War fatalities—and especially those from terrorist or insurgent attacks—seem particularly and cruelly random. But some scientists think they have found the key to predicting just when these deadly assaults will come.

The findings are not based on new reconnaissance technology or intelligence breakthrough, but rather on some relatively simple number crunching. As it turns out, whether it is fatal roadside bombings in Kabul in 2008 or lethal terrorist attacks from a separatist group in the 1970s, the frequency of successful strikes comes at a relatively consistent rate of escalation, according to a new paper published in the July 1 issue of in Science. And to some researchers, that rate looks an awful lot like a learning curve.

When faced with a challenging task, groups of people tend to get faster the more they do it—whether that task is building an airplane or performing multistep surgery. The same holds true, the authors of the new paper argue, for organizing and executing successful militant attacks.

After analyzing reams of publicly available data on casualties from Iraq, Afghanistan, Pakistan and decades of terrorist attacks, the scientists conclude that "insurgents pretty much seemed to be following a progress curve—or a learning curve—that's very common in the manufacturing literature," says physicist Neil Johnson of the University of Miami in Florida and lead author of the study.

"Their goal is to manufacture or produce a fatal day for the military," he explains, apologizing for the glib terminology. To engineer the next fatal attack as quickly as possible, "they are of course trying to learn from what they've done in the past," he says.

This inclination helps to explain the most striking feature of the rate curve that Johnson and his colleagues found: its direction, up. As time passed, most groups seemed to be able to increase their frequency of "successful" (that is, deadly) attacks on their targets. And that is "the particular power curve that is associated with learning," Johnson says. In other words, he adds, even for terrorists, "practice makes perfect."

Predicting death
To arrive at the model, Johnson and his colleagues noted the first two days with fatal attacks in any given conflict—whether it was an Afghan province or a Hezbollah suicide bombing in Israel—and the subsequent escalation of frequency with which the group executed successful attacks. (The fatality data came from Operation Iraqi Freedom from 2003 to 2010, Operation Enduring Freedom in Afghanistan from 2001 to 2010, suicide bombings from Pakistan militant and Hezbollah incidents between 1995 and 2008, and 3,143 other attacks executed between 1968 and 2008.)

The model seems to successfully predict when the next day of fatal attacks might arise just based on the time between the first two attacks and the subsequent rate of escalation. As a result, Johnson explained in a Science podcast, the researchers could predict the number of days between the 50th and 51st deadly attacks.

But if these calculations are so simple, will not the insurgents and terrorists simply steer their planning around them to thwart counter-efforts? Johnson and his colleagues are confident that such a move will not necessarily be the case for the same reason commuters, knowing when traffic is worst, join the rush hour nonetheless.

The stark upward curve also highlights the finding that as conflicts continue, fatal attacks grow increasingly likely. Although the trend is apparent through Johnson's analysis, he says that he has not heard this pattern discussed much. If knowing that adversaries become predictably more efficient over time, financial, political and human calculations of the costs of war might be tabulated differently.

Conflicting conflict models
Not all researchers see the same pattern Johnson perceives. Aaron Clauset, a computer scientist at the University of Colorado at Boulder, who was not involved in the new paper, used a similar model in 2009 to describe attacks in the Afghanistan conflicts. He calls the mathematical approach "a wonderful way of comparing very different contexts" in an effort to figure out "the general rules and general patterns for large human conflicts."  From his assessment of Afghanistan casualty data, Clauset is not entirely convinced that the new learning curve tells the correct story. Instead, he suggests that "the size of the organization—in other words, the number of militants that are working—defines the sequence of events."

Drilling down more deeply into the data should help academics and policymakers alike better understand the forces behind the rate of attack escalation. Particularly crucial insight might be gleaned from data points that lie well beyond the main curves in the attack reports. "That could be quote–unquote 'noise' or it could be telling us something"—that personnel have changed, that a group has gotten better information or better technology, Johnson says. "If we go back and we know a bit more, and a bit more narrative goes in from the social sciences, we might be able to unravel a little bit more" about the reasons for attack frequency timing, Johnson suggests. And that could drive more effective prevention strategies for the future.

Evolving strategies

The data also might also indicate new patterns in how combatants are responding to one another. Specifically, the rate of fatal attacks is not only a measure of group's improvement, but also their ability to stay ahead of coalition forces that are presumably working to limit the frequency of these strikes.

Johnson sees a similar pattern in nature as predators and prey continuously adapt and evolve to outdo the other. This so-called evolutionary arms race (also known as the Red Queen hypothesis) can be tracked over the eons as each species adapts new strategies to outwit their predators—and/or their own prey—making the dynamic a two-way street.

In the war data, too, the researchers could glean patterns of adaptation from the rates of attacks. Not all offenses seemed to be met with equal futility from counterinsurgency and counterterrorism efforts. The militants, for example, did not pull ahead as quickly with improvised explosive device (IED) attacks, which "suggests that the coalition military counteradapts to IEDs better than to other threats," Johnson and his colleagues noted in their paper.

The group also found that the rate of fatal attacks in Kabul and Zabul Province in Afghanistan stayed steady, "implying that the military is managing to contain further escalation." So by looking for these trends, policymakers might be able to assess just how well insurgencies were being contained—and what strategies seem to be keeping the rate of deadly attacks statistically low.

Johnson hopes to see if the model can be applied to other conflicts, such as the ongoing one in Libya as well as ancient Greek wars. He also sees potential for it in other realms, including cyber attacks. "This same approach doesn't have to be related to people on the ground," he says. "It's groups of people trying to get their act together to inflict damage."

Despite his enthusiasm for new applications, Johnson is also quick to point out the model's limitations. In many conflicts, such as Hollywood style battles in which opposing armies line up to fight at predetermined times or even in World Cup soccer matches, the progress curve rate of escalation does not hold up. So applying it to other instances, such as the ongoing conflict in Libya (which, Clauset points out looks more like a traditional civil war than Afghanistan- or Iraq-style insurgent attacks), is dicey. "We'd like to think that there are similarities, but we should be very careful to recognize the differences," Clauset says.

But at least for insurgent and terrorist attacks, the new model could be an important tool for keeping soldiers and civilians safer by offering "a really direct estimate of the future," Johnson says. "It's not a crystal ball, but it's an estimate." And that would be more useful than a seemingly random flood of fatalities.

Want to try the calculations for yourself? Johnson and his team used public data on military fatalities from the site icasualties.org, terrorism attacks from the Memorial Institute for the Prevention of Terrorism databases and suicide bombing data from the Chicago Project on Security and Terrorism. And to crunch the numbers, they employed free Open Office software. Details of their calculations are available in their supporting online material.