# Interpreting interracial crime numbers

### Both Kareem Carr and his critics are wrong.

**Written by Noah Carl.**

Yesterday, there was another big debate about interracial crime on the site formerly known as Twitter.

The debate began when user End Wokeness posted a chart showing “interracial violent incidents per capita of offending race” for different racial comparisons (black-on-white, white-on-black etc.). According to the chart, blacks commit violent crimes against whites at 42 times the rate that whites commit violent crimes against blacks. The post went viral, and even Elon Musk replied with an exclamation mark.

Self-proclaimed “data scientist” Kareem Carr then posted a thread purporting to debunk the chart. “I looked into this before,” he wrote. “This is a false narrative designed to promote racial grievance”. He proceeded to point out that the total number of black-on-white violent incidents is small compared to the total number of white-on-white violent incidents.

A commenter accused Carr of having misinterpreted the original chart: “The point is that interracial crime is skewed to black-on-white crime by a ridiculously high margin”. Carr responded that it's “not skewed” to a “ridiculously high margin”. And when pressed, he stated: “The cases of black-on-white and white-on-black crime are not symmetric. The null hypothesis isn’t that they would be the same.”

Carr is wrong here. But so is the original chart, and so are most of the people criticising Carr. The truth is that blacks *do* commit more violent crimes against whites than whites commit against blacks – but the ratio isn’t anywhere close to 42.

As I explained in a previous article, interracial crime numbers should *not* be adjusted for the population of the offender race. The reason is that interracial crimes involve *encounters, *and the number of times blacks encounter whites has to be equal to the number of times whites encounter blacks.

For comparing black-on-white crime to white-on-black crime, it is sufficient to divide the total number of crimes committed by blacks against whites by the total number of crimes committed by whites against blacks. And as a matter of fact, the null hypothesis *is* that they would be the same.

If a population is made up of two groups, one large and one small, and they commit crime at the same rate and do not target each other, the expected number of crimes committed by the large group against the small groups is* *equal to the expected number of crimes committed by the small group against the large group.

Many people find this very counter-intuitive. They assume that the large group must commit more crimes against the small group than vice versa. But that isn’t the case. The large group does have more potential offenders, but it also has more potential victims. So the ratio of large-on-small crimes to small-on-large crimes is exactly 1.

Think about it like this. Suppose the large group comprises 90 people and the small group comprises 10 people. Now consider an offender picked at random from the population. There’s a 90% chance that he’s from the large group and a 10% chance that he’s from the small group. Now suppose he commits a crime. There’s a 90% chance that his victim is from the large group and a 10% chance that his victim is from the small group. So most of the offenders are from the large group, but so are most of the victims.

For comparing levels of interracial crime when there are *more* than two groups, the figures do need to be adjusted – but not by the population of the offender race. Rather, they need to be adjusted by the combined population of the victim and offender races – specifically by the product of their populations.

Consider a population made up of three groups: one large, one medium and one small. Suppose they all commit crime at the same rate and do not target each other. In that case, the expected number of large-on-small crimes is bigger than the expected number of medium-on-small crimes, and the expected number of small-on-large crimes is bigger than the expected number of small-on-medium crimes. Let’s look at some actual data.

The chart posted by End Wokeness is based on figures from a report by the US Department of Justice (which I analysed in my previous article.) Here are the total numbers of violent incidents broken down by race of victim and offender:

These are the figures you get when you multiply the numbers of violent incidents experienced by each victim race by the proportions of offenders from each offender race.

Now let’s compare the two approaches for adjusting the figures: dividing by the population of the offender race (the wrong approach), and dividing by the product of the populations of the victim and offender races (the right approach). First: dividing by the population of the offender race.

These are the figures shown on the chart posted by End Wokeness (with a few exceptions). It’s immediately obvious that they are wrong. Look at the figure for Asian-on-white crime. It is 18 times larger than the figure for white-on-Asian crime. Is this plausible? And it’s almost four times larger than the figure for black-on-Asian crime. Is it plausible that Asians commit four times more crime against whites than blacks commit against Asians?

The reason the Asian-on-white figure is so large is simple: the white population is big and the Asian population is small. So when you count up the number of crimes against the former, and then divide by the latter, you get a large number. Dividing by the population of the offender race is therefore biased against small groups.

Now the second approach for adjusting the figures: dividing by the product of the populations of the victim and offender races.

These figures make a lot more sense. The figure for Asian-on-white crime is only 1.8 times larger than the one for white-on-Asian crime. (This is slightly unexpected, given that whites commit more crime than Asians do in general; it’s most likely attributable to the fact that Asians are much younger than whites.) And the Asian-on-white figure is only one third as big as the black-on-Asian one.

Another way to see these figures are correct is by checking that the ratios for particular comparisons (e.g., black-on-white to white-on-black) are the same as in the first table above. For example, the ratio of 66 to 7 is the same as the ratio of 547,948 to 59,778. Both are equal to 9.2. This means that blacks commit 9.2 times more violent crimes against whites than whites commit against blacks – a huge disparity but nowhere near 42.

Dividing interracial crime numbers by the population of the offender race leads to very misleading conclusions. The correct approach is dividing by the product of the populations of the victim and offender races.

*The original version of this article stated that the correct approach for adjusting interracial crime numbers when there are more than two groups is dividing by the sum (rather than the product) of the populations of the victim and offender races. This error was pointed out by Twitter user Kalle Leppälä.*

**Noah Carl is an Editor at Aporia Magazine.**

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it feels like Kareem Carr has been a PhD student on Twitter forever lol

I just checked his LinkedIn and yup he is in his 8th year of his PhD

certified lemon

Very good. Thanks for eliminating the confusion. One should always examine the procedure used to process data.