Historical records show that of 69 rulers of the unified Roman Empire, 43 (62 percent) suffered violent deaths - assassination, suicide or combat. Historical accounts typically examine each death as a single, random event alongside individual contributing factors such as allegiances and wealth. The military got a bonus from a new Emperor so there were periods when turnover was linked to the financial effect, for example.
By applying statistical methods frequently used to test the reliability of components in engineering, Dr. Joseph Saleh, an aerospace engineer from the Georgia Institute of Technology, modeled the typical length of time between the beginning of an emperor's reign and their subsequent death.
Didius Julianus was Emperor from March to June, 193, thanks to the Praetorian Guard vowing no new emperor would be chosen without their approval and holding an “auction” to decide. That did not stand with the real military and Lucius Septimius Severus had 16 legions - the entire Rhine/Danube army. The Praetorian Guard had no interest in defending this Julian once he revealed he didn't have the money to pay them after all and the second emperor in the “Year of the Five Emperors” was assassinated. Image: Ancient History Encyclopedia.
Saleh found parallels between the seemingly random failures of components in engineering and the seemingly random deaths of emperors, a "bathtub" curve where they would fail right away or after prolonged use: "In engineering, the reliability of a component or process is defined as the probability that it is still operational at a given time. The time it takes for a component or process to fail is referred to as its time-to-failure and this shows similarities to the time-to-violent-death of Roman emperors."
Roman emperors faced a high risk of violent death during their first year of reign, much as when engineering components fail early - often they were not not up to the specification. The risk of death stabilized by the eighth year but increased again after 12 years of rule, a pattern similar to the failure of components because of fatigue, corrosion or wear-out. When data points were aligned on a graph, the failure rate of Roman emperors displayed a bathtub-like curve, a model widely seen with mechanical and electrical components.
Data was obtained from the De Imperatoribus Romanis, an online encyclopedia of Roman emperors. The author cautions that the limitations of the data should be acknowledged, as sources of ancient history are often inconsistent and the exact causes of death may differ between accounts. Further studies could explore why emperors repeatedly met a violent end and whether other historical events may be analyzed in this way.
"It's interesting that a seemingly random process as unconventional and perilous as the violent death of a Roman emperor--over a four-century period and across a vastly changed world--appears to have a systematic structure remarkably well captured by a statistical model widely used in engineering. Although they may appear as random events when taken singularly, these results indicate that there may have been underlying processes governing the length of each rule until death," said Saleh.