2021-10-16 22:25:26 UTC
They also did an analysis of death risk over time. The highest risk, unsurprisingly, was immediately following their accession, and that risk declined precipitously over the next few years, stabilizing about four years in at a relatively low level. Then there was a spike in death probability at about 13 years, to as high as it was within the first two years, before again dropping off to minimal. Presumably a dozen years was about how long it took for the emperor to get complacent, for his base of support to drop off, for him to accumulate enough new enemies, and for the next set of rivals to conclude the time was ripe for taking a go at him rather than just waiting for him to die or risk having someone else take him out and losing their chance.
For what its worth, when they added in the Eastern Roman Emperors, the ratio of natural deaths rises, so they met fewer violent ends, on average, than in the west. Some other findings: there was no difference in the death statistics when comparing Italian to non-Italian-born emperors, but there was a difference between those who inherited the throne as opposed to those who seized it, with the former having longer average spans. In light of this, it is also unsurprising that average time to death was less in the later centuries than in the first century of the empire (when succession was more orderly).
While most royalty during the medieval period would presumably not follow this pattern because of the hereditary nature of most crowns, I have to wonder if an analogous pattern of post-succession death might be observed with those kingdoms not practicing male-preference primogeniture, though I am not sure we have enough information on any of them for a statistically-valid evaluation.