graph of guns vs. gun homicide by state. 
Its a weak (not significant to probability .95) negative correlation. More guns less murder with guns, or if you require solid statistical significance, then guns and murder with guns are uncorrelated in the US.
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Vox also voxsplains to us about America’s unusually high gun homicide rate.
Having presented this graph, they say that “To understand why that is, there’s another important statistic: The US has by far the highest number of privately owned guns in the world.”
Even granting, as we saw above, that gun ownership does indeed increase homicide rates, this is not the most important factor in explaining America’s higher homicide rate, or even close to the most important factor. Let me give a few arguments for why this must be the case:
1. The United States’ homicide rate of 3.8 is clearly higher than that of eg France (1.0), Germany (0.8), Australia (1.1), or Canada (1.4). However, as per the FBI, only 11,208 of our 16,121 murders were committed with firearms, eg 69%. By my calculations, that means our nonfirearm murder rate is 1.2. In other words, our non-firearm homicide rate alone is higher than France, Germany, and Australia’s total homicide rate. Nor does this mean that if we banned all guns we would go down to 1.2 – there is likely a substitution effect where some murderers are intent on murdering and would prefer to use convenient firearms but will switch to other methods if they have to. 1.2 should be considered an absolute lower bound. And it is still higher than the countries we want to compare ourselves to.
2. There are many US states that combine very high firearm ownership with very low murder rates. The highest gun-ownership state in the nation is Wyoming, where 59.7% of households have a gun (really!). But Wyoming has a murder rate of only 1.4 – the same as right across the border in more gun-controlled Canada, and only about a third of that of the nation as a whole. It seems likely that the same factors giving Canada a low murder rate give Wyoming a low murder rate, and that the factors differentiating the rest of America from Wyoming are the same factors that differentiate the rest of America from Canada (and Germany, and France…). But this does not include lower gun ownership.
3. There are many US states that combine very low firearm ownership with very high murder rates. The highest murder rate in the country is that of Washington, DC, which has a murder rate of 21.8, more than twenty times that of most European countries. But DC also has the strictest gun bans and the lowest gun ownership rate in the country, with gun ownership numbers less than in many European states! It seems likely that the factors making DC so deadly are part of the story of why America as a whole is so deadly, but these cannot include high gun ownership.
slatestarcodex.com
6. Commenter Elias brings up this meta-analysis by Gary Kleck claiming that the 40 guns-and-states style studies he could find were split almost exactly half and half in terms of whether they found a significant guns-homicide correlation or not. He further claimed that the better the study, the less likely it was to find a significant correlation.
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