Tracking this claim to its source is a good example of heading down an Alice in Wonderland-style rabbit hole.

Checking back to the article you cite, it's clear that the claim is based on a new and really quite exceptionally broad survey of violence among all mammal populations. This was published in Nature this week as Gomez et al, "The phylogenetic roots of human lethal violence." Superficially this means the source is an impressive one, since Nature is certainly one of the most prestigious scientific journals in the world. However, it's worth noting that the paper appears as a "Letter" rather than as a full fledged article, and that Nature has a surprising history of publishing high-profile but what can politely be termed "controversial" articles, such as one offering a scientific name for the Loch Ness Monster based on underwater photographs of what later turned out to be almost certainly a tree stump.

In this case The Atlantic itself sounds some cautionary notes about the evidential basis of the violence survey. It is a meta-analysis, and by its nature not a very comprehensive one (that is, it does not include any original research, but collates the results of earlier surveys) that attempts to compare the levels of violence among a huge variety of different mammal populations across the whole of the archaeological record. A total of 1024 species are surveyed, humans being just one of them. So it's reasonable to wonder exactly how much effort was put into making sure the human sample was comprehensive and representative, and problems associated with the data had been completely thought through.

The Atlantic has a few pertinent comments about the team's methodology:

1. "First, he and his team compiled everything they could find on causes of death for various mammals, accumulating some 3,000 studies over two years."

2. As for the sources of information for the human sample: they did this "by poring through statistical yearbooks, archaeological sites, and more, to work out causes of death in 600 human populations between 50,000 BC to the present day."

As for the way in which the data has been handled: "Polly Wiessner, an anthropologist from the University of Utah ... is unimpressed with the study’s human half. “They have created a real soup of figures, throwing in individual conflicts with socially organized aggression, ritualized cannibalism, and more. The sources of data used for prehistoric violence are highly variable in reliability. When taken out of context, they are even more so.”

"Richard Wrangham from Harvard University has similar concerns about the mammalian data, noting that Gómez have folded a lot of different kinds of killing—infanticide, adult deaths, and more—into a single analysis. And from an evolutionary standpoint, it matters less whether two related species kill their own kind at a similar rate, but whether they do so in a similar way."

To go further into this requires a close reading of the original article, which is available online here. It's worth noting that the article itself gives very inadequate sources for most of the information it contains, which is not surprising when it is based on such a vast meta-analysis. To find out what the actual sources are we have to go to the "Supplementary material" section which is separately available here.

Let's summarise what we can discover about the sources used and their comprehensiveness and reliability by reading through these two sources.

First, the Letter itself.

This points out that the human violence figures available were divided into four categories by socio-political organisation: bands, tribes, chiefdoms and states. This is a categorisation widely used in the social sciences (eg anthropology) but one that I'd say a lot of historians find unhelpful. After all, there's a vast historical literature devoted entirely to trying to define what a "state" actually is.

There are also some acknowledgements of potential bias that give some clues as to the sorts of sources being used: "The level of violence inferred from skeletal remains could be under-estimated because many deadly injuries do not damage the bones..." And there's also a reference to "statistical yearbooks" being a prime source of information. So it would appear that the data for the medieval period is going to be based on the archaeological record, rather than the written record. There's not much clue yet as to how broad the sample will be, geographically or temporally, but if a lot of reliance is being placed on "statistical yearbooks" then that sounds some pretty loud warning bells for me when it comes to making accurate assessments of the medieval period, since, of course, no such contemporary sources exist for this period.

That's about it for the Letter itself, and the bibliography offers no further clues as to the exact sources of information. To go deeper we have to look at the "Supplementary information:" document. This contains a couple of useful additional bits of information. First, by "medieval period" the authors mean the period 1300-500 BP, which is 716-1516 A.D. Second, their data is based on a sample of 17,372 human remains. Again this sounds warning bells, since such as sample size is not going to be enough to provide proper coverage of the whole human population across the whole globe for that whole period. It's a real drop in the ocean sort of a figure – a sampling. Actually, we're told that figures from 600 different populations were compiled for the survey as a whole (covering the period from 50,000 BP to now), which in one sense is quite impressive, but which also implies that very likely no one population is followed in a consistent and systematic way across the whole period.

Third, there is a better definition of "lethal violence" offered: for the purposes of the paper, this is defined as "the percentage of the people that died owing to interpersonal violence." If we think about that for a moment in the context of earlier cautions, this sets off more alarm bells. If we're looking at archaeological data, it's going to be very difficult to distinguish for example between interpersonal violence and accidents and suicides in many of these records. Was a broken leg inflicted in a battle or a fall? If the researchers have been scrupulous, I would expect this factor would result in a form of understating of figures for the medieval periods, since they should only be counting wounds that were clearly inflicted by weapons. Again though we have to recognise that this whole debate goes on in the wider context of the difficulty of identifying some marks of violence from purely skeletal remains. Many arrow wounds, not to mention cut throats, deaths by poison etc etc are not going to show up readily in the archaeological record.

Finally, we can use the data supplied here to be much more explicit about the precise sources consulted. I've copied the portion of the survey data that refers to the medieval period here.

This shows the site of the remains surveyed, rough date and number of remains, and (final column) a source, which you can chase up in the bibliography if you're so inclined. They are anthropological and archaeological, not historical. Just to give one example, one of the sources for Serbian violence is Djuric MP, Roberts CA, Rakocevic ZB, Djonic DD, Lesic AR (2006). "Fractures in late Medieval skeletal populations from Serbia." American Journal of Physical Anthropology 130: 167-178.

From all this we can see that the survey is very limited - it covers only the UK, Ireland, Portugal and Spain, Scandinavia, Germany, Poland and Croatia. Even allowing for my earlier comments about the lack of comprehensiveness here, in my opinion this is a ridiculously limited pool of data from which to extrapolate a worldwide, pan-medieval figure. There are many reasons for supposing that even if the European figures are representative (which we can't know, but look at some of the specifics - two Viking cemeteries, a burial pit associated with the Battle of Towton (the bloodiest battle, probably, in British history), a royal graveyard in Croatia, and some monks' graveyards ... it would be so easy to argue that these are very unrepresentative samples), these figures are just not very useful.

All we can really conclude from this is that a survey of remains from 40 different, broadly medieval, European sites, containing a very varied number of bodies, from very varied periods that include some periods of war, estimates deaths by violence at an average of 12%. Even in this limited context, I immediately have hundreds of questions about how typical these sites are, what sorts of violence, how we know who inflicted what wounds in what circumstances, and even whether the victim survived them to die a natural death much later. None of these questions are answered by the Letter and to focus on something as specific as deaths in the medieval period is to use the paper itself for purposes it was not really intended for.

tl;dr The figure of violent deaths (as a whole - not merely murder) is drawn from data too limited and imprecise to be reliable – and to use this paper as a source for the proportion of violent deaths in the medieval period is to use it for a purpose it is plainly not intended for.