# Crime, Race and Lethal Force in the USA — Part 3

• Перевод

This is the concluding part of my article devoted to a statistical analysis of police shootings and criminality among the white and the black population of the United States. In the first part, we talked about the research background, goals, assumptions, and source data; in the second part, we investigated the national use-of-force and crime data and tracked their connection with race.

Let's recall the intermediate inferences that we were able to make from the available data for 2000 — 2018:

• White police victims outnumber black victims in absolute figures.
• Use of lethal force results in an average of 5.9 per one million Black deaths and 2.3 per one million White deaths (Black victim count is 2.6 greater in unit values).
• Year-to-year scatter in Black lethal force fatalities is nearly twice the scatter in White fatalities.
• White fatalities grow continuously from year to year (by 0.1 — 0.2 per million on average), while Black fatalities rolled back to their 2009 level after climaxing in 2011 — 2013.
• Whites commit twice as many offenses as Blacks in absolute numbers, but three times as fewer in per capita numbers (per 1 million population within that race).
• Criminality among Whites grows more or less steadily over the entire period of investigation (doubled over 19 years). Criminality among Blacks also grows, but by leaps and starts; over the entire period, however, the growth factor is also 2, like with Whites.
• Fatal encounters with law enforcement are connected with criminality (number of offenses committed). The correlation though differs between the two races: for Whites, it is almost perfect, for Blacks — far from perfect.
• Lethal force victims grow 'in reply to' criminality growth, generally with a few years' lag (this is more conspicuous in the Black data).
• White offenders tend to meet death from the police a little more frequently than Black offenders.

Today, as I promised, we'll be looking at the geographical distribution of these data across the states, which ought to either confirm or confute the previous conclusions.

However, before we take up geography, let's make a step back and see what happens if we analyze only the most violent offenses instead of 'All Offenses' as the source data for criminality. Many of my readers have pointed out in their comments that this would have been more proper, since 'All Offenses' incorporate those which should not (in practice) be associated with aggressive behavior provoking police shooting, such as petty larceny or selling drugs. I cannot whole-heartedly agree with this reasoning because, as I see it, any offense can arouse or heighten attention from the law enforcement, which in turn may wind up sadly… Still, let's just be curious enough to check!

## Assault and Murder Instead of All Offenses

We just need to change one line of code where we form the crime dataset. Replace this line

df_crimes1 = df_crimes1.loc[df_crimes1['Offense'] == 'All Offenses']


with this:

df_crimes1 = df_crimes1.loc[df_crimes1['Offense'].str.contains('Assault|Murder')]


Our new filter now lets through only offenses connected with assault (simple and aggravated) and murder / non-negligent homicide (negligent / justifiable homicide / manslaughter cases are not included).

We leave the rest of the code as it was.

The number of crimes per 1 million population within each race now looks as follows:

We can see that, though the scale (Y-axis) is much lower, the shape of the curves is almost identical to the All Offenses ones we saw previously.

The criminality vs. lethal force victims curves for both races:

And the correlation matrix:
White_promln_cr White_promln_uof Black_promln_cr Black_promln_uof
White_promln_cr 1.000000 0.684757 0.986622 0.729674
White_promln_uof 0.684757 1.000000 0.614132 0.795486
Black_promln_cr 0.986622 0.614132 1.000000 0.680893
Black_promln_uof 0.729674 0.795486 0.680893 1.000000

The correlation between criminality and lethal force fatalities is worse this time (0.68 against 0.88 and 0.72 for All Offenses). But the silver lining here is the fact that the correlation coefficients for Whites and Blacks are almost equal, which gives reason to say there is some constant correlation between crime and police shootings / victims (regardless of race).

Now for our 'DIY' index — the ratio of lethal force deaths to the number of crimes (both per capita):

The difference here is even more apparent. The inference is the same: White criminals are more likely to get killed by the police than Black criminals.

The summary is that all our prior conclusions hold true.

Well, down to geography lessons now! :)

## Source Data

To investigate criminality in individual states, I used different source endpoints in the FBI database:

Unfortunately, I didn't manage to get complete data on committed offenses with the offense state, year and offender race, much as I tried. The returned results had large gaps, for example, some states were totally omitted. But the alternative data on arrests is quite sufficient for our humble research.

The first dataset contains crime counts for all the 51 states from 1991 to 2018, for the following offense categories:

1. violent crime (murder, rape, robbery and aggravated assault)
2. homicide (all types, including negligent / justifiable)
3. rape legacy (using outdated metrics — before 2013)
4. rape revised (using updated metrics — from 2013 on)
5. robbery
6. aggravated assault
7. property crime
8. burglary
9. larceny
10. motor vehicle theft
11. arson

For our purposes, we'll be using the 'violent crime' category, in keeping with the rest of the research.

The second dataset features the number of arrests for the 51 states from 2000 to 2018, with details on the arrested persons' race (refer to the previous part for the race categories). Since the arrest dataset uses a different offense classification and doesn't provide the combined 'violent crime' category, the requests and retrieved results are for the four constituent offenses — murder / non-negligent manslaughter, robbery, rape, and aggravated assault.

## Crime Distribution (No Racial Factor)

First, we'll look at the distribution of violent crimes across the states regardless of the offenders' race:

import pandas as pd, numpy as np

CRIME_STATES_FILE = ROOT_FOLDER + '\\crimes_by_state.csv'
usecols=['year', 'state_abbr', 'population', 'violent_crime'])


The resulting dataset:

year state_abbr population violent_crime
0 2016 AL 4860545 25878
1 1996 AL 4273000 24159
2 1997 AL 4319000 24379
3 1998 AL 4352000 22286
4 1999 AL 4369862 21421
... ... ... ... ...
1423 2000 DC 572059 8626
1424 2001 DC 573822 9195
1425 2002 DC 569157 9322
1426 2003 DC 557620 9061
1427 2016 DC 684336 8236

1428 rows × 4 columns

Adding the full state names (the list of states we already used in our research — CSV) and optimizing / sorting the data:

df_crime_states = df_crime_states.merge(df_state_names, on='state_abbr')
df_crime_states.dropna(inplace=True)
df_crime_states.sort_values(by=['year', 'state_abbr'], inplace=True)


Since the dataset already has population values, let's calculate the number of crimes per million people:

df_crime_states['crime_promln'] = df_crime_states['violent_crime'] * 1e6 /
df_crime_states['population']


Finally, we'll turn the data into a table spanning the 2000 — 2018 period transposing the state names and dropping the redundant columns:

df_crime_states_agg = df_crime_states.groupby(['state_name',
'year'])['violent_crime'].sum().unstack(level=1).T
df_crime_states_agg.fillna(0, inplace=True)
df_crime_states_agg = df_crime_states_agg.astype('uint32').loc[2000:2018, :]


The resulting table contains 19 rows (year observations from 2000 through 2018) and 51 columns (by the number of states).

Let's display the top 10 states for the average number of crimes:

df_crime_states_agg_top10 = df_crime_states_agg.describe().T.nlargest(10, 'mean').\
astype('uint32')


count mean std min 25% 50% 75% max
state_name
California 19 181514 19425 153763 165508 178597 193022 212867
Texas 19 117614 6522 104734 113212 121091 122084 126018
Florida 19 110104 18542 81980 92809 113541 127488 131878
New York 19 81618 9548 68495 75549 77563 85376 105111
Illinois 19 62866 10445 47775 54039 64185 69937 81196
Michigan 19 49273 5029 41712 44900 49737 54035 56981
Pennsylvania 19 46941 5066 39192 41607 48188 51021 55028
Tennessee 19 41951 2432 38063 40321 41562 43358 46482
Georgia 19 40228 3327 34355 38283 39435 41495 47353
North Carolina 19 37936 3193 32718 34706 38243 40258 43125

We'll also make it more graphic with a box plot:

df_crime_states_top10 = df_crime_states_agg.loc[:, df_crime_states_agg_top10.index]
plt = df_crime_states_top10.plot.box(figsize=(12, 10))
plt.set_ylabel('Violent crime count (2000 - 2018)')


The 'Hollywood' state easily and notoriously beats the rest 9. The 'prizewinners' are California, Texas and Florida, all three in the South, the regular settings for most Hollywood criminal blockbusters.

You can also see that criminality has changed considerably over the observed period in some states (California, Florida and Illinois), whereas in others (like Georgia) it has remained almost constant.

I tend to think the crime rates are in some way connected with population :) Let's see the top 10 states by population in 2018:

df_crime_states_2018 = df_crime_states.loc[df_crime_states['year'] == 2018]
plt = df_crime_states_2018.nlargest(10, 'population').\
sort_values(by='population').plot.barh(x='state_name',
y='population', legend=False, figsize=(10,5))
plt.set_xlabel('2018 Population')
plt.set_ylabel('')


Same old mugs here :) Let's check the correlation between crimes and population:

df_corr = df_crime_states[df_crime_states['year']>=2000].groupby(['state_name']).mean()
df_corr = df_corr.loc[:, ['population', 'violent_crime']]
df_corr.corr(method='pearson').at['population', 'violent_crime']


The calculated Pearson correlation coefficient is 0.98. Q.E.D.

But the per capita crime counts give a staringly different picture:

plt = df_crime_states_2018.nlargest(10, 'crime_promln').\
sort_values(by='crime_promln').plot.barh(x='state_name',
y='crime_promln', legend=False, figsize=(10,5))
plt.set_xlabel('Number of violent crimes per 1 mln. population (2018)')
plt.set_ylabel('')


There's a pretty kettle of fish! The leaders by per capita crimes are the least populated states: District Columbia (with the US capital) and Alaska (both home to some 700+ thousand people as of 2018), as well as one medium-populated state — New Mexico, with 2 mln. people. Only one state from our previous toplist is featured here — Tennessee, which gives this state a less-than-desirable reputation.

We will then display these results on the US map. To do this, we need the folium library:

import folium


First, the 2018 absolute crime counts:

FOLIUM_URL = 'https://raw.githubusercontent.com/python-visualization/folium/master/examples/data'
FOLIUM_US_MAP = f'{FOLIUM_URL}/us-states.json'

m = folium.Map(location=[48, -102], zoom_start=3)

folium.Choropleth(
geo_data=FOLIUM_US_MAP,
name='choropleth',
data=df_crime_states_2018,
columns=['state_abbr', 'violent_crime'],
key_on='feature.id',
fill_color='YlOrRd',
fill_opacity=0.7,
line_opacity=0.2,
legend_name='Violent crimes in 2018',
bins=df_crime_states_2018['violent_crime'].quantile(
list(np.linspace(0.0, 1.0, 5))).to_list(),
reset=True

m


The same in per capita values (per 1 million):

m = folium.Map(location=[48, -102], zoom_start=3)

folium.Choropleth(
geo_data=FOLIUM_US_MAP,
name='choropleth',
data=df_crime_states_2018,
columns=['state_abbr', 'crime_promln'],
key_on='feature.id',
fill_color='YlOrRd',
fill_opacity=0.7,
line_opacity=0.2,
legend_name='Violent crimes in 2018 (per 1 mln. population)',
bins=df_crime_states_2018['crime_promln'].quantile(
list(np.linspace(0.0, 1.0, 5))).to_list(),
reset=True

m


In the first case, as we can see, crimes are more or less evenly distributed in the North to South direction. In the second case, it's mostly the Southern states plus DC and Alaska that make the trend.

## Lethal Force Fatalities Across States (No Racial Factor)

We are now going to look at lethal force used in individual states across the country.

To prepare the dataset, we'll complement the UOF (Use Of Force) data we used previously by the full state names, group the cases by states, and constrain the observations to years 2000 through 2018:

df_fenc_agg_states = df_fenc.merge(df_state_names, how='inner',
left_on='State', right_on='state_abbr')
df_fenc_agg_states.fillna(0, inplace=True)
df_fenc_agg_states = df_fenc_agg_states.rename(columns={'state_name_x': 'State Name'})
df_fenc_agg_states = df_fenc_agg_states.loc[:, ['Year', 'Race', 'State',
'State Name', 'Cause', 'UOF']]

df_fenc_agg_states = df_fenc_agg_states.\
groupby(['Year', 'State Name', 'State'])['UOF'].\
count().unstack(level=0)
df_fenc_agg_states.fillna(0, inplace=True)
df_fenc_agg_states = df_fenc_agg_states.astype('uint16').loc[:, :2018]
df_fenc_agg_states = df_fenc_agg_states.reset_index()


Top 10 states for police victims in 2018:

df_fenc_agg_states_2018 = df_fenc_agg_states.loc[:, ['State Name', 2018]]
plt = df_fenc_agg_states_2018.nlargest(10, 2018).sort_values(2018).plot.barh(
x='State Name', y=2018, legend=False, figsize=(10,5))
plt.set_xlabel('Number of UOF victims in 2018')
plt.set_ylabel('')


Let's also review the data for the entire period as a box plot:

fenc_top10 = df_fenc_agg_states.loc[df_fenc_agg_states['State Name'].\
isin(df_fenc_agg_states_2018.nlargest(10, 2018)['State Name'])]
fenc_top10 = fenc_top10.T
fenc_top10.columns = fenc_top10.loc['State Name', :]
fenc_top10 = fenc_top10.reset_index().loc[2:, :].set_index('Year')
df_sorted = fenc_top10.mean().sort_values(ascending=False)
fenc_top10 = fenc_top10.loc[:, df_sorted.index]

plt = fenc_top10.plot.box(figsize=(12, 6))
plt.set_ylabel('Number of UOF victims (2000 - 2018)')


Yep! The same 'unholy trio' of California, Texas and Florida, with their other two Southern sidekicks — Arizona and Georgia. The leaders again show large scatter indicative of year-to-year changes.

## Connection Between Lethal Force Fatalities and Crimes

As in the previous part of this research, we are investigating the possible connection between criminality and deaths at the hands of law enforcement. We'll start without the racial factor, to see if such a connection exists in principle and how it varies from state to state.

At first, we must merge the UOF and (violent) crime datasets, setting the observation period to 2000 — 2018:

# add full state names
df_fenc_crime_states = df_fenc.merge(df_state_names, how='inner',
left_on='State', right_on='state_abbr')
# rename some columns
df_fenc_crime_states = df_fenc_crime_states.rename(columns={'Year': 'year',
'state_name_x': 'state_name'})
# truncate period to 2000-2018
df_fenc_crime_states = df_fenc_crime_states[df_fenc_crime_states['year'].between(2000,
2018)]
# group by year and state
df_fenc_crime_states = df_fenc_crime_states.groupby(['year', 'state_name'])['UOF'].\
count().reset_index()
# join with crime data
df_fenc_crime_states = df_fenc_crime_states.merge(df_crime_states[df_crime_states['year'].\
between(2000, 2018)], how='outer', on=['year', 'state_name'])
# set missing data to zero
df_fenc_crime_states.fillna({'UOF': 0}, inplace=True)
# unify data types
df_fenc_crime_states = df_fenc_crime_states.astype({'year': 'uint16', 'UOF': 'uint16',
'population': 'uint32', 'violent_crime': 'uint32'})
# sort data
df_fenc_crime_states = df_fenc_crime_states.sort_values(by=['year', 'state_name'])


Resulting dataset

year state_name UOF state_abbr population violent_crime crime_promln
0 2000 Alabama 7 AL 4447100 21620 4861.595197
1 2000 Alaska 2 AK 626932 3554 5668.876369
2 2000 Arizona 11 AZ 5130632 27281 5317.278651
3 2000 Arkansas 4 AR 2673400 11904 4452.756789
4 2000 California 97 CA 33871648 210531 6215.552311
... ... ... ... ... ... ... ...
907 2018 Virginia 18 VA 8517685 17032 1999.604353
908 2018 Washington 24 WA 7535591 23472 3114.818732
909 2018 West Virginia 7 WV 1805832 5236 2899.494527
910 2018 Wisconsin 10 WI 5813568 17176 2954.467893
911 2018 Wyoming 4 WY 577737 1226 2122.072846

As you will remember, the UOF column contains the number of deaths from encounters with law enforcement officers (who I sometimes call here just 'the police', but who include, of course, other agencies such as the FBI) where lethal force was used intentionally.

We will also make a separate dataset with year-average values:

df_fenc_crime_states_agg = df_fenc_crime_states.groupby(['state_name']).\
mean().loc[:, ['UOF', 'violent_crime']]


Now let's look at the year averages for crimes and lethal force fatalities for all the 51 states on one plot:

plt = df_fenc_crime_states_agg['violent_crime'].plot.bar(legend=True, figsize=(15,5))
plt.set_ylabel('Number of violent crimes (year average)')
plt2 = df_fenc_crime_states_agg['UOF'].plot(secondary_y=True, style='g', legend=True)
plt2.set_ylabel('Number of UOF victims (year average)', rotation=90)
plt2.set_xlabel('')
plt.set_xlabel('')
plt.set_xticklabels(df_fenc_crime_states_agg.index, rotation='vertical')


Looking closely at this combined chart, one can see the following:

• the connection between crime and use of force is plainly trackable: the green UOF curve tends to repeat the shape of the crime bars
• the more criminal states (such as Florida, Illinois, Michigan, New York and Texas) evince proportionately less use of force compared to the less criminal states

Let's also make a scatterplot:

plt = df_fenc_crime_states_agg.plot.scatter(x='violent_crime', y='UOF')
plt.set_xlabel('Number of violent crimes (year average)')
plt.set_ylabel('Number of UOF victims (year average)')


Here it becomes conspicuous that the ratio between crime and use of lethal force is affected by the crime rate. Speaking crudely, in states with the number of violent crimes below 75k the number of police victims grows more slowly; whereas in the states with the crime count above 75k this growth is quite steep. This latter group includes, as we can see, only four states. Let's look them 'in the face':

df_fenc_crime_states_agg[df_fenc_crime_states_agg['violent_crime'] > 75000]


UOF violent_crime
state_name
California 133.263158 181514.578947
Florida 54.578947 110104.315789
New York 19.157895 81618.052632
Texas 64.368421 117614.631579

Will you be surprised? We've got the same 'four horsemen of the Apocalypse': California, Florida, Texas and New York.

Correspondingly, let's calculate the correlation coefficients between our data for three cases:

1. states with the year average crime count up to 75,000
2. states with the year average crime count above 75,000
3. all the states

For the first case:

df_fenc_crime_states_agg[df_fenc_crime_states_agg['violent_crime'] <= \
75000].corr(method='pearson').at['UOF', 'violent_crime']


— we obtain 0.839 as the correlation coefficient. This is a statistically valid value, although it doesn't reach 0.9 due to scatter across the 47 states.

For the first case:

df_fenc_crime_states_agg[df_fenc_crime_states_agg['violent_crime'] > \
75000].corr(method='pearson').at['UOF', 'violent_crime']


— we get 0.999 — an ideal correlation!

For the last case (all states):

df_fenc_crime_states_agg.corr(method='pearson').at['UOF', 'violent_crime']


— the correlation is estimated at 0.935. This overall correlation may be considered very good.

Let's now look at the geographical distribution of our 'offender shootdown' index (the term is coined here for brevity). As before, we divide the number of lethal force fatalities by the number of crimes:

df_fenc_crime_states_agg['uof_by_crime'] = df_fenc_crime_states_agg['UOF'] /
df_fenc_crime_states_agg['violent_crime']
plt = df_fenc_crime_states_agg.loc[:, 'uof_by_crime'].sort_values(ascending=False).\
plot.bar(figsize=(15,5))
plt.set_xlabel('')
plt.set_ylabel('Ratio of UOF victims to number of violent crimes')


It is interesting to observe that our erstwhile leaders have shifted toward the center or even the rightmost end of the chart, which must mean that the most criminal states don't have the most 'bloodthirsty' police (towards real or potential offenders).

Intermediate conclusions:
1. The number of violent crimes is directly proportionate to population (good call, Captain Obvious!)
2. The most populated states (California, Florida, Texas and New York) are also the most criminal, in absolute values.
3. In per capita values, Southern states are more criminal than Northern states, with the exception of Alaska and District Columbia.
4. Lethal force deaths are correlated to criminality with an average coefficient of 0.93 across all the states. This correlation reaches almost unity (strictly linear) for the most criminal states and only 0.84 for the rest.

## Racial Factor in Criminality and Lethal Force Fatalities Across States

Proving that crime rates do affect police victim rates, let's add the racial factor and see what it affects. As I explained above, we'll be using the arrest data for this purpose as being the most complete and covering the main offenses for all the states. There is, of course, no such state or country where one could equate the number of committed crimes to the number of arrests; yet these parameters are closely related. As such, we can do very well with arrest data for our statistical analysis. And, as we already agreed, only violent offenses (murder, rape, robbery, aggravated assault) will be taken into account.

Let's load the source data from the CSV file and routinely add the full state names:

ARRESTS_FILE = ROOT_FOLDER + '\\arrests_by_state_race.csv'
# arrests of Blacks and Whites only
usecols=['data_year', 'state', 'white', 'black'])
# sum the four offenses and group by states
df_arrests = df_arrests.groupby(['data_year', 'state']).sum().reset_index()
df_arrests = df_arrests.merge(df_state_names, left_on='state', right_on='state_abbr')
# rename / remove columns
df_arrests = df_arrests.rename(columns={'data_year': 'year'}).drop(columns='state_abbr')
# peek at the result


year state black white state_name
0 2000 AK 140 613 Alaska
1 2001 AK 139 718 Alaska
2 2002 AK 143 677 Alaska
3 2003 AK 173 801 Alaska
4 2004 AK 163 765 Alaska

We'll also create a dataframe with year average values:

df_arrests_agg = df_arrests.groupby(['state_name']).mean().drop(columns='year')


Arrests of Whites and Blacks in 51 states (year average counts)

black white
state_name
Alabama 2805.842105 1757.315789
Arizona 1378.368421 7007.157895
Arkansas 2387.894737 2303.789474
California 26668.368421 87252.315789
Connecticut 2097.631579 2981.210526
Delaware 1356.894737 1048.578947
District of Columbia 111.111111 4.944444
Florida 12.000000 7.000000
Georgia 8262.842105 3502.894737
Hawaii 81.052632 368.736842
Idaho 44.000000 1362.263158
Illinois 5699.842105 1841.894737
Indiana 3553.368421 5192.263158
Iowa 1104.421053 3039.473684
Kansas 522.315789 1501.315789
Kentucky 1476.894737 1906.052632
Louisiana 5928.789474 3414.263158
Maine 63.736842 699.526316
Maryland 7189.105263 4010.684211
Massachusetts 3407.157895 7319.684211
Michigan 7628.157895 6304.157895
Minnesota 2231.210526 2645.736842
Mississippi 1462.210526 474.368421
Missouri 5777.473684 5703.368421
Montana 27.684211 673.684211
New Hampshire 68.368421 640.789474
New Jersey 6424.157895 6043.789474
New Mexico 234.421053 2809.368421
New York 8394.526316 8734.947368
North Carolina 10527.947368 7412.947368
North Dakota 61.263158 277.052632
Ohio 4063.947368 4071.368421
Oklahoma 1625.105263 3353.000000
Oregon 445.105263 3373.368421
Pennsylvania 11974.157895 11039.473684
Rhode Island 275.684211 699.210526
South Carolina 5578.526316 3615.421053
South Dakota 67.105263 349.368421
Tennessee 6799.894737 8462.526316
Texas 10547.631579 22062.684211
Utah 167.105263 1748.894737
Vermont 43.526316 439.210526
Virginia 4100.421053 3060.263158
Washington 1688.947368 6012.105263
West Virginia 271.263158 1528.315789
Wisconsin 3440.055556 4107.722222
Wyoming 27.263158 506.947368

Looking at this table, one can't overlook some oddities. In some states the arrest counts reach hundreds and thousands, while in others — only dozens or fewer. That's the case with Florida, one of the most populated states: it counts only 19 arrests per year (12 Blacks and 7 Whites). Surely, some data is missing here; let's check:

df_arrests[df_arrests['state'] == 'FL']


And indeed we see that data for Florida is available only for 2017. Well, we'll have to put up with this, I suppose. All the other states have complete data. But the ten / hundred-fold difference should be accounted for by population. Let's add population-by-race data and have a look.

The population data was taken from the US Census Bureau website (which is for some reason not accessible in Russia). You can download the prepared CSV file with 2010 — 2019 data from here.

Unfortunately, no state population data exist for prior periods (2000 — 2009). We have therefore to narrow down our observation period to 9 years (from 2010 through 2018) for this part of the research.

POP_STATES_FILES = ROOT_FOLDER + '\\us_pop_states_race_2010-2019.csv'
# the source CSV has a specific format, so some trickery is required :)
df_pop_states = df_pop_states.melt('state_name', var_name='r_year', value_name='pop')
df_pop_states['race'] = df_pop_states['r_year'].str[0]
df_pop_states['year'] = df_pop_states['r_year'].str[2:].astype('uint16')
df_pop_states.drop(columns='r_year', inplace=True)
df_pop_states = df_pop_states[df_pop_states['year'].between(2000, 2018)]
df_pop_states = df_pop_states.groupby(['state_name', 'year', 'race']).sum().\
unstack().reset_index()
df_pop_states.columns = ['state_name', 'year', 'black_pop', 'white_pop']


White and Black population across states

year black_pop white_pop
state_name
Alabama 2010 5044936 13462236
Alabama 2011 5067912 13477008
Alabama 2012 5102512 13484256
Alabama 2013 5137360 13488812
Alabama 2014 5162316 13493432
... ... ... ...
Wyoming 2014 31392 2167008
Wyoming 2015 29568 2177740
Wyoming 2016 29304 2170700
Wyoming 2017 29444 2148128
Wyoming 2018 29604 2139896

Merging this data with the arrests dataset, we can calculate the per-million arrest counts:

df_arrests_2010_2018 = df_arrests.merge(df_pop_states, how='inner',
on=['year', 'state_name'])
df_arrests_2010_2018['white_arrests_promln'] = df_arrests_2010_2018['white'] * 1e6 /
df_arrests_2010_2018['white_pop']
df_arrests_2010_2018['black_arrests_promln'] = df_arrests_2010_2018['black'] * 1e6 /
df_arrests_2010_2018['black_pop']


And again let's calculate the year averages:

df_arrests_2010_2018_agg = df_arrests_2010_2018.groupby(
['state_name', 'state']).mean().drop(columns='year').reset_index()
df_arrests_2010_2018_agg = df_arrests_2010_2018_agg.set_index('state_name')


Combined arrest dataset with absolute and per-million counts

state black white black_pop white_pop white_arrests_promln black_arrests_promln
state_name
Alabama AL 1682.000000 1342.000000 5.152399e+06 1.349158e+07 99.424741 324.055203
Alaska AK 255.000000 870.555556 1.069489e+05 1.957445e+06 445.199704 2390.243876
Arizona AZ 1635.555556 6852.000000 1.279172e+06 2.260403e+07 302.923002 1267.000192
Arkansas AR 1960.666667 2466.000000 1.855574e+06 9.465137e+06 260.459917 1055.854934
California CA 24381.666667 79477.000000 1.007921e+07 1.128020e+08 704.731408 2419.234376
Colorado CO 1377.222222 5171.555556 9.508173e+05 1.882940e+07 274.209456 1439.257054
Connecticut CT 1823.777778 2295.333333 1.643690e+06 1.165681e+07 196.712775 1114.811569
Delaware DE 1318.000000 914.111111 8.354622e+05 2.635794e+06 347.374980 1582.395733
District of Columbia DC 139.222222 4.777778 1.288488e+06 1.154416e+06 4.112547 108.101938
Florida FL 12.000000 7.000000 1.415383e+07 6.498292e+07 0.107721 0.847827
Georgia GA 8137.222222 4271.444444 1.279378e+07 2.500293e+07 170.939250 639.869143
Hawaii HI 81.333333 383.777778 1.124298e+05 1.453712e+06 264.353469 725.477589
Idaho ID 51.888889 1373.777778 5.288222e+04 6.154316e+06 223.151878 978.205026
Illinois IL 4216.000000 1284.222222 7.554687e+06 3.980927e+07 32.199075 557.493894
Indiana IN 2924.444444 5186.111111 2.522917e+06 2.267508e+07 228.699515 1155.168768
Iowa IA 1181.000000 2999.222222 4.305640e+05 1.141794e+07 262.666753 2760.038539
Kansas KS 539.555556 1512.111111 7.116182e+05 1.006714e+07 150.232160 758.851182
Kentucky KY 1443.888889 2173.666667 1.442174e+06 1.558094e+07 139.526970 1001.433470
Louisiana LA 5917.000000 3255.333333 6.021228e+06 1.174245e+07 277.277874 981.334817
Maine ME 78.000000 678.000000 7.667733e+04 5.059062e+06 134.024032 1019.061684
Maryland MD 6460.444444 3325.444444 7.229037e+06 1.426036e+07 233.317775 893.942720
Massachusetts MA 3349.555556 6895.111111 2.249232e+06 2.226671e+07 309.745910 1505.096888
Michigan MI 6302.444444 5647.444444 5.645176e+06 3.170670e+07 178.111684 1116.364030
Minnesota MN 2570.000000 2686.777778 1.311818e+06 1.867259e+07 143.902882 1986.464052
Mississippi MS 1251.000000 418.777778 4.478208e+06 7.122651e+06 58.753686 279.574565
Missouri MO 4588.333333 5146.111111 2.854060e+06 2.023871e+07 254.292323 1608.303611
Montana MT 34.222222 788.333333 2.210444e+04 3.660813e+06 214.944902 1525.795754
Nebraska NE 618.888889 1154.888889 3.701520e+05 6.709768e+06 172.269972 1687.725359
Nevada NV 2450.000000 4480.333333 1.052192e+06 8.647157e+06 517.401564 2316.374085
New Hampshire NH 89.777778 784.777778 7.873600e+04 5.012056e+06 156.580888 1141.127571
New Jersey NJ 5429.555556 4971.888889 5.241910e+06 2.595141e+07 191.427955 1037.217679
New Mexico NM 260.111111 3136.000000 2.053876e+05 6.905377e+06 454.129135 1268.115549
New York NY 6035.777778 6600.222222 1.373077e+07 5.534157e+07 119.253616 439.581451
North Carolina NC 9549.000000 6759.333333 8.804027e+06 2.844145e+07 238.320077 1088.968561
North Dakota ND 100.666667 386.222222 6.583289e+04 2.583206e+06 149.190455 1536.987272
Ohio OH 3632.888889 3733.333333 5.879375e+06 3.844592e+07 97.107129 617.699379
Oklahoma OK 1577.333333 3049.000000 1.189604e+06 1.160567e+07 262.904593 1326.463864
Oregon OR 375.444444 3125.000000 3.292284e+05 1.402225e+07 222.819615 1148.158169
Pennsylvania PA 11227.000000 10652.111111 5.945100e+06 4.232445e+07 251.598838 1893.415475
Rhode Island RI 274.888889 595.000000 3.275551e+05 3.592825e+06 165.605635 837.932682
South Carolina SC 4703.222222 3094.111111 5.365012e+06 1.324712e+07 234.287821 877.892998
South Dakota SD 103.777778 448.333333 6.154533e+04 2.903489e+06 153.995184 1641.137012
Tennessee TN 7603.000000 9068.666667 4.460808e+06 2.070126e+07 438.486812 1708.022356
Texas TX 10821.666667 21122.111111 1.345661e+07 8.628389e+07 245.051258 803.917061
Utah UT 193.222222 1797.333333 1.558876e+05 1.079659e+07 166.431266 1240.117890
Vermont VT 54.222222 520.555556 3.017111e+04 2.376143e+06 219.129918 1785.111547
Virginia VA 4059.555556 3071.222222 6.544598e+06 2.340732e+07 131.178648 620.504151
Washington WA 1791.777778 5870.444444 1.147000e+06 2.289368e+07 256.632241 1566.862244
West Virginia WV 294.111111 1648.666667 2.597649e+05 6.908718e+06 238.517207 1132.059057
Wisconsin WI 3525.333333 4046.222222 1.516534e+06 2.018658e+07 200.441064 2325.622492
Wyoming WY 28.777778 464.555556 2.856356e+04 2.151349e+06 216.004646 1005.725503

Let's visualize this stuff.

1. Absolute arrest counts

plt = df_arrests_2010_2018_agg[['white', 'black']].sort_index(ascending=False).\
plot.barh(color=['g', 'olive'], figsize=(10, 20))
plt.set_ylabel('')
plt.set_xlabel('Year-average arrest count (2010-2018)')


Tall image

2. Arrest counts per million population (for each race)

plt = df_arrests_2010_2018_agg[['white_arrests_promln', 'black_arrests_promln']].\
sort_index(ascending=False).plot.barh(color=['g', 'olive'], figsize=(10, 20))
plt.set_ylabel('')
plt.set_xlabel('Year-average arrest count per 1 mln. within race (2010-2018)')


Another tall image

What can we infer from this data?

First of all, we see that the number of arrests is affected by population — this is observed for both races.

Secondly, Whites get busted somewhat more often than Blacks in absolute figures. The 'somewhat' — because this rule isn't universal for all the states (exclusions are North Carolina, Georgia, Louisiana, etc.); at the same time, the difference is but slight in most states, except a few (like California, Texas, Colorado, Massachusetts and a few others).

Last but not least, Blacks get arrested much more often in all the states in per capita values.

Let's back these observations by numbers.

Difference between the average White and Black arrest counts:

df_arrests_2010_2018['white'].mean() / df_arrests_2010_2018['black'].mean()


— we get 1.56. That is, the observed 9 years saw on average one and a half times more Whites being arrested than Blacks.

Then in per capita values:

df_arrests_2010_2018['white_arrests_promln'].mean() /
df_arrests_2010_2018['black_arrests_promln'].mean()


— the ratio is 0.183. That is, a Black person is on average 5.5 times more likely to get arrested than a White person.

Thus, the previous conclusion of higher criminality among Blacks (compared to Whites) is confirmed by the arrest data for all the states of the USA.

To understand how race and criminality are connected with lethal force victims, let's merge the two datasets.

First, we prepare the use-of-force data with the victims' race details:

df_fenc_agg_states1 = df_fenc.merge(df_state_names, how='inner',
left_on='State', right_on='state_abbr')
df_fenc_agg_states1.fillna(0, inplace=True)
df_fenc_agg_states1 = df_fenc_agg_states1.rename(columns={
'state_name_x': 'state_name', 'Year': 'year'})
df_fenc_agg_states1 = df_fenc_agg_states1.loc[df_fenc_agg_states1['year'].\
between(2000, 2018), ['year', 'Race', 'state_name', 'UOF']]
df_fenc_agg_states1 = df_fenc_agg_states1.groupby(['year', 'state_name', 'Race'])['UOF'].\
count().unstack().reset_index()
df_fenc_agg_states1 = df_fenc_agg_states1.rename(columns={
'Black': 'black_uof', 'White': 'white_uof'})
df_fenc_agg_states1 = df_fenc_agg_states1.fillna(0).astype({
'black_uof': 'uint32', 'white_uof': 'uint32'})


Resulting UOF dataset

Race year state_name black_uof white_uof
0 2000 Alabama 4 3
2 2000 Arizona 0 11
3 2000 Arkansas 1 3
4 2000 California 19 78
... ... ... ... ...
907 2018 Virginia 11 7
908 2018 Washington 0 24
909 2018 West Virginia 2 5
910 2018 Wisconsin 3 7
911 2018 Wyoming 0 4

Then we're merging it with the arrest data:

df_arrests_fenc = df_arrests.merge(df_fenc_agg_states1,
on=['state_name', 'year'])
df_arrests_fenc = df_arrests_fenc.rename(columns={
'white': 'white_arrests', 'black': 'black_arrests'})


Example data for 2017

year state black_arrests white_arrests state_name black_uof white_uof
15 2017 AK 266 859 Alaska 2 3
34 2017 AL 3098 2509 Alabama 7 17
53 2017 AR 2092 2674 Arkansas 6 7
72 2017 AZ 2431 7829 Arizona 6 43
91 2017 CA 24937 80367 California 25 137
110 2017 CO 1781 6079 Colorado 2 27
127 2017 CT 1687 2114 Connecticut 1 5
140 2017 DE 1198 782 Delaware 4 3
159 2017 GA 7747 4171 Georgia 15 21
173 2017 HI 88 419 Hawaii 0 1
192 2017 IA 1400 3524 Iowa 1 5
210 2017 ID 61 1423 Idaho 0 6
229 2017 IL 2847 947 Illinois 13 11
248 2017 IN 3565 4300 Indiana 9 13
267 2017 KS 585 1651 Kansas 3 10
286 2017 KY 1481 2035 Kentucky 1 18
305 2017 LA 5875 2284 Louisiana 13 5
324 2017 MA 2953 6089 Massachusetts 1 4
343 2017 MD 6662 3371 Maryland 8 5
361 2017 ME 89 675 Maine 1 8
380 2017 MI 6149 5459 Michigan 6 7
399 2017 MN 2513 2681 Minnesota 1 7
418 2017 MO 4571 5007 Missouri 13 20
437 2017 MS 1266 409 Mississippi 7 10
455 2017 MT 50 915 Montana 0 3
474 2017 NC 8177 5576 North Carolina 9 14
501 2017 NE 80 578 Nebraska 0 1
516 2017 NH 113 817 New Hampshire 0 3
535 2017 NJ 4859 4136 New Jersey 9 6
554 2017 NM 205 2094 New Mexico 0 20
573 2017 NV 2695 4657 Nevada 3 12
592 2017 NY 5923 6633 New York 7 9
611 2017 OH 4472 3882 Ohio 11 23
630 2017 OK 1638 2872 Oklahoma 3 20
649 2017 OR 453 3222 Oregon 2 9
668 2017 PA 10123 10191 Pennsylvania 7 17
681 2017 RI 315 633 Rhode Island 0 1
700 2017 SC 4645 2964 South Carolina 3 10
712 2017 SD 124 537 South Dakota 0 2
731 2017 TN 6654 8496 Tennessee 4 24
750 2017 TX 11493 20911 Texas 18 56
769 2017 UT 199 1964 Utah 1 5
788 2017 VA 4283 3247 Virginia 8 17
804 2017 VT 75 626 Vermont 0 1
823 2017 WA 1890 5804 Washington 8 27
842 2017 WV 350 1705 West Virginia 1 10
856 2017 WY 36 549 Wyoming 0 1
872 2017 DC 135 8 District of Columbia 1 1
890 2017 WI 3604 4106 Wisconsin 6 15
892 2017 FL 12 7 Florida 19 43

OK, time to calculate the correlation coefficients between arrests and lethal force fatalities, as we did before:

df_corr = df_arrests_fenc.loc[:, ['white_arrests', 'black_arrests',
'white_uof', 'black_uof']].corr(method='pearson').iloc[:2, 2:]


white_uof black_uof
white_arrests 0.872766 0.622167
black_arrests 0.702350 0.766852

Again we've produced quite good correlations: 0.87 for Whites and 0.77 for Blacks. It's curious that these values are very close to those we obtained for All Offenses in the previous part of the article (0.88 for Whites and 0.72 for Blacks).

What about our 'offender shootdown' index? Let's check:

df_arrests_fenc['white_uof_by_arr'] = df_arrests_fenc['white_uof'] /
df_arrests_fenc['white_arrests']
df_arrests_fenc['black_uof_by_arr'] = df_arrests_fenc['black_uof'] /
df_arrests_fenc['black_arrests']
df_arrests_fenc.replace([np.inf, -np.inf], np.nan, inplace=True)
df_arrests_fenc.fillna({'white_uof_by_arr': 0, 'black_uof_by_arr': 0}, inplace=True)


To see how this index is distributed geographically, let's take the 2018 data point:

plt = df_arrests_fenc.loc[df_arrests_fenc['year'] == 2018,
['state_name', 'white_uof_by_arr', 'black_uof_by_arr']].\
sort_values(by='state_name', ascending=False).\
plot.barh(x='state_name', color=['g', 'olive'], figsize=(10, 20))
plt.set_ylabel('')
plt.set_xlabel('Ratio of UOF victims to violent crimes (2018)')


Tall image again

The index for Whites is greater in most states, with some exclusions (Utah, West Virginia, Kansas, Idaho, and District Columbia).

Let's compare the values for Whites and Blacks averaged for all the states:

plt = df_arrests_fenc.loc[:, ['white_uof_by_arr', 'black_uof_by_arr']].\
mean().plot.bar(color=['g', 'olive'])
plt.set_ylabel('Ratio of UOF victims to violent crimes (2018)')
plt.set_xticklabels(['White', 'Black'], rotation=0)


The index is 2.5 times greater for Whites than for Blacks. If this index really says something, it means that a White criminal is on average 2.5 times more likely to meet death from the police than a Black criminal. Of course, this index varies much from state to state: for example, in Idaho a Black criminal is twice as likely to become a law enforcement victim, whereas in Mississippi — four times less likely.

Well, that's it really. Time to summarize our research.

## Conclusions

1. In the US, criminality is a function of population. The most 'criminal' states that we are used to watching movies or read about are simply the most populated. When analyzing per capita crime rates, the top positions are taken by some quite unexpected states like Alaska, District Columbia (with Washington City) and New Mexico.
2. Southern states are on average more criminal than Northern states (in per capita crime values).
3. Per capita crimes and arrests are unevenly distributed among the US white and black populations: black persons commit 3 times more crimes and are 5 times more often arrested than white persons.
4. A black person is on average 2.5 times more likely to get killed in an encounter with law enforcement than a white person.
5. Lethal force fatalities correlate well with criminality: the higher the crime rate, the more people get killed by the police. This correlation holds true for most states and for both races, although it is somewhat more pronounced among the white population. This is also confirmed by the difference in the victim-to-crime ratio between the races: white criminals are more likely to get killed by the police.

As a final word, I'd like to say thanks to my readers for their valuable comments and advice.

P.S. In a future (separate) article I am planning to continue analyzing crime and its connection with race in the US. We can first look into hate crimes and then discuss the law enforcement / offender interfaces from a reversed point of view, investigating line-of-duty fatalities among US police officers. I'd appreciate if you let me know in the comments if this subject is of interest.

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