Facts about deaths of Roman emperors

Of the 69 rulers of the unified Roman Empire, from Augustus (d. 14 CE) to Theodosius (d. 395 CE), 62% suffered violent death. This has been known for a while, if not quantitatively at least qualitatively. What is not known, however, and has never been examined is the time-to-violent-death of Roman emperors…

Nonparametric and parametric results show that: (i) emperors faced a significantly high risk of violent death in the first year of their rule, which is reminiscent of infant mortality in reliability engineering; (ii) their risk of violent death further increased after 12 years, which is reminiscent of wear-out period in reliability engineering; (iii) their failure rate displayed a bathtub-like curve, similar to that of a host of mechanical engineering items and electronic components. Results also showed that the stochastic process underlying the violent deaths of emperors is remarkably well captured by a (mixture) Weibull distribution.

That is from a new paper by Joseph Homer Saleh, via the excellent Kevin Lewis.


I believe Gibbon notes that the first Roman Emperor to retire was Diocletian in the early 300s.

Two factors count against early retirement: campaigning was tough (life in the camps = disease), and lifespans in the Roman times were shorter (no decent doctors).

Bonus trivia: Augustus, arguably the most successful person in history, was the adopted son Caesar, and who put the biological son of Caesar, sired with Cleopatra when Caesar was 55 years old, to death, fratricide being common in ancient times as a way to preserve power. And "Et tu, Brute?" is a fictional phrase of Shakespeare. I can resist, this being a top post by SS, in citing this well made parody: https://www.youtube.com/watch?v=oOm_2dGzqp0 Shaka Zulu vs Julius Caesar. Epic Rap Battles of History

How many autocratic rulers in modern times have retired? It's not common. Even many politicians in democratic countries try to stay in office until extreme old age.

These people are extremely ambitious, hard-working, and desire power. They don't quit easily.

Joe Biden certainly doesn't quit easily - he first ran for president in 1988.

Roman era Impeachment.

Actually the "fictional phrase" comes from Suetonius and the original quotation is in Greek: "καὶ σύ, τέκνον?"

Shakespeare may have had, in the words of Jonson, "little Greek and less Latin," but at least he did his homework.

Good points. Minor correction: “small Latin and less Greek”, said Jonson. But that’s when Shakespeare was his rival not later when Shakespeare was his acknowledged better.

Major correction: read critically Johnson's actual words, to wit "And though thou hadst small Latin and less Greek ...".

Then join the argument at:

Caesarion was illegitimate under Roman law and as a foreign monarch he would not have been allowed inside the city of Rome (Cleopatra wasn't either. During her time in Rome she had to live in the suburbs).
To his credit Octavian soared Cleopatra's children by Mark Antony, and his sister Antony's cast off wife Octavia fostered them.

Fun analogy. Being a Roman emperor was like playing Russian roulette with four cartridges loaded in the six cylinders.

Yes, and your own troops were charged with pulling the trigger.

Some were born in the purple. Some achieved the purple. And, some had the purple thrust upon them.

PSA: Revolver Gun Safety. Avoid inadvertent discharge. Always keep unloaded the next (to fire) cylinder. Don't shoot yourself in the foot.

I thought you were supposed to keep the cylinder under the hammer unloaded so it wouldn't discharge if dropped on the hammer?

This is why term limits is better than lifetime appointment. It is good for the health of the nation and for the health of its leaders.

"remarkably well captured by a (mixture) Weibull distribution."

This is more a statistical fluke considering manufacturing time to failure and imperial time to violent death have very different generating processes; one physical and the other social. The social science dream of Asimov's psychohistory mathematically describing population behavior is still alive. Unfortunately Asimov is now being posthumously #metoo'd on social media so maybe forget the whole deal?

Leaders face an early test of competence, and if they pass this then failure rates fall. However, over time problems may accumulate, and their own abilities degrade with age.

This is analogous to component failures, first due to defects and later due to wear.

I don't think it's a fluke, but rather a generalizable observation about certain types of processes (much like the normal distribution applies to many disparate things).

I read a book of investing advice by Ruchir Sharma from around 2011. One of his arguments was that new national leaders who are successful tend to have the personalities that are needed at the moment. E.g., when I was in Moscow in 2001, I asked a coed what she thought of Putin, and she said, "Compared to Yeltsin, at least he is sober and healthy enough to show up for work."

Sharma pointed to Putin and Erdogan of Turkey as guys who had the right traits for what their countries needed in the early 2000s, but were rapidly becoming obsolescent.

In 2011, this struck me as a brilliant insight. But in 2020, I notice that Putin and Erdogan are still around. So what do me and Sharma really know? Forecasting is hard, especially forecasting the future.

Getting in power and staying in power are different. One requires being the person for the moment, the other requires killing a few journalists.

Very good points. Also, for this reason when you get a new Roman Emperor you should never buy the extended warranty. They always only start after the early assassination threat is over, and end before the emperor gets old and useless.

For sure. Under the system they had the only way to get rid of an Elagabulus was to kill him. Very inefficient.

Under today's reigning World War T, we'd have to worship Elagabulus as a god.

The term limits employed by various African tribes in years past might alleviate some of the problems with incumbency we see today:

Per the Encyclopedia Britannica: When a king began to grow old, it was said in Africa: “The grass is fading.” To preserve the growth and well-being of the land, it was necessary to kill the aging king so that his power could be transferred to a successor. The compulsory killing of the king was widespread among many of the non-Semitic peoples in northern Africa; and among some peoples the killing of the king occurred after a specified period of time and was integrated into the cosmic ritualistic rhythm. The real meaning of the killing of the king showed itself in rituals in which the blood of the murdered king is mixed with the seed corn, which then became especially fertile.

I've wondered what the probability of being a good emperor was when factoring in how the person became emperor (i.e. adoption by the previous emperor, natural hier, usurpation, something else).

From casual observation, it seems like adoption was the most reliable form of succession that resulted in good governance.

I'll bet that the people of Oman wonder about the probability of being a good Sultan; the chap who has just died seems to have done a decent job.

Judged by the standards of the Roman Empire he might have been one of the Good Emperors. Or am I being too starry-eyed about him?

The late Sultan of Oman for the last 50 years was an extreme Anglophile -- he overthrew his dad, with London's help, after his dad disapproved of his Gilbert & Sullivan record collection and locked him up.

Adoption of your best junior officer seems like a good system. Of course, in "Gladiator," Emperor Marcus Aurelius (Richard Harris) fails to succeed in adopting General Maximus (Russell Crowe), allowing his useless son Commodus (Joaquin Phoenix) to take the throne ...

Failing to succeed is the worst kind of failure.

I've never seen anyone mention it, but Gibbon, a fan of royal succession by birth as befits an Englishman of his time, made much sport of the Roman way of succession, yet he thought Caracalla and Commodus among the worst emperors, and yet they both succeeded by lineage.

Gibbon was particularly revolted by morality and sexual practices of those two degenerates. He would have a similar feeling about current American political elites.

Is Commodus where we got the word 'commode'?

Adopted sons were given more favor by their fathers than biological sons. Why is that? Was it because biological sons (children) were often the offspring of cousins and thus exhibited less capacity for achievement? In ancient Greece and Rome, the "household" was the economic unit (household, as the term implies, is broader than "family"). The "household" did not include the wife; instead, she remained in her father's (grandfather's) household. The purpose was to prevent the union of two households to form a stronger unit. Compare that to later years of England, Spain, France, etc. where it was common for a royal from one country to marry a royal from another for that very reason. As for the instability of government in ancient Rome, I was taught that it was the result of all that in-breading (cousin marriage). Was the instability a feature or a bug? Or was it the result of the absence of democracy? One will recall that those who favor the ancients today disfavor democracy. Be careful what you ask for.

I know, there's no "bread" in inbreeding.

There, there.

So that is what we become. A 21th Century Rome led by a mad Emperor who twitters while the Empire burns.

Just statistically, the pool of potential adopted sons is much larger than the pool of potential biological sons so you’d expect the best adopted son to be better than the best biological son.

Reversion to the mean in biological offspring?

Romans couldn't marry foreigners and, as today, the elite preferred to marry other elite. The population of elite was small enough it was almost impossible not to marry someone to whom you were related.

What's the ideal age difference between ruler and successor? Ten years?

What's the best tradeoff in Roman history? Trajan the conqueror to Hadrian the consolidator? They differed by 23 years in age. (Trajan's predecessor Nerva ruled only from 66 to 68.)

I suspect that 23 years is more than ideal, but pretty normal. Trajan was emperor from age 55 to 73. Hadrian was emperor from age 41 to 62. Hadrian is probably my favorite Roman emperor: he was less in favor of invading the world and more in favor of building cool stuff like the Pantheon.

Hadrian's successor Antoninus Pius was emperor from 52 to 75. His successor Marcus Aurelius was emperor from 40 to 59.

These are the second thru fifth of the Five Good Emperors denoted by Machiavelli and Gibbon.


So that is probably about as fortuitous as succession can get.

I rank Hadrian as my 70th favorite Roman Emperor, just below Caligula.

Analyzing the hour patterns of violent death, we find a dagger-shapped distribution around midnight.

“Is that a dagger shaped distribution I see before me? The handle toward my hand?”

All those supposedly intelligent people complaining about democracy and elections seem to forget that this is the alternative.

If you really really insist, I'm sure we could all oblige and hang you.

It's not the alternative. In the modern world autocrats are rather secure. They don't get overthrown after one year or after twelve years, or at all.

Coups against autocratic or democratically-elected governments alike have become quite rare, even in parts of the world where they were routine half a century ago.

The Shah of Iran, Anwar Sadat, Ceausescu, Ferdinand Marcos, Saddam Hussein, maybe even Hosni Mubarak might all differ, as might handfuls of others less prominent.

Political assassinations and wars were common during the Roman Republic period too. The violent nature of the Roman polity had more to do with their plunder-and-enslavement-based economy, which made violence and conquest profitable.

Yes and so? Except for the statistical and quantitative mystification, I find the basic summary of reign length and cause of death conveniently assembled in the closing pages of The Classical Compendium by Philip Matyszak (Thames & Hudson, 2009).

Forty-eight murdered emporers out of seventy for the period Saleh cites (although Rome's last field army died with Valens in 378, Matyszak continues through 476 with the retirement of Romulus Augustus--another five emperors died violently between 378 and 476).

Four out of five Julio-Claudians died violently, all four emperors in the Year of the Four Emperors ditto.

From 211 to 253 all fifteen emperors died violently. Of the twenty-five emperors East and West from Constantine the Great to Romulus Augustus, "only" eleven died violently.

Augustus himself significantly enjoyed one of the longest reigns (thirty-five years).

--but instead of comparing emperors to engineering, it might be at least as helpful to compare ancient engineering with modern and contemporary engineering. How many engineering feats accomplished across (formerly Roman) Europe since, oh say, 1500 CE continue to stand? vs. those Roman feats largely or even partly intact after roughly two thousand years (including paved roads)? (Sure, we've excavated and restored some since.)

Their mathematics surely was not quite comparable to ours, they relied on slave labor for construction: but by comparison, was the Roman pretense of "permanence" any more pretentious than contemporary pretense concerning the sure extension of mythical Progress?

The biggest share of Roman road construction was done by the Roman army.

The original "army corps of engineers"?

Are there any stats on the causes of mortality for Eastern Empire emperors, which limped on until 1453 AD?

The Byzantines were not immune to palace intrigues, at all, but I don't know of a convenient source summarizing the fates of their emperors.

In a handful of history bibliographies on my shelves, I find gaps in Byzantine coverage that are telling but (from west European and American perspectives) not terribly surprising.

Regicide certainly happened in Byzantium (Irene blinding her own son with fatal result is my favorite horrible example) but it was less common. Despised emperors might be exiled or blinded or simply left in a palace under guard with some servants where they could pretend they were still rulers.

I wrote a detailed comment but it seems to have been removed. So suffice it to say that although the article is a well-written introduction to survival analysis, it astoundingly totally ignores demography.

Demographers invented many of the very techniques that the article uses, in particular there's no need for tortured analogies to reliability engineering and "failure rates" because demographers study the very thing that this article studies: survival times and mortality rates.

I might point newbies to this article as a smooth introduction to survival analysis, but the ignorance of demography and mortality rates is a serious concern, as is the article's de-emphasis of hazard rates. Looking a graph of the hazard function is a basic step in figuring out what's going on in survival analysis; the article's use of a Weibull plot is cool but it's a serious mistake to not tell the reader more about hazard rates. (The article does talk about failure rates aka hazard rates but doesn't describe why they're so vital in survival analysis.)

I had a lot more comments but don't have time to re-enter them (and maybe they'd get deleted?).

The Economist, in its overview of national governments around the world, said that leaders tend to become detached from reality after about a decade at the top.

That was written back in the 1980s, but I'm sure it's a universal and eternal truth.

Comments for this post are closed