The severity of terrorist attacks follows a power-law distribution.

The writers used the MIPT Terrorism Database. Between 1968 and 2004, there were 19,907 terrorist attacks resulting in 7,088 attacks that killed at least one person. They compared the frequency and severity of the attacks and discovered a universal pattern.

Using the tools of extremal statistics, we characterize the relationship between the severity and frequency of terrorist events. By severity, we simply mean the number of individuals injured or killed by an attack. We show that this relationship may be well-characterized by the simple mathematical function, the power law P(x) ∼ x−^y, where y is the scaling exponent.

The y is 2.0 for all terrorist attacks in the database. This is a scale-free distribution as seen in this graph

We can study the risk of terrorist attacks. We can estimate the probability (p) of casualties (x). The p(x) tells us that high casualty events are extremely infrequent while low casualty events are frequent.

Another fact emerges from this study: Terrorism in the G7 states have a y of 1.7 while non-G7 States have a y of 2.5. This also suggests that Terrorism requires an certain ecology.

An important fact is the x (max) and the x (mean). The x(mean) is very low. The average terrorist attack kills a handful of people. The x(max) of fatalities was 2,973. That is the maximum number of casualties inflicted by a single terrorist attack. That would be 9/11.

Weapons affect the average casualties. Chemical and bioweapons are potentially the deadliest, but also the rarest and as of 2004 made up 0.4% of terror attacks. Explosives
Fire, Firearms, and Knives appear in decreasing order of effectiveness. Explosives are the most popular tool of terrorism.

Terrorism requires advanced technology that increases the productivity of the attack to increase the severity of casualties. As productivity rises, we can expect more casualties from terrorism.

The power-law tells us something very important. Rare catastrophic attacks are not “outliers” or exceptions to the rule. They are the rule.

9/11 greatly exceeded the average severity of a terrorist attack. Yet the powerlaw curve suggests that with growing firepower and capability, even more severe attacks can occur, but with a low probability. We can predict infrequent attacks in the future causing 6,000 and 12,000 casualties.

Terrorism appears to be ineffective in the aggregate. I’ve noted before that terrorism fails as a political strategy. I partly attributed that to the “maximalist” goals of terrorists instead of pragmatic ones. Another part of the explanation is the ineffectiveness of terrorist attacks against civilians. It is insufficient to disrupt or destroy a society.

Terrorists must find a way to raise the severity of casualties per attack to a truly catastrophic amount (e.g. 100,000 casualties)
OR greatly increase the number of terrorist attacks (e.g. 100,000 attacks)

Both are theoretically possible, but very unlikely. So terrorism will continue to fail as a strategy.