in when they make a stop that leads to an arrest. It’s not perfect, and the market over obtaining data can be brutal: read the terms of service for sites like

However, through an agreement with SpotCrime, this author was able to obtain dispatch record data (which includes calls of gunshots when in reality it was a car backfire) and did analysis on this in the city of Milwaukee, WI this past year. In the article, we found that a significant number of calls came from areas within the African-American community, which indicates that police are summoned more often than usual (relative to population distribution)  and therefore tend to patrol African American regions with a much higher frequency. So let’s take a look from the 2010 data from SpotCrime.

From the Milwaukee analysis, violent crime was prevalent in African American regions, with the exception of robberies, which also occurred in the mixed Hispanic and White areas south of Interstate-94, near West Allis. However, property crime (burglaries and theft) tended to be more frequent in non-African American homes. In 2010, the Milwaukee police department reported  6181 burglaries and 21212 thefts. While the bulk of these crimes tended to be in southern and central areas of the city (predominantly white), the police focused efforts in the violent crime areas in the northern areas of the city (predominantly black). This led to police efforts focused in more African American regions of the city and led to higher arrest rates in these communities; and more importantly, a higher incidence rate for fatal shootings. This patrolling increase is defined by the Black Lives Matter movement as targeting.

From the SpotCrime data set, we found that arrests for crimes were highest in African American and Hispanic neighborhoods, despite many robberies occurring in white sections of the town.

Screen Shot 2015-11-26 at 12.29.27 PM

Distribution of robberies in Milwaukee, WI. (Data provided by SpotCrime.)

So much so, that the Kullback-Leibler divergence on comparing the distribution of robbery arrests and robberies reported is nearly 7, indicating that the distribution of arrests in black communities is disproportionately higher than the reported robberies.

VERDICT: African Americans are more likely to be targeted but may be done so incidentally; dependent on multiple factors such as patrolling strategies associated with violent crime. 

Result 3: …due to the nature of violent crimes.

This result take a look at the FBI UCR data from 2014; as 2015 has yet to be published. Here, we take a look at solved murders in the United States as a function of race of victim and race of offender. In 2014, there were 5703 homicides where the races of both parties were known. These are given as follows:

V \ O White Black Asian Other Totals
White 2488 446 35 52 3021
Black 187 2205 15 44 2451
Asian 47 25 93 3 168
Other 34 17 3 9 63
Totals 2756 2693 146 108 5703

The Chi-Square goodness-of-fit test identifies that there is indeed a strong relationship between the race of the victim and the offender. In this case, the test statistic is 5185.38 with 9 degree of freedom. This results in a p-value much less than 0.000001; indicating the relationship. The main culprits are Asian-on-Asian crime (1829.28), Black-on-Black crime (948.27), white-on-black crime (839.98), white-on-white crime (723.99) and black-on-black crime (673.98).

Now, let’s break this down further. If we look solely at offender data, we find that of the 5703 reported arrests from the FBI UCR data, 2756 are committed by white offenders, 2693 are committed by black offenders, and 146 are committed by Asian offenders. Compare to the population distribution of races in the United States (77.1 white, 13.3 black, 5.6 Asian), the marginalized murder rates (48.33 white, 47.22 black, 5.30 Asian); we have that the test statistic is 5640.37; primarily contributed to by the African American community. Again with a p-value well below 0.0000001, we have that there is a disproportionate amount of violent crime in black communities.

VERDICT: African American communities are significantly more likely to have violent crime prevalent in their communities. Reasons why are not clear from crime data alone.  

Result 4: African Americans are more likely to be fatally shot unarmed.

So what have our results led us to at this point? Violent crime is prevalent in African American communities, which tends to lead to profiling and targeting by police departments. With these increased encounters, African Americans therefore have an increased (approximately 2.4 times higher than whites in the same situation) chance of being fatally shot by a police officer, despite no racial bias in the shooting death. And these trends are not showing any signs of slowing down.

So let’s take a look at one last set of data from where we started with the Washington Post catalogue. Over the course of these two years, the shooting of unarmed persons have steadily stayed the course. The distribution of such between the three major races (according to the Washington Post) are given as follows:

  Fatally Shot Unarmed
Black 457 54
Hispanic 307 25
White 878 53

You read this right. The highest number of unarmed persons fatally shot by police is African American. Nearly 12 percent of African Americans fatally shot by police are unarmed. The definition of unarmed is exactly that: no knives, no “toy weapon”, but rather only hands and the clothes on their backs. Compare this to 6 percent of white persons who are fatally shot unarmed by police.

Building this test, we assume the hypothesis that there is no relationships between race and chance of being fatally shot by police unarmed. This test is again a Chi-Square test. In this case, we assume that since race does not play a role in unarmed shootings, we should have an approximately uniform chance of being fatally shot. Thus the table is given as follows:

  Armed Unarmed Totals
Black 403 54 457
Hispanic 282 25 307
White 825 53 878
Totals 1510 132 1642

If the probability of being fatally shot unarmed by police is not dependent on race, we should expect to see approximately 37 African Americans unarmed, 25 Hispanics unarmed, and 71 Caucasians unarmed. The resulting test statistic is 13.59; which yields a p-value of 0.001119; which is significant enough to claim there is a dependence. In this case, taking a closer look at the numbers, we find that the main contributors are black unarmed deaths (8.11) and white unarmed deaths (4.38). Combined these make up 92% of the variation. Thus there is a decidedly heavy bias towards officers fatally shooting unarmed African Americans.

VERDICT: African Americans are much more likely to be fatally shot by a police officer despite being unarmed. 

Case Study…

Sounds familiar, doesn’t this? Consider the case study of Tony Robinson. He was one of the 54 listed above that was fatally shot by an officer despite being unarmed. Does that make him a victim? If what the Madison police department states is true, then ‘No.’ Physical violence upon a police officer will typically result in a shooting; or potentially less harmful. But there is a significant chance of losing your life in a physical altercation with an officer.

But does this make the officer justified? If the officer attempted a forced entry, as claimed on the Guardian and this resulted in having a drawn weapon on an unarmed person without back-up present, then a case can be made to say ‘No.’ as well.

The difficulty in evaluating these situations is that every little details needs to be taken into account. For instance, 18 seconds is actually a very long time in an altercation. Details have never been fully released with the altercation. And to this point, we may never know who is truly justified and who is really at fault.


In our analysis, we have come up with one controversial truth: African Americans are not more likely to be fatally shot during a confrontation with police. Data from the Washington Post proves this.

However, African Americans are more likely to be targeted, increasing their chances to be fatally shot during a confrontation with police. This was proven in a more round-about way through a series of multiple tests. First, we show that African American communities tend to have a higher violent crime rate. Due to this, it is more likely to have aggressive patrolling; in such a way that African American communities are more likely to be stopped and confronted by police for lesser crimes that are more commonly performed in other communities. And at this point, even with no discrimination in shootings, the rate becomes higher than random chance.

Unfortunately, despite no discrimination of fatally shooting during an altercation with police, African Americans are much more likely to be shot during an altercation when unarmed. This suggests that police officers are more likely to consider an unarmed; particularly male, black person to be more imposing than a white person. So much so that the unarmed shooting rate is almost twice as high (1.96 times).

So Now What?

Now we can ask for better data. For instance, all police cruisers have GPS installed. Why not collect the location data of all police cruisers and make it available to academics to study. This author, for instance, could use patrolling patterns to identify targeting and profiling patterns in police. We could also correlate crime activity relative to police positioning and response times and identify crime trends relative to police activity.

Such tools could actually help police departments train staff on profiling avoidance and stick to the crime work; instead of assuming small crimes in violent neighborhoods could potentially remove a violent criminal off the street.

Instead, we find situations where police are in areas they are sworn to protect and find themselves in unfamiliar territory attempting to restore order in a manner they were not entirely trained for; but rather trained to the best of the departments ability.

Similarly, by identifying case reports for incidences of physical altercations that resulted in fatal shootings; as well as altercations that ended in a much different manner, will help researchers aide police departments in identifying de-escalation techniques that are sorely needed. Because if you recall from our first bullet point.

Police shootings aren’t going down. Not by a long shot. Even with the spotlight shining on them.

But protesting isn’t going to reduce the shootings and crime. Advocating improved data collection and analysis to help improve training and reduce profiling will help. This includes open data and transparency into resolved police actions without giving away tactics and techniques for police departments.

Let’s see where this type of awareness can go.


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