For what it's worth, I ranked quite a lot of historical figures to create dozens of scoring scales for a highly specialized mod of Civilization 4. It's not exactly the same problem — it was only leaders, and they were only compared against people of their own country/civilization, and the ranking was going from "great" to "bad or ridiculous" rather than considering importance per se — but maybe a sandboxed version of the problem can help us.
I wrote about it here: etiennefd.substack.com/p/things-i-learn…
In practice, the heuristic I relied on the most was looking at whether the introductory paragraph on the Wikipedia page of any given figure said things like "widely considered to be one of the greatest king [COUNTRY] ever had", and the like. After doing a lot of those, though, patterns emerge. Greatest leaders are often the ones who conquer stuff, win wars, or preside over some particularly prosperous period. Patronizing the arts and sciences help. Some get extra credit for humanitarian reasons, like Gandhi or Lincoln. Often it helps to have had a long reign.
Bad leaders are most often the ones whose reign leads to the end of their country, or are otherwise removed from power against their will (Louis XVI, Nicholas II, etc.); or whose bad policies lead to a clear weakening of their country; or who lose wars; or, in some cases, were known for their cruelty and other negative personal qualities. Of course, some of those can be "important" despite being bad.
In the middle of the lists were important leaders who were neither clearly great nor bad. Almost all the leaders I put in my lists (I selected 16 per civilization) are "important"; otherwise I would just not select them. If I try to grasp what made me decide whether to include a leader on the list, I think it's a mix of: 1) Have I heard of the person? 2) Are most people likely to have heard of them? 3) Is the Wikipedia article long? 4) Does the Wikipedia article say they were influential, left a legacy, etc.?
It's all awfully intuitive, but I think the process supports the event-centered hypothesis in the post. People who were involved in a lot of important events will have a longer Wikipedia article (and maybe subarticles). They're more likely to be heard of, because of their connection to events.
But there's something to be said about the intention-centered hypothesis, too, or something close to it. Maybe "innovation." What matters isn't whether the person intended to do something that turned out to be influential, but whether they were the first to do it. Napoleon's mom didn't do anything special: she just gave birth. Napoleon's doctor treated Napoleon the same as any doctor would at the time. (If he didn't, and he was particularly innovative in his methods, then we'd rightly consider him important.) Napoleon's soldiers were just doing their soldier job. Napoleon was the first to become Emperor of the French, to try to blend together revolutionary democratic ideals and autocratic monarchy, to reform the laws into a Civil Code, to conquer a version of Europe that was markedly different from previous versions of Europe, and so on.
That last point seems important: there were pan-European conquerors before, but Europe is a complex thing that changes a lot over the years, so there are continuously new opportunities to be "the first" to do something with Europe. So important people will probably often be connected to complex systems, like politics (just being in power usually makes you important, because you'll have to deal with a lot of new situations, especially if you're in power for a long time), or difficult to understand natural phenomena like the human body or evolution or physics. Also art movements and religions. And the economy. In short: fields where you can do the difficult task of creating or discovering something new.
In many cases, an innovation would likely have been made a bit later if the innovator weren't there, e.g. Darwin, or, you know, Jeff Bezos. Someone else would have created something like Amazon within a few years, right? That doesn't matter: innovation is hard enough that making it happen just a bit earlier is worth the praise.
Being innovative turns out to be a great way to be at the center of events, since you create new events. It also usually is connected to intentionality, but not necessarily for every possible consequence of your innovation. Jesus was recognized as (intentionally) innovative in his preaching, even if he wasn't intentionally innovative in the sense of founding the largest religion ever. We can recognize the impact of an innovation in hindsight. Of course the process is imperfect: we can be mistaken in crediting innovation, and accidentally raise the importance of a figure over another. (I'm guessing that some religious innovations that are credited to Jesus actually came from various later people. And Wallace should perhaps get as much credit as Darwin, but clearly didn't.)
