Why armed guards in schools are a bad idea

I just saw this tweet from National Rifle Association (NRA):

On the assumption that this is a genuine query, I thought I’d take a moment to talk about some simple statistics and probabilities.


First, Wikipedia notes that four presidents (Lincoln, Garfield, McKinley and Kennedy) have been shot by assassins. For simplicity, we will leave aside the failed assassination attempts on thirteen other presidents (and the failed attempts on the lives of Lincoln and Kennedy before the successful ones). Let’s consider the time from Lincoln’s death to now (147 years from 1865 to 2012), and say that the chance of a president being shot dead in any given year is 4 in 147, or about one in 40. (The real chance is surely much higher than that — note that there have been attempts on the lives of all the last eight presidents.)

The population of the US is 315 million, of which 27.3% are under 20 years of age. Let’s assume that about half of those are school age (between 5 and 15), which is 43 million schoolchildren. In 2012, there have been seven notable school shootings, but “only” 29 children murdered as a result. So let’s say that the chance of schoolchild being shot dead in any given year is 29 in 43 million, or about one in 1,500,000.

There were 600 accidental deaths by gunshot in the USA in 2010. Somewhere in the range of 30-34% of adults own a gun. Given that there are 230 million adults in the USA (and assuming that the number of children owning guns is negligible), that means there are about 74 million gun owners in the USA. So the chance of any gun owner accidentally killing someone in a given year is 600 in 74 million, or about one in 123,000.

In reality, of course the armed guards who protect the president are the best of the best: very highly trained, and much less like to have accidents than the general gun-owning population. But even assuming they are no more competent than hypothetical armed school guards, here’s how it works out.

  • Giving the president an armed guard increases his chance of being shot, due to accident, by one in 123,000. Given that his chance of being shot is already one in 40, this is negligible.
  • Giving children an armed guard increases their chance of being shot, due to accident, by one in 123,000. Given that their chance of being shot was previously one in 15,000,000, it means they are now 122 times as likely to be shot.

These numbers are all approximate. I could easily be wrong by a factor of two or more. Even if I’m wrong by a factor of six, it still means that the president is much, much, much better off with an armed guard where as a schoolchild would be twenty times as likely to be shot.

I hope that clears things up.

13 responses to “Why armed guards in schools are a bad idea

  1. An additional statistic: There were 40 student deaths in 2011 due to althetics/sports programs, and 50 in 2010. (http://www.youthsportssafetyalliance.org/docs/stats-december2011.pdf). If we split the difference and say 45 deaths per year, a student’s odds of dying from a sports injury are 1/955,555, significantly greater than their odds of being shot.

    Anyone who says such a thing on national television, though, will be… uhm… shot. Probably not even metaphorically.

    (I am not a mathematician, so I hope I did the math correctly; if I didn’t, I will be suitably chastened and humbled. if I did the math right, but misunderstood the statistics, or chose an unreliable source, I will likewise apologize.)

  2. One minor addendum: While I cannot find, in the time allotted to me between compilation cycles, a well-researched paper on this, it is generally believe (oh boy, do I hate saying things like that) that some not-insignificant percentage of “accidental” shootings are suicides, either made to look like an accident by the victim, or reported as an accident by the survivors, for legal and social reasons. I will understand if you dismiss this due to lack of any more rigor than “I think I read this on the Internet once”, but I did want to mention it.

  3. Or put easier..

    No one with guns in the school – chance children accidentally shot: zero
    Guns in the school — chance children accidentally shot.. >0.

    Better idea: pit traps under ever floor tile (without deadly spikes or crocodilians at the bottoms.) When shit goes down, start opening pits, fetch out the people later. (Or as normal people put it, in hospitals for mental patients, the doors can be locked with the only way to open them by police; if thigns get Hairy, emergency button is pressed, and the casulty limit is suddenly very small.)

    Why do so many Americans (NRA etc) jump first to.. _more guns is good_.


  4. @Jeff… if you’ve got a plan to get rid of the 74 million guns that already exist, let me know.

    All of our social structures are built on balancing costs and benefits. A mandatory speed limit of 20MPH (with obvious exceptions for emergency vehicles and special cases) would save a tremendous number of lives, it would save gas (you could build much lighter cars if they only had to protect the passenger from a 20MPH collision vs. a 60MPH one) and reduce CO2 emissions, it would restore a greater sense of community (if you’re willing to spend ~20 minutes, at most, to drive to a store, etc, it would need to be within only 2-3 miles of your home, not 20+ miles), and so on. But the costs would be outrageous, compared to the benefits, so, we don’t do it, and we accept the lives lost to auto accidents as part of life. Anyone who says “You can’t put a price on human life!” is an idiot; we constantly and continuously put a price on human life, and we constantly and continuously decide, because needs will always exceed resources, which lives are worth more. It’s well worth debating how those decisions are made and who should make them; it’s not worth debating if they should be made at all. They can’t NOT be.

    You can’t create life with absolutely 0 risk, and each reduction in risk has increased costs for the same degree of reduction. The easiest steps are the most cost effective and produce the biggest benefits; ironically, the safer the world gets, the more any violent incident scares us, precisely because it is rare. The usual far-right pundits are screaming about how we’re in a “world of unprecedented violence because we’ve abandoned God”, but violent crime per capita in America is FAR LOWER than it has historically been. Despite this fact, no reporter I’ve seen has ever stopped one of these morons mid-rant and said “Look. Here’s the facts. How can you say things are ‘worse than ever’ when they provably, objectively, are not?” (This is because the media thrives on fear, not on truth.)

  5. Naturally, first to blame is video games since its blasse and discredited to blame rock and roll and dungeosn and dragons anymore :) (and blaming video games is also discredited, but the average journalist still wants something easy to cling to that stirs up a ruckus..) Certainly, adding more laws won’t help since generally the violence is criminals or crazy people, neither of which who will generally care about the rules. But if somethign is cheap and easy and may help.. why not? (I’m very anti TSA and other stupidity; I’m also first in line to say ‘these are isolated and rate incidents, and although highly horrible, we can’t make decisions on one school or one nuclear accident..’.. but there have been a few of these issues ‘lately’, so they should be investigated and options considered.)

    Obviously there is no easy solution, but the ‘gun culture’ _is_ undeniably _odd_. I doubt as many %age Americans have firearms as the numbers would suggest (probably fewer people have more firearms, skewing the averages or somesuch), but .. _why_ do so many people want them in the first place? whats the fetish?

    (In respect to the quick findings noted below, let me update the above to simply ‘gun culture’ and not ‘American gun culture’)

    I’m Canadian, and I know I’m 30 years out of date with kids in school.. but growing up, I never had to worry much at school; we’d get bulled, we’d get in a fight, and come home with a bloody nose; didn’t have to worry about being shot. Bot by the sounds of it, some what, 30-40% of homes have a firearm available? Thats pretty damned weird. Why isn’t it more like .. 1%?

    I’ve never seen a firearm of any kind, except on a cops hip or in a museum. One friend of mine got one, for taking shots at the firing range. That rather creeped me out, but at least he was super responsible about it (locked safe and so forth in the basement, had no kids.) I’m in the city, so no need for hunting or the like admittedly, but still..

    — did a quick look up, and .. I don’t get it.
    Some study noted that in Canada (with accuracy hard to know for sure) estimating 22% of households having a firearm (due to heavy hunting in many parts of the country.) Still.. 20%? 1-in-5? Who are these people and why? So at least its half the US estiamted percentage, but the US also has a lot of areas with hunting and so on.

    So I can’t really play the cards above if my own coutnry seems so quiet yet still ranks what I would consider freaking high percentage.


    Bloody humans.

  6. I’m not in favor of armed school guards, at all. But you’re abusing statistics and logic, and I need to point it out :-)

    This argument – “Giving children an armed guard increases their chance of being shot, due to accident, by one in 123,000. Given that their previous chance of being shot was one in 15,000,000, their likelihood of being shot increases by 122x” – doesn’t make sense. The chance of a schoolchild being shot was never as low as one in 15,000,000. They could still be shot accidentally by a neighbor, or family member, or police officer, or whoever. By your numbers, odds of being shot dead accidentally are 600/311,000,000 (population of USA) : about 1 in 518,000. Assuming that children are just as likely to be shot dead accidentally as anyone else (and ignoring other ways of being shot dead), your starting point for getting shot as a child is 1/518,000 + 1/15,000,000.

    What you said is that every gun owner has a 1/123,000 chance of accidentally shooting someone. I think you’re arguing that by adding guards, we’re increasing the number of gun owners, therefore increasing the number of accidental deaths overall and increasing the likelihood of children being shot accidentally. But the number of gun owners added by creating school guard jobs is not going to be very high – the people hired probably already own firearms. Still, say this policy added a ridiculous number of gun owners – say 100,000, roughly one per public school in the USA (http://www.infoplease.com/askeds/number-us-public-schools.html). You’ll increase the number of accidental shootings by 1/123,000 * 100,000, from 600 to (maybe) 601. Odds of accidental death have increased from 600/311,000,000 to 601/311,000,000. Nowhere near 122x.

  7. 1/123,000 is the risk *per gun owner*. You erroneously use it as the risk *per child*. To calculate the latter correctly you need to divide by the number of schoolchildren per guard, say 1000. So the risk per child would be 1/123,000,000. Comparing to your original figure of 1/1,500,000 (and not the erroneous 1/15,000,000 that you use later) we see that children would be 82 times safer.

    Congratulations, you have proved the NRA right!

  8. I’m not sure I agree with your statistical argument here, but I’d say that what the numbers you cite are really telling us is that the chance of a child being shot in a mass school shooting is negligible. The NRA obviously can’t come out and say that though.

    Jeff, I’m a citizen of both the US and Canada. When I was in my teens I lived in Vermont, which had the laxest gun laws of any state in the Union at the time (no license required to carry concealed, etc.) and spent a lot of time in Southern Quebec.

    At one point I lived in Northeastern Vermont, where just about every household had at least one firearm, and most had several. There wasn’t really a “fetish” about it, but they had some utility. First, most people up there hunt deer. Second, when you live up in the hills up there you are a long way from any help. Breaking and entering was a common pastime for the disaffected youth of the region, but one thing that was very uncommon was home invasion (forcible entry of a house when its residents were home.) Violent crime rates in that region were pretty low by national standards.

    As to who owns guns in Canada… well the part of Southern Quebec I lived near had very high rates of gun ownership, for much the same reasons the part of Vermont I lived in did. I had some friends up there who were kind of bad kids, and did break into houses occasionally. One of the main reasons they did so was to steal rifles, and almost every place they broke into had at least one. So yeah, in some parts of Canada just about _everyone_ owns a rifle.

    My father is from Alberta, and while I don’t know him very well one of the things he’s talked to me about is growing up on a farm and hunting. He’s a pretty expert marksman, actually. He’s pretty progressive, and gets annoyed by his family’s Alberta conservatism, but the last I checked he still liked to shoot.

    I don’t own a gun, and haven’t had one since I was in my teens. I certainly don’t fetishize them, but I’m not terrified of them either. But I grew up around guns, and what you could call “the gun culture” and I understand it. It’s really not as weird as you seem to think it.

  9. In Israel where I live, every school, institution or large enough business (supermarkets etc.) HAS an armed guard. This is the result of years of terrorist attacks, and in the narrowest sense it paid off: some terrorist attacks were prevented, and in others cases, the death toll was reduced. I do not recall a case where a guard shot an innocent person by purpose or mistake *on duty*. However, there were too many incidents where these guns were used in cases of domestic violence, were stolen or were forcefully taken by criminals (arms regulations on citizens are very strict).

    I don’t know the specifics of the NRA proposal – e.g. are they suggesting to give the guards authority to search visitors? – so I can’t tell how relevant this information is…

  10. Lies, damned lies, and statistics, right?

    Nice post and good analysis. Of course its much more complicated than that.

    Ironically, last year, our school board tired to impose a ban on peanuts in the schools due to the high number of kids with peanut allergies. The school board president actually said, “If we can save just one child with this policy, it would be worth the trouble.” He made a political enemy of me that day. Anyone who is so absolutist in the elimination of risk is not to be trusted with political power because for them the ends _always_ justify the means. Thankfully peanut butter sandwiches are not illegal in our schools because of the backlash to the district’s poorly thought policy. But had they been enacted, I would have endeavored on a campaign to end the dangerous Football (American) program from the school to keep any kids from being injured…

  11. There appears to be a general belief in the media that the majority of deaths by shooting in USA schools are not randomly distributed among all schools, but actually tend to cluster within schools (like deaths from flying in commercial airplanes). The NRA’s argument addresses this perception and is therefore not so much about reducing isolated single incidents, as reducing massacres: “Given that someone has started shooting at your son’s classmates (however unlikely), the risk that your son will subsequently be killed is now very high. Having armed guards in school would reduce that risk”.

    The NRA is effectively claiming that although the prior probability of Johnny being shot in a USA school is vanishingly low, the conditional probability of his classmates also being shot, given that Johnny has already been shot is alarmingly high. But this is quite untrue. Atrocities like Virginia Tech, Columbine and Sandy Hook are not in any way representative of USA school shootings. Since 1966 there have only been 4 school shootings in the USA in which 15 or more people have lost their lives, out of a total of 126 significant events – i.e. just 3.15%. The vast majority of these events result in no deaths at all or just the death of the gunman (often by suicide). The problem is that tragedies like Columbine are statistically significant with regard to overall fatalities: those four events together account for 91 of the 274 lives lost. So it is very tempting just to look at the 30% human cost of these few events and to ignore completely the fact that they occur very rarely. But emotionalism vindicated by non-representative samples is no basis for a system of government.

  12. A few questions
    Do you think that kids aren’t human because the fact that 4 presidents have been assassinated and that 29 children have been killed makes me believe that you don’t value the lives of those children or that you value them less then 4 adult presidents ? (if so question your morals)
    Does every gun owner ‘accidentally’ shoot someone because I’ve known respectful gun owners to never shoot anyone, but I accept there are some people who accidentally discharge a round but should these people be allowed guns in the first place?
    Would a well trained member of our beloved armed services be so careless with a firearm around children?
    Have you ever considered that if the schools were protected with an armed person then maybe there would be no dead children at all?
    You blame the NRA for questioning this idea but still you believe that a gun is a dangerous object that shouldn’t be used to defend innocent children and yet how have armies across the world protected its people from exterior violence?
    Thanks, that is my rant finished

  13. Do you think that kids aren’t human

    No. A nice easy one to start with, there.

    … because the fact that 4 presidents have been assassinated and that 29 children have been killed makes me believe that you don’t value the lives of those children or that you value them less then 4 adult presidents ? (if so question your morals)

    Then you have evidently not understood the article at all.

    Does every gun owner ‘accidentally’ shoot someone

    No. Another easy one.

    … because I’ve known respectful gun owners to never shoot anyone

    Well, good for them!

    Have you ever known anyone without a gun to shoot anyone? Me, neither.

    But I accept there are some people who accidentally discharge a round but should these people be allowed guns in the first place?

    No. And since we can’t know in advance who will do this, the only rational thing is not allows guns to anyone.

    Would a well trained member of our beloved armed services be so careless with a firearm around children?

    It happens less often. But it happens. Not only that, well-trained members of your beloved services sometimes deliberately shoot children dead. With guns. Guess how often that happens in Britain? (Clue: our police don’t carry guns.) Answer at the bottom.

    Have you ever considered that if the schools were protected with an armed person then maybe there would be no dead children at all?

    Yes. Considered it, discarded it. We don’t have to guess. We know.

    ˙suǝddɐɥ ɹǝʌǝu ʇı :ɹǝʍsuɐ

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