### Murder Most Foul

I was intrigued by Paul Mirengoff's Power Line post, Interracial violence in America, by the numbers. He quotes Heather Mac Donald:

Between 2012 and 2015, blacks committed 85.5 percent of all black-white interracial violent victimizations (excluding interracial homicide, which is also disproportionately black-on-white). That works out to 540,360 felonious assaults on whites. Whites committed 14.4 percent of all interracial violent victimization, or 91,470 felonious assaults on blacks.

And Paul adds his own statistical contribution:

Blacks commit around 70 percent of black-white interracial homicides. I take it that, as a statistical matter, the “expected” number is 50 percent for all forms of black-white interracial violent crime.

That "expected" bit kind of tweaked my old brain. Is that really true? I mean, there are more white people than black, right? So…

Well, it depends on what you expect, I suppose. I did some math. Simple math, because that's all I'm up to these days.

Paul links to 2016 data. Fine, but more recent data is available, let's look at the equivalent table for 2018: the FBI's Expanded Homicide Data Table 6.

We'll snip out the bits of the table that deal with the race of offender and victim:

 Race of victim Total Race of offender White Black orAfricanAmerican Other Unknown White 3,315 2,677 514 61 63 Black or African American 2,925 234 2,600 17 74 Other race 220 54 39 122 5 Unknown race 110 46 24 7 33

One thing is immediately clear: White people mostly kill other White people, and Black/African American people mostly kill other Black/African American people. (I hear you saying: "duh".)

And (wince) there are slightly more White than Black/African American homicide victims, there are slightly more Black/African American than White offenders.

Let's simplify things a bit by throwing out the "Unknown" edges (although thumbs up to the law enforcers who neglect/refuse to pigeonhole victims and perpetrators by race, which is a mere social construct). And put everything in percentage terms:

 Race of victim Total Race of offender White Black orAfricanAmerican Other White 51.32% 42.37% 8.14% 0.97% Black or African American 45.28% 3.70% 41.15% 0.27% Other race 3.41% 0.85% 0.62% 1.93%

On to my mathematical contribution. Assume:

• A mythical country with three population groups we'll call W, B, and O.
• W's make up 76.5% of this country's population, B's are 13.4%, and O's are 10.1%. (Any resemblance to an actual country is entirely intentional.)
• And let's assume that homicide perpetrators are equally likely to come from any group, and are "blind" to the group their victims are in.
What can we "expect" in that situation? Well, imagine we're picking balls from an urn, with a W, B, or O printed on each, in the above percentages. First we pick an "offender" ball, then a "victim" ball. (And assume a lot of balls in the urn so picking the first ball doesn't affect the probability of picking the second.)

Under those assumptions, the probability that a W offender kills a B victim is 76.5% times 13.4%, or 10.3%.

And the probability that a B offender kills a W victim is 13.4% times 76.5%, or… 10.3%. So, yes, under "blind" assumptions, Paul's correct that you would "expect" the same fraction of W-B homicide as B-W homicide.

The complete table for our mythical country:

 Race of victim Total Race of offender W B O W 76.5% 58.5% 10.3% 7.7% B 13.4% 10.3% 1.8% 1.6% O 10.1% 7.7% 1.6% 1.0%

Yes, our actual numbers are wildly out of whack with the ideal country where everyone's equally likely to be a killer or their victim. But (oddly enough) our actual black-on-white homicide fraction is slightly less than you'd expect from a color-blind country.

On the other hand, the black-on-black homicide fraction is nearly 23 times what you'd expect from that "ideal" country.

You can play the same game with sex, by the way: see the second set of numbers in the FBI table linked above. Using another imaginary urn, this time sex-blind to pick offenders and victims would give (approximately) 25% of each "type" of homicide. Instead:

• 62.6% male offender/male victim
• 26.6% male offender/female victim
• 8.0% female offender/male victim
• 2,8% female offender/female victim

Again, very lopsided. Guys, this is why we should have ratified the Equal Rights Amendment.

But what this really shows is that the good-hearted folks who decry racial disproportionality in law enforcement need to take into account the disproportion among criminals. Example: Jacob Sullum in Reason: George Floyd’s Horrifying Death Highlights Stark Racial Disparities in the Use of Police Force. While I'm not excusing what happened to Floyd, Sullum says things like:

Whenever a Minneapolis officer draws his gun, deploys a dog, or grabs, shoves, slaps, punches, kicks, tackles, pins, strangles, tases, or pepper-sprays someone, he is supposed to report that use of force. Blacks, who account for a fifth of the city's population, were on the receiving end of such violence nearly three-fifths of the time during the last five years, according to official records analyzed by The New York Times. Whites, who account for more than three-fifths of Minneapolis residents, were involved in less than a quarter of those incidents.

The relevant question being: yes, that three-fifths number is out of whack with Minneapolis's population, but is it out of whack with the fraction of offenders? Jacob doesn't look at that data, nor (as near as I can tell) does the New York Times report he's relying on.

I bet there's also a disproportionate amount of force used against males compared to females. So?

There might be a problem. If so, I'd like to see it documented with non-sloppy statistics.