The Roman Empire was ruled by 175 men, from Augustus (63 BCE-19 CE) to Constantine XI (1405-53), including the Eastern or Byzantine Empire after the split in 395 CE, but excluding those who did not rule in their own right because they were minors during regencies or co-emperors.
Only 24.8% of the 69 rulers of the Western Empire died of natural causes. The rest died a violent death on the battlefield or in palace plots. Considering all 175, 30% were murdered, committed suicide or died in battle.
Researchers at the University of São Paulo's Institute of Mathematical and Computer Sciences (ICMC-USP) in São Carlos (state of São Paulo, Brazil) investigated the underlying mathematical patterns associated with the reigns of the Roman emperors, showing that they followed what statisticians call a "power law."
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https://royalsocietypublishing.org/doi/10.1098/rsos.210850