Being the ruler of one of the world’s greatest empires might sound like a cushy job, yet it turns out that Roman emperors had one of the most dangerous occupations in human history. And while it’s well known that many of those who reigned over Rome met rather sticky ends, new research has revealed that their deaths were governed by the same mathematical principle that determines the severity of earthquakes and the number of social media followers a person has.
Presenting their research in Royal Society Open Science, the study authors reveal that of the 175 men who ruled over the Roman Empire, just 24.8 percent died of natural causes, with the rest being murdered, killed in battle, or forced to kill themselves. What’s interesting about this finding is that it suggests that the fates of these leaders can be described using a mathematical pattern known as a power law.
“Although they appear to be random, power-law distributions of probabilities are found in many other phenomena associated with complex systems, such as lunar crater sizes, earthquake magnitudes, word frequencies in texts, the market value of companies, and even the number of ‘followers’ people have on social media,” explained study author Francisco Rodrigues in a statement.
In statistics, a power law describes a relationship between two quantities whereby a relative change in one produces a proportional change in the other. The particular power law at play, in this case, is known as the Pareto principle or the 80/20 rule, which states that a common occurrence has an 80 percent probability while a rare event has a 20 percent chance of occurring.
The Pareto principle has been used to describe the relationship between small earthquakes, which are common, and large seismic events, which are rare. Similarly, the proportion of people with a small following on social media versus those with thousands of followers can be explained using this same power law.
In the case of Roman emperors, death by natural causes is clearly a rare occurrence, and is significantly outweighed by the more common eventuality of a violent demise. Among those who fell foul of this rule were the likes of Emperor Claudius, who was poisoned by his wife Agrippina in the year 54 AD so that her son, Nero, could ascend the throne. Not that this did Nero much good, as he was overthrown and forced to kill himself 15 years later.
In contrast, a host of famous Roman emperors including Augustus, Vespasian, Hadrian and Marcus Aurelius managed to remain on the right side of the Pareto principle and expire under more peaceful circumstances.
Delving deeper into the data, the researchers discovered that emperors were at the greatest risk of suffering a violent death immediately after taking power. “This finding may be related to the struggles in handling the demands that the position requires and the lack of political skills of the new emperor,” they write.
The chances of suffering a bloody demise then decrease steadily until an emperor has ruled for 13 years, after which the probability rises sharply once again. This, the authors, say, may reflect the fact that new adversaries tend to arise once a certain period of time has elapsed, while old enemies also may also regroup.
As an aside, the emperor Trajan is believed to have been caught up in a major earthquake at Antioch in the year 115 AD but died two years later of natural causes, proving that it’s possible to end up on both sides of the Pareto Principle.