“Ah, he's not the first psycho to hire us, nor the last. You think that's a commentary on us?”
by Captain Malcolm Reynolds




"walls of the city" logo conceptualized by Oleg Volk and executed by Linoge. Logo is © "walls of the city".

graphics matter – we do requests

Over the weekend, the below email came in from Miguel at Gun Free Zone:

Have you done a correlation/whatever is called between the number of guns in a country and the # murders and/or violent crimes?

The attachment is a list of countries and their number of guns according to the Small Arms Survey which the antis can’t bitch about because it is a group on their side. I used this wikipedia link to get the number of Homicides per country.


According to that, it only "takes" Great Britain 4,709 guns to have a homicide. The US requires 20,000 guns to have a homicide.

OK, so I have no clue about statistics and every time I open Excel I go "What kind of sorcery is this?" but I think you get the idea.

One of your graphics work there perhaps?

Attached to the email was the 2011 update to the Small Arms Survey, complete with a table supposedly showing "Civilian gun ownership for 40 countries, in descending order of averaged civilian firearms"… except, after looking at the source information for the table, it shows no such thing, so I am not even going to bother linking to the 2011 document in this post.

Anywise, the question intrigued the statistician in my mind, so here we are. We are all familiar with the tried-and-false "argument" of the anti-rights cultists that "more guns = more deaths" – a hypothesis we have already tested and found significantly wanting. However, assume for a moment that we accept that we take complete leave of our senses and logic and accept that hypothesis as true; given that basis, how many more guns does it take to yield another murder?

After all, if more guns results in more murder, then there must be some kind of metric one could build indicating that if you add X more guns to the population, you will get Y more murders. So how many firearms does it "take" to "cause" a murder?

As with all such questions, the answer is complicated. Given that most individual states in America do not document how many firearms their residents own (as they should not, and never should do), we are going to have to look farther abroad for our dataset and instead consider this question across international borders. Instead of simply limiting ourselves to the numbers included in the 2011 Small Arms Survey update, we will instead return to the original 2007 document (*.pdf warning) which documents, estimates, and straight-up guesses at firearm ownership in 178 different countries (I used the average of the Low Total From Outside Sources and High Total From Outside Sources where available, Registered if not). Of those countries, I will use the numbers for every country in North, South, and Central America; North, South, Eastern, and Western Europe; Oceania; and a few other odds and ends to round out a good sample body of 90. (Do note that some useful countries were omitted from the Survey, like Denmark, India, and Luxembourg.)

Much though I hate to use Wikipedia as a source for… anything, really, we will also use the page Miguel linked to in his email, simply because it has hundreds of countries’ statistics all in one conveniently, easily-sourced location.

So what is the end result? Probably not what you think:


(You will probably want to download this thing to view locally; it is huge, and the text is, obviously, small.)

First off, way to go Iceland for messing with the curve, by only having one murder in 2010. Bravo.

Moving on, the numbers at the far right end of the orange bar indication how many firearms there are in the country per murder transpiring in the country. Given that Iceland has somewhere around 90,000 firearms in-country and all of one murder, it’s number is obvious. America has somewhere around 270,000,000 (probably far north of that, but that is the official number) firearms and we had 12,996 murders in 2010, so it "takes" somewhere around 20775 firearms to "create" an unlawful killing. Obviously firearms do not create murders any more than spoons cause obesity, but, as I said at the beginning, we surrendered logic and reason in order to adopt the "more guns = more deaths" hypothesis and further examine it.

Now, remember that higher numbers are "better", in that it "takes" more guns to "cause" a murder. So consider the countries above us… and then the countries below us. For example, observe how the functional theocracies typically rank over us, at least if they have not suffered a war recently. Likewise, those countries with a strong history in firearms – or just an absurdly low population or population density – are up there with us or above us. Now, take a look at where the United Kingdom – the oft-vaunted example of "ideal" "gun control" – falls on the chart: apparently their firearms are four times more deadly than ours. Or how about Mexico, where private ownership of firearms is functionally impossible, but "murder" seems to be the recreational sport of choice? Hell, Fiji has functionally no guns (all of 1538, or "what I have buried in my back yard"), but they managed to crank out 23 murders despite that.

While this interesting chart does answer Miguel’s question – with the answer being "it depends" – it is also not as honest as it could be; after all, Fiji has a population of under a million souls, while Switzerland has over 7 million folks on its rolls. So how does the rate of firearm ownership affect the rate of murders in these various countries?

Wrong question. Just seeing if you all are paying attention – as always, I am not here to document that guns affect murders, or even crime in general; I am sorely equipped to do so (read: "underpaid") and the examination of that kind of causal relationship would require a lot more consideration and information than I have available at the moment. So, the right question is, "How does the rate of firearm ownership correlate to the murder rate in these various countries?" Kind of like this:


That line slanting to the lower-right and disappearing beneath the x-axis is the trendline for the datapoints, and the equation for that line tells you everything you need to know. Specifically, there is a correlation coefficient of -0.2055 between the rate of firearm ownership and the rate of murders in the 90 countries I have documented on the bar chart above. In other words, using those countries’ data from a single year as our test population, countries with higher gun ownership rates tend to enjoy lower murder rates and vice versa. However, this is a very weak correlation, and thus does not hold true in all cases.

As always, there are more forces at play here than just the number of firearms in public circulation; after all, the median household income for Switzerland is somewhere around $27,000 USD, while Mexico’s is more like $5,000 USD. Likewise, population density is not really a problem for those crazy folks in Iceland (though I would imagine other things are), but Brazil is largely uninhabited too… in a bad way for the millions of folks living there.

In any case, given the negative correlation between firearm ownership rates in various countries and murder rates in those same countries, the causality outright claimed by "more guns = more deaths" cannot exist, even across international borders. If there were even a chance of a causal relationship, the trendline in the above graphic would be sloping up to the right, rather than down, as the hypothesis would clearly indicate.

I sincerely wish there were a simple and easy way of reducing murders and other violent crimes, but the simple, honest, rational truth is that restricting/controlling/banning inanimate lumps of machined metals does not work. It has not worked before, it has not worked in other countries, and it is not working here; how about we consider alternatives, and try to find something that does work?

(Source Excel spreadsheet available here.)

(Updated in 2014 with labels on the second chart.) 

14 comments to graphics matter – we do requests

  • Yet another great and honest study, well played.

    Unfortunately those who advocate for removing firearms from lawful hands are likely on the lower side of the IQ bell curve, so they’ll generally scratch their heads at it and then simply declare your methods “Biased”, and simply “support” their next argument with a VPC “Study”.

  • […] Miguel came up with a great idea, and Linoge turned it into a study. […]

  • As always, I am not trying to reach them; I am trying to reach those people who would be mislead / misinformed / confused by the misinformation those organizations and individuals publish with reckless abandon.

    This particular one is not as useful as others for the purpose, but it gets the point across.

  • TS

    Yeah, I did something similar myself. I mined the INSA website (it is great to throw their own stats against them) and compiled it into a table. I had a similar correlation (-0.12), though my data is not complete as of yet. I was getting frustrated by the time it was taking, and the very erratic data on their site. As an example, Cameroon showed a murder rate of 16.1 one year and 2.3 the next. There were many countries that were all over the board like that, yes most of them with small populations, but not small enough to explain that kind of variation. I was trying to take the most recent year, though eventually figured calculating an average would be better based on what I was seeing (and the years reported were all over the place). Based on how long it was taking, I put it off, or save it for someone who can write a script to mine the data. I was including suicides, accidents, whether or not INSA dubbed them “permissive” or “restrictive”- basically everything useful. It would be nice to have a table of INSA data that could be passed around the blogging circuit.

    What is notable is that we don’t feel the need to resort to trickery, and are not afraid to be honest about what the data means. You mentioned wealth of countries, which has a similar negative correlation with murder rates. Basically there are a lot of very poor countries with little to no gun ownership (because the population can’t afford them) with high murder rates- and those countries drive the gun correlation negative. If you remove the United States from the sample the correlation gets closer to zero. The antis would flip-out over the concept that the US data actually helps our cause! But that is what happens when our murder rate is well below the global average and our gun ownership rate is a high outlier. Hence their use of the word “civilized” or “industrialized” as a way of excluding the places that have a seriously bad violence problem and get the data such that the USA’s murder rate is on the high side. They’d have to get crafty, because they need to set the GNI bar at 30,000 to exclude the Bahamas in order to show a correlation in their favor (which would comically cut off England & Wales).

    All this goes to show that international data is very unreliable. When making wealth cut-offs, there are not a lot of counties in the data pool, and correlations can be driven by the outliers. Removing the Bahamas or the United States shifts the numbers dramatically. Our own state data is much better for this: the data is collected by the same institutions in the same manner, the demographics across all the states is much more similar than across countries, and there is a higher sample size of 50. Of course we have already showed them countless times by countless people that this data yields no correlation.

  • AMB

    Excellent work, as always!

    Something struck me looking at your graphs side-by-side. It’s possible that there’s a causative relationship for both lower violent crime and increased firearm ownership in the form economic prosperity.

    In short, I wonder if richer countries have lower violent crime rates (due to better education, enforcement, lower poverty, etc.) and also more disposable income means more people can afford guns for fun and protection. Therefore the correlation between firearm ownership and lower violent crime rates is really just a product of national wealth.

    Whatever the case, I think it’s pretty clear that the supposed positive correlation between firearm ownership and higher murder rates is basically non-existent.

    [sarcasm]It’s almost as if murder is a social problem rather than an inanimate object problem.[/sarcasm]

  • Braden Lynch

    Thank you Linoge. I understand your simplified approach to get the point across. It works.

    I have two takes on this.

    First, with a really small sample size of N=1 (i.e. me) the need for my shotgun in the dead of the night when someone is breaking into my house trumps all scientific studies.

    Two, we need firearms to keep our government from ever considering adoption of sharia law, Nazi genocidal activities, or 100% taxation rates (i.e. communism). Our Second Amendment and self-defense rights trump any study, any safety initiative, compliance with international norms, or other “justifications” dreamed up by would be tyrants.

  • @ TS: Well, in honesty, I would observe that the data from inside our own country has actually shown a strong, negative correlation in the past, which actually hurts their cause rather than has no real bearing on it (as a “no correlation” finding could be massaged into appearing).

    But, yeah, I much prefer doing math on inside-the-US numbers, for exactly the reasons you mention. I have no way of knowing that all of those countries counted all of their murders (like, say, Mexico for example), and then you have those countries currently engaged in war or something like war – what counts as a murder, and what counts as a casualty?

    And, likewise, you hit exactly on the head why I did not engage in any trickery with “civilized” or “industrialized” countries – such abuse-of-statistics results in intentionally, maliciously biased results, and, after a fashion, dehumanizes those people in not-so-advanced countries. After all, their murders and deaths literally do not count to the anti-rights cultists, so what does that say about the value those cultists place on their lives?

    @ AMB: Hm. Actually, it would not be too hard to go through and add a GDP column to the chart, and then run up some graphs somewhat similar to these showing the correlation between GDP and crime, and GDP and firearm ownership rates. Granted, GDP does not really speak to the money individual citizens have available to them, or whatever financial troubles the countries in question might be going through, but it is the only number really comparable across international lines.

    Thanks for the idea! Maybe this weekend… 😉

    @ Braden Lynch: The problem is that simplifying the concept also removes some of the accuracy, and leads to people saying stupid things like “more guns = more crime”. There is a fine line between ‘simplifying to the point where you can understand’ and ‘simplifying to where it looks like stupid “solutions” will work’, and that is always a hard one to tread.

    Anywise, I would remind you that Tam’s immortal quote of the day was at the end of previous “graphics matter” posts, and would have been here as well if I had remembered ;).

  • TS

    I’d be interested in seeing the strong negative correlation to which you speak. If you are talking about your “graphics matter” series, that is different than what I am talking about (though equally relevant). That was a dynamic look at murders vs. guns over time, while the above is a static look at murder vs. guns with respect to geography. When I compiled stats domestically of gun ownership by state using numbers THEY provided (LCAV) vs. murder rates I came up with -0.09 correlation (effectively zero).

    Also lost in their exclusion of poor countries is the fact that their logic dictates that guns would make their murders worse too. Poor countries with high murder rates don’t correlate to gun ownership either*, but their logic dictates that where there are more guns versus clubs and edged weapons, obviously there would be more murders.

    *in my incomplete data set I am showing a 0.1 Pearson correlation among countries with a GNI under $2,000 US.

  • Whoops, sorry, we were talking about two different things, and I missed the distinction.

    I have no strong correlation for what you are talking about, unfortunately, only for the country as a whole. Still, I dare say a trend is starting to develop for the applicable statistics in general, and that trend is not looking good for the opposition.

  • Martin

    @ Linoge:
    Nice. wouldn’t it be better to show firearms per capita, which would eliminate the rather large (but non-descript) blue bars for some countries..


  • Per-capita is always better, but that is what the scatterplot is for – showing both murders and firearm ownership per capita. The thing is you cannot mix “per capita” and “normal” numbers in the same chart, or compare them against one another. The claim is invariably “more guns = more deaths”, but the “gun control” extremists never really get around to thinking about the influence of populations.

  • Volfram

    Huh. I had always thought there was a direct, inverse correlation between gun ownership and violent crime. Guess I have to concede that point.

    The chart DOES indicate, however, that there is absolutely no positive correlation between gun ownership and violent crime, but while the second chart shows an inverse correlation, it’s not really strong enough to draw any conclusions from.

    I’d like to see similar charts indicating relationships between murders and income level, religious practice, government spending, taxation, welfare, privately-funded charities, standard of living… all the other stuff that everyone claims is a cause or prevention of crime but nobody’s ever really sat down and done that kind of study on.

    I bet a chart on government spending would be another hard pill for the anti-rights crowd to swallow.

  • @ Volfram: Well, your willingness to admit to information that indicates your previous conclusions might be wrong already shows your superiority to your average “gun control” extremist. 😉

    But, yeah, a complete and utter lack of positive correlation basically means that causality is functionally impossible.

    The problem with all of these charts is that they are taking a single variable and attempting to hold it responsible for all crime. It is entirely possible that one variable or another has more responsibility for crime than others, but the world is, obviously, an obscenely complex system, and the study of what causes what would need to go a lot deeper.

    @ RKV: Thank you :).