Probing the pattern. Ongoing adaptation by the Red Queen (i.e., insurgents or terrorist group) and counteradaptation by the Blue King (i.e., coalition military or counterterrorism organization) leads to a pattern in the escalation of fatal attacks.

The MITRE Corporation/Brian Tivnan

Is There a Way to Predict 'Random Violence' in War?

The Taliban-backed suicide bombing that left 21 dead in a hotel in Kabul on Tuesday appeared to come out of nowhere. Insurgent attacks on coalition forces in Iraq and Afghanistan have also proved unpredictable, with weeks or even months between one burst of deadly fighting and the next. But according to a new study, attacks that seem sporadic in the beginning can begin to show a pattern as the aggressors refine their methods. The finding may provide a way for military leaders to gauge the timing of future attacks in a conflict, helping them allocate troops, weapons, and resources more safely and efficiently. The research may even lead to ways of anticipating such seemingly random events as suicide bombings.

To look for order amid the chaos of war, physicist Neil Johnson of the University of Miami in Florida and colleagues sifted through publicly available data of military fatalities during the 10-year period of fighting in Afghanistan and from 2003 to 2010 in Iraq. Analyzing the data with open-access software, the researchers found that, after an initial gap between the first two "fatal days" (attacks or bombings resulting in deaths), subsequent attacks came faster and closer together in a way that follows a particular mathematical pattern.

That pattern is the so-called power curve, in which more experience leads to less and less time needed to complete a task. "It's the same pattern of adaptation we find in shipbuilding, manufacturing, software development, even surgery," Johnson says. "You get better by doing."

The interval between the first two fatal days so strongly predicted the momentum of future attacks that the researchers were able to devise an equation, and an accompanying graph, that they could use to estimate the course of hostilities in many situations.

For example, if a suicide bombing like the one at the hotel in Kabul were followed by another approximately 3 months (say, 100 days) later, the researchers would plug 100 days into the equation. The resulting rate of escalation would place the third attack approximately 2 months (66 days) after the second, with the fourth an estimated 52 days after that.

When the researchers tested the equation in other arenas, it proved to be consistent. In addition to the fighting in Iraq and Afghanistan, the researchers tried out their graph on over 3000 fatal attacks by worldwide terrorist groups, as well as on suicide bombings committed by the Lebanon-based militant group Hezbollah and by militants in Pakistan. Finally, they checked attacks using improvised explosive devices on coalition forces in Afghanistan and Iraq.

In all of these situations, the escalation of fatalities estimated by the researchers' mathematics closely matched the course of actual deaths, the team reports online today in Science. Since suicide bombers in Lebanon are unlikely to be coordinating with insurgents in Afghanistan, for example, the consistency of unfolding attacks points to a common principle of adaptation, Johnson says.

Johnson likens this principle to the Red Queen hypothesis in evolutionary biology, named after the character in Alice in Wonderland who must keep running faster just to stay in the same place.

He explains that although the enemy is stepping up its pace through experience, the good guys are adapting as well. "In any arms race, one side is always a little ahead until the other side adapts to its actions," Johnson says. "By using our data to see when, and by how much, the Red Queen [i.e., the insurgent or terrorist group] is ahead, the military can evaluate precisely what it's doing, what's working, and what isn't."

Economist Michael Spagat of Royal Holloway, University of London, finds it "amazing" that the researchers uncovered the relationship between the spacing of early attacks and the timing of future ones. "It would be good to see if the same pattern holds up in even more contexts and other wars," says Spagat, who has collaborated with Johnson in other research but was not involved in the current study. He cautions that the work is not yet at a point where it could predict the date and time of an individual attack.

Johnson's group is now working on a larger study funded by the United States Office of Naval Research, hoping to estimate military and civilian fatalities more accurately with more comprehensive data. Johnson also believes the approach will be useful in learning to cope with cyber attacks. "It doesn't just apply to boots on the ground," he says.