For soldiers and civilians alike, insurgency wars are not only deadly but also frustrating in their apparently random spikes of violence. In a study in Nature, however, researchers put forth a mathematical model that shows terrorist attacks and insurgencies are not so scattershot as they seem.

The team searched for statistical similarities across nine historic and ongoing insurgencies including those of Iraq, Afghanistan and Northern Ireland [BBC News]. That meant compiling more than 50,000 acts of violence. And despite the fact that these events happened in different countries in different times, Neil Johnson and his team found a relationship between the size of an attack in casualty terms and how often it occurs.

By plotting the distribution of the frequency and size of events, the team found that insurgent wars follow an approximate power law, in which the frequency of attacks decreases with increasing attack size to the power of 2.5. That means that for any insurgent war, an attack with 10 casualties is 316 times more likely to occur than one with 100 casualties (316 is 10 to the power of 2.5) [Nature].

Researchers have used power laws to try to find order in natural phenomena, like a size vs. frequency pattern in earthquakes or avalanches. Johnson and his colleagues argue that the pattern arises because insurgent wars lack a coherent command network and operate more as a “soup of groups”, in which cells form and disband when they sense danger, then reform in different sizes and composition [Nature]. Also, he says, terrorist groups compete for media attention, which could help drive the pattern.

Other researchers doubt the reliability of the model. For one thing, terror cells battle one another and probably aren’t as free to break up and reform as the study suggests, terrorism modeler Roy Lindelauf says. And the number of insurgents in a fight might not stay close to constant, as the model presumes. But the math could have real-world practicality, team member Michael Spagat argues. “We could never say with certainty that there were going to be 10 attacks on one day, for example,” [BBC News] he says, but the model could predict whether a given day carried a lighter or heavier probability for a deadly attack.

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Image: flickr / :.phoenix.: