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In a recent post, “a quick check on long-term violence in the US,” we posted the following graph:

You see the lines are fairly similar, though killing of police offers drops below police killings, where police killings per capita remains somewhat constant.

We noted originally that the officer death rates were per 100k, and the police justifiable homicide rates were per 10 million. We concluded from this that police were killed at a rate of 100x the rate that they killed other people.

This was dead wrong.

For two reasons: 

First, only about 50% of police deaths are from a homicide of some sort. Others are crashes and other line-of-duty hazards. So that cuts the number in half.

But the other thing worth noting is that there are about 800k police officers, and about 242 million adults in the US. This means there is about 1 police officer per 300 adults in the US.

So the rates actually change dramatically. We divide the 100:1 number by 2 (for half homicides) and then by 300 (for population scale), and the killing rate changes.

Police actually kill people 6x as often as they are killed by other people. So I was off by a rate of 600. 

(This pointed out by reader Dan; thank you.)

It actually took me a minute or two to figure this out. I’m not great at statistics.

How can you figure this out quickly? You can use an extreme edge case.

Let’s say that there were only 10 police officers. They kill one in a million people, so that’s 2.42 people. They have a 10% death rate, so one of them is killed.

It would mean that the death rate of police officers is 1 in 10, and the death of citizens is only 1 in a million. So does this mean that they’re a million times more likely to be killed, than to kill? No, not at all: they’re 2.42 times more likely to kill than be killed.

When you’re fact-checking, those head-checks are really important to not blow it by a factor of 600.

Why is this important?  

Whether there is one sort of problem or another, the numbers do matter. Data isn’t everything–you do need to think about what you really care about, what your values are–but when you want to help people understand the scale of a problem, and whether it should be your priority, you gotta get your numbers right.

42 Comments

  • Tim Martin, October 25, 2016 @ 5:28 pm Reply

    Em… I appreciate the commitment to getting things right, but I think you just made this wronger.

    First, you’ve got a typo:
    "They kill one in a million people, so that’s 2.42 people."
    "and the death of citizens is only 1 in 10 million. "
    Is it 1 in a million or 1 in 10 million?

    Typos aside, I find this metric very hard to make sense of.

    Let’s just say that the two lines on the graph are at the same level (since they are close). This means that in 2012…
    police officers killed = 10/100,000
    justifiable homicides by police = 10/10,000,000

    You wrote that the number of police homicides is actually half that, so let’s use the following numbers, and also express them as decimals.
    police officers killed = 5/100,000 = .00005
    justifiable homicides by police = 10/10,000,000 = .000001

    These numbers can also be thought of as "the probability of a police officer being killed in a given year" and "the probability of a citizen being justifiably killed by a police officer in a given year." You can see that the former probability is 50 times larger than the latter.

    You say there are 800,000 police officers and 242,000,000 adults in the US. Given the above probabilities of homicide, how many of each group died in 2012?
    800,000 * .00005 = 40 police officers
    242,000,000 * .000001 = 242 citizens

    From this you concluded that "Police actually kill people 6x as often as they are killed by other people." Which I guess is true – cops kill 242 citizens per year, and are killed at a rate of 40 per year – but that’s not the way I would phrase it. Cops are 50x more likely to be killed than citizens are. In a world of 800k cops and 800k civilians, each year 40 cops would be killed (by homicides) and .8 civilians would be killed by cops (assuming these rates didn’t change as the population changed, but I’ll have to ignore that for now.)

    Ultimately this seems like a useless metric, since rates of police killing civilians have to be evaluated in terms of how many lethally violent civilians are out there.

    • Erik Fogg, October 25, 2016 @ 5:38 pm Reply

      Mrf. First, thanks for the typo check.

      Agreed that cops are still 50x more likely to be killed than an average citizen. Perhaps I can rephrase it?

      For every meeting between a cop and a person, there’s a chance that one of them is going to die. For every cop that is killed, there are 6 citizens that are killed. And the number of cop-person interactions is, by definition, equal. It’s just that cops are involved in 100% of those interactions, and people are involved in very few. So they’re obviously at far higher risk than an average citizen, but per interaction, they’re far more likely to kill than be killed. I think that’s right? Looking forward to your check on that.

    • Tim Martin, October 25, 2016 @ 11:57 pm Reply

      Hmm… your wording is still somewhat opaque to me, to be honest. But I think it’s kind of a moot point; this metric still doesn’t seem meaningful. Let me expound on that for a sec:

      So we’re comparing the ratio of "civilians killed by cops" to "cops killed by civilians" in a year. That ratio is 242:40, or approximately 6:1. The purpose of any metric is to be useful for something. For example, it would be useful if this metric could be used to set a threshold for what ratio of civilian deaths to cop deaths is too much.

      Well, imagine three different scenarios:
      1. In the future, police officers are outfitted with cheaper armor. The number of police officers killed goes up, and the number of civilians killed stays the same. All other variables also stay the same.

      Now the civilian death:cop death ratio is smaller, but this is not because anything got better. In fact, things got worse.

      1. In the future, cops receive better training in defusing dangerous situations. As a result, fewer conflicts escalate to the point where a threatening civilian is (justifiably) shot. The number of police deaths, however, remains the same, because civilians who were planning on shooting an officer do not care about defusing the situation.

      As a result, the civilian death:cop death ratio got smaller, and this time it is a good thing.

      1. In the future, cops receive better marksmanship training. They only shoot at violent criminals who are a legitimate threat, but when they do shoot, they are better able to hit their target. As a result, they justifiably kill more threatening civilians. All other variables stay the same.

      Now the civilian death:cop death ratio is larger than before, and this is arguably an improvement. Before, cops were shooting and missing; now they’re shooting and hitting.

      Given the above hypotheticals, the civilian death:cop death ratio seems to be orthogonal to whether things are getting better or worse. The ratio can be up or down, and – depending on the reason for the change – this can represent something good or bad.

      Also, maybe the increase in dangerous civilian deaths causes a decrease in innocent civilian deaths. The metric above doesn’t take into account what’s important.

      Lastly, it’s the job of a cop to go where the dangerous people are. So… yeah, they’re going to end up confronting and possibly shooting more people per cop than a civilian shoots per civilian. But I’m not sure what that means or how I should feel about it.

      So what’s the point of the metric? Even to describe it accurately seems to engender unnecessary confusion.

    • Tim Martin, October 25, 2016 @ 11:59 pm Reply

      Ugh, this HTML parsing is killing me. Sorry for the big, bold orange text? Although it’s pretty cool. Let’s see if I can replicate it…

  • Tim Martin, October 25, 2016 @ 5:29 pm Reply

    Ugh, it parsed my asterisks as italics. My first comment should read:

    800,000 x .00005 = 40 police officers
    242,000,000 x .000001 = 242 citizens

  • Tim Martin, October 25, 2016 @ 5:33 pm Reply

    Sorry, last comment.

    I just wanted to say that it looks like you edited your original post to remove the mistake? That’s not a very good practice. Now all the links and commentary on your post don’t make sense to people who only see the new one (you didn’t even link to the erratum!)

    It’d be better if you edited the post and posted the original text at the bottom of it.

    • Erik Fogg, October 25, 2016 @ 5:38 pm Reply

      Ah! I’ll put that back in. Thanks 🙂

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