Race, Police Shooting, and Probability

I just read a Facebook comment by someone who was apparently downplaying the Black Lives Matter movement by pointing out that the police shoot more white Americans than black Americans.

True, but it’s a classic error in statistical reasoning. The vast majority of drivers involved in accidents are sober, but it doesn’t follow that one is more likely to have an accident if one is sober than if drunk. That is, the probability that a person was drunk given that he was in an accident is very low, but the probability that someone will be in an accident given that he is drunk is very high.

Whites comprise 62% of the population, while African-Americans are only 13%. Of people killed by police officers, 49% are white and 24% are black. Since Jan 1, 2015, roughly 1,500 people have been shot and killed by police in the United States.1 This tells us that a person who has been killed by police is twice as likely to be white than black, exactly as the commenter stated. As is often the case with statistics, though, what we’re given is not what we want to know, but it can be used to derive what we want to know.

Let W be white, B be black, and K be killed by police. The probability that someone is white if they are killed by police, \Pr (W \vert K), is 0.49. The probability that someone is black if they are killed by police, \Pr (B \vert K), is 0.24. What we need to know, though, is the probability that someone will be killed by police given their race. To do this, we need to use Bayes’ theorem.

\Pr (K \vert R) = \Pr (K) \times \frac{\Pr (R \vert K)}{\Pr R}

Since \Pr(K) is the same for both whites and blacks, we can safely ignore it when determining how much more likely a person is to be killed given that their race. We simply need to compare \frac{\Pr (W \vert K)}{\Pr (W)} to \frac{\Pr (B) \vert (K)}{\Pr (B)}$.

\frac{\Pr (W \vert K)}{\Pr (W)} = \frac{0.49}{0.62} = 0.79

On the other hand,

\frac{\Pr (B \vert K)}{\Pr (B)} = \frac{0.24}{0.13} = 1.84

That is, a person that is an African-American is 2.34 times more likely to be killed by police than a White-American.

All lives do indeed, objectively, equally matter. Unfortunately, though, we must confess that America has a history of black lives not mattering subjectively to those who have held social power. When a truth has been ignored, even suppressed, for so long, it must be emphasized to gain its rightful standing in our social reality. To do otherwise, that is to simply say “All lives matter,” is to maintain an unjust status quo that serves the interests of some, but not all Americans.

UPDATE (October 2, 2016): I want to be careful to note what I am arguing here, and more importantly what I am not arguing. I am merely pointing out the fairly trivial claim that \Pr(A \vert B) does not necessarily equal \Pr(B \vert A), and, in this case, actually does not.

I am not accusing the police of being racist, and I have not endeavored to show that anyone has been unjustly shot. I am simply showing that, even though more white Americans are killed by police, black Americans are more likely to be killed by police. There are many possible explanations for this, ranging from racial bias in the police force to high rates of violent crime in predominately African-American communities. There are significant studies that conclude that the former is more likely than the latter to be the correct explanation, but that will have to wait for another post.


  1. Wesley Lowery, The Washington Post, July 11, 2016. [return]

A Parent’s Love

Saturday afternoon, protestors lined the bridge at Rogers Avenue and Interstate 44 in Lawton, Oklahoma. They held signs demanding that the children currently detained for illegal immigration be sent back to their home countries.

National Public Radio recently reported on another protest:

This week outside the southern Arizona town of Oracle, Marla and Bruce Bemis — along with several dozen of their neighbors — were lined up along a road waving American flags and holding signs, as patriotic music occasionally played in the background. Word had come that the federal government was planning to bring some of the detainees to a local academy for troubled youth.

“You know it’s a shame that they’re kids, if they’re kids, but I guess their parents didn’t care that much to send them on that journey to here,” says Marla Bemis.

This brought to mind the story of Moses:

A man from the family of Levi married a Levite woman. The woman became pregnant and had a son. She saw there was something special about him and hid him. She hid him for three months. When she couldn’t hide him any longer she got a little basket–boat made of papyrus, waterproofed it with tar and pitch, and placed the child in it. Then she set it afloat in the reeds at the edge of the Nile.

Exodus 2:1-3

How much love must it take to send one’s child into the unknown? These are parents who care very much indeed.


God of love,

Jesus took a little child
into his arms, and said,
“Whoever welcomes a child
in my name, welcomes me.”

There are days
when the Kingdom seems so near,
but others when it seems so far.

Today, as the death toll rises
in the land where
the Prince of Peace once walked,
help me to honor your words
with more than just my lips.

Amen

A Mosque in NYC

I’ve been following the debate over the proposed Mosque near the site of the World Trade Center in New York City. Baptists have historically been champions of religious liberty, and denying Muslims the right to build a house of worship is contrary to historic Baptist principles.

The question to ask is this – would you be happy with a Christian Church at the same location? If so, then do not deny Muslim-Americans the same rights that you are willing to give Christian-Americans.

It is relevant to consider the setting for the proposed Mosque. This is not a Mosque on the grounds of a tranquil place for reflection dedicated to the memory of those who perished. Instead, this is a Mosque in a neighborhood where people live, work, and deserve to have places to worship as their conscience demands. For pictures of the neighborhood, see this post from Daryl Lang.

Reconciliation and Hope

The year that I was born, 1963, was marked by these significant events:

  • In April, Martin Luther King was arrested and jailed in Birmingham.
  • In May, “Bull” Connor, the Commissioner of Public Safety in Birmingham used police dogs and fire hoses on a demonstration in Birmingham.
  • In June, Medgar Evers, the NAACP Field Secretary for Mississippi, was murdered outside his home.
  • In August, Martin Luther King delivered his famous “I Have a Dream” speech at the Lincoln Memorial in Washington, D.C.
  • In September, four young girls were killed in the bombing of the Sixteenth Street Baptist Church in Birmingham.

Tuesday, an African-American man was elected President of the United States.

The country has certainly come far. European countries are generally viewed as far more progressive than the United States, but, as far as I can tell, no European country is even remotely close to being able to select a member of a minority racial group as head of government.

That said, we still have a long ways to go before we can claim to have achieved racial reconciliation. On November 5, David Garland, President of Baylor University, issued a statement concerning recent incidents of racial conflict on Baylor’s campus. We cannot hope to achieve reconciliation in this country if we are not even able to achieve it in the Church. It is time for the Church to not only ask forgiveness for our past sins regarding slavery, but to recognize that failing to take action to create a better future is itself a sin.

If nothing else, this week’s election is a sign of hope.

Concern for the Middle Class and Matthew 25

Both presidential candidates seem to be stressing the importance of adopting policies that are good for the middle class. I have to admit that such talk resonates with me, probably because I am a member of the middle class. Today, though, I saw a title of a blog post by Adam Taylor that is making me rethink my assumptions about the priority of the middle class.

It was titled “Just as You Did for the Middle Class, You Also Did for Me.”

Ouch…

Climate Change and Objectivity

The Washington Post reports something today that is unfortunate but unsurprising. NASA’s inspector general has determined that political appointees have controlled and distorted information about research on climate change conducted by NASA scientists. This is why it is so difficult for the layperson like myself to make informed decisions about the severity of the problem and the best response to the problem. Such decisions should be made on the basis of the best science, but what we know about the science has been distorted by those who have already decided what is to be done.