Rod Liddle said, “do the math”. So I did.

So I was coaxed to actually upload something to this site by the hateful idiocy of this excerpt from a Rod Liddle column in Liverpool’s favourite red-top (which came to my attention via @SunApology):

‘Do the math’, he says. Well, a mathematical analysis begins with a well-posed problem. Let’s suppose a black man in America asks himself:

“If I am murdered, is it more likely to be by another black man, or by a police officer?”

The figures Liddle quotes imply, of course, that he is more likely to be killed by a black man. However, this question ignores what statisticians call a confounding variable: a factor you don’t mention that affects your results. These are sometimes more colourfully called lurking variables, because they are by definition hidden, although in this case the factor is so obvious that you really have to try and ignore it:  there are many more black people than police officers in the US. It takes a particularly wilful kind of stupidity to ignore something like that, especially if you’re a professional columnist writing in what is lamentably Britain’s largest daily on an inflammatory topic.

More Americans each year are killed by toddlers who manage to get hold of firearms than by terrorists or by tigers. This is not because toddlers are inherently more dangerous than a tiger, but because there are lots of them in a country with lots of guns. Now, I’d agree that this is part of a compelling argument for gun control in the US, but if your neighbour owns a Siberian tiger, getting into interpretations of the 2nd amendment is at best an unhelpful distraction from what you probably regard as the more pressing issue of 300kg of carnivore going for a stroll on the other side of your hedge.

Let us then suppose instead that our black male US citizen asks:

“If I find myself alone in a dark alley with another man, is he more likely to kill me if he’s another black man or a police officer?”

To work this out, you multiply the ratio of killings of black men committed by these two groups (black men and police officers) by the inverse ratio of the corresponding numbers of each group. A formal justification of this can be given by Bayes’ theorem, but the intuitive idea is clear: although the guy standing in front of you is more likely to be black than a police officer, we only care about comparing your chances of getting killed once each of those outcomes is realised; so you rescale the actual numbers of deaths by the different populations so that the likelihood of an individual shooting you can be fairly compared.

Liddle’s article quoted some figures on the gun deaths. For the numbers of black US citizens and police officers, a quick Google gave the following figures:

765,000  full-time police officers with arrest powers

37,685,848 Black or African Americans

Again, just to be clear, Liddle set the bar for “trigger happy” US police to commit fewer murders on aggregate than 12.2% of the US population (and a disproportionately poor section at that).

If our black US male were to use these figures together with Liddle’s, to carry out the exercise in conditional probability described above, he would conclude that the police officer was 20% more likely to kill him. [i.e. (100/4000)x(37,685,848/765,000)=1.2]

Now, we should make some allowances for the fact that US police are routinely armed, and that if you come into contact with a police officer that is (again using Bayesian reasoning) automatically likely to be a situation involving conflict. But these factors are no less true when police officers arrest white people, and one study suggests that black people are three times more likely to die at the hands of police. That demands explanation, at the very least. More than that, it demands change. Yet Liddle refers to the “Black Lives Matter” campaign demanding that change as a “thuggish, racist, deluded movement”. (Yes, I read the full article, so you don’t have to.)

Readers who followed that last link to the fourth chart will have made their way past ones comparing the different race-on-race murder rates, and noting that the black-on-black murder rate is by far the highest.

This might perhaps make it more shocking that they are still more likely to be killed by a police officer (in the sense we described above), not less so.

Moreover, no-one who spends more than about 10 minutes examining this issue with the intent of improving it could possibly hide from the black-on-black murder rate. But the bloody-minded wrongness of Liddle’s claims should encourage us to look for lurking variables that might explain this. Are black people more likely to be poor? (Yes.) Are poor people more likely to commit crime? (Yes.) Are black people likely to find it harder to earn their way out of poverty? (Yes.) Is a black person more likely to flee a police officer, knowing the disproportionately higher risk of that encounter resulting in their death? (Wouldn’t you?)

Trying to identify such confounding variables is a mechanism through which people who care try and improve the situation. The idea of a PC -brigade who are blinkered to it is a myth, promulgated by those who don’t care. To fail to identify confounding variables is to assert that black people are more likely to kill each other because they are black. There’s an irony here: Liddle began that article by bemoaning that

He then went on to advocate that murder statistics relating to race were best interpreted at face value, using race itself as the explanatory variable.

I’ll just leave this here.