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Notes -
Has anyone run the numbers on what percentage of male-line preferred monarchs/rulers in history failed to produce a son?
By male-line preferred I mean to include not just pure primogeniture inheritance, but also cases like Imperial Rome where a son wasn't necessarily the heir, and one could have an heir without having a son, but if possible a son was preferred. In both cases one imagines that such a ruler tried very hard to produce a son.
I don't have the numbers off the top of my head, but it varied wildly between dynasties. Notably, the Kings of France were extremely good at having male heirs (and, generally, having them young enough to succeed as adults), which was a huge part of their ability to centralize into a functioning state. The one time there was a really disputed succession, it kicked off the Hundred Years War. In Germany, on the other hand, comparable houses were much less fecund. The Ottonians died out quickly, in part thanks to their insistence on sending Imperial princesses to the Church, and the only eldest son of the Hohenstaufen to succeed directly was Frederick II, after a 17-year struggle and some minor miracles (Barbarossa was succeeded by first his third and then his tenth child). The Habsburgs did somewhat better, until they got too inbred...
Shower thought: "trying for an heir" was probably notably easier for some kings than others. Medieval kings moved around a lot, because of the need for personal rulership and the heavy demands the royal household placed on any given host. The Kings of France were mostly in and around the Paris area, having the closest thing to a settled capital. Except on Crusade, they were rarely far from their marital bed, their doctor's workshop, etc. The Holy Roman Emperors, by contrast, often spent most of their reigns on the move all across Germany/Italy, reducing fertility for two reasons - firstly, that military travel, particularly in the disease-ridden swamps of medieval Italy, was a terrible environment to have a healthy child in, and, secondly, that their wives often stayed somewhere else to act as regents or co-rulers. Poor relations with the Popes also meant that it was harder for German and English rulers to divorce wives who were infertile or refused to sleep with them, like Barbarossa's first wife. In the end, the difference between dynasties was probably a fair number of little things and a lot of luck.
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To give one data point: 18 out of 40 monarchs of England (I'm counting William and Mary as one and beginning with William the Conqueror because that's where the wikipedia article detailing the history of the succession I'm looking at starts. I'm also just kind of eyeballing this and wouldn't be surprised if my counts are one or two off) have been succeeded by someone other than their son. Though this includes situations such as where King Stephen was forced to pass over his own young son in favor of Henry of Blois, or when the throne passed to Edward III's grandson due to his son predeceasing him, as well as monarchs who would probably have passed the throne to an heir but for being deposed.
So, at least in terms of final results, amd at least for England, slightly under half. If you mean failed to produce a son period, including sons who died young and never inherited, the proportion drops down to around 10%. Most monarchs are capable of producing at least one son. It's just that, between the pre-modern era's abundance of infant mortaility and battlefields where princes were expected to actively participate, many didn't survive to inherit.
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