- Are polymaths technically savants over a variety of subjects or are they just jacks of all trades?
It depends which polymath you refer to and how you are framing ingenuity and intelligence in the first place.
Some people measure by output only, so they'd always dismiss the genius that didn't achieve much or perform very well. Others only value words, others science skills etc.
I don't think a Savant is what that guy in the other thread said drove his own savantism of sorts; OCD. I think that a Savant is simply very naturally good at someone in some way and what they decide to dedicate their life or approach within that realm to is that specific way of doing it.
It is difficult to realise that savants are talented and refine it because it looks to many like they just obsessed over something enough to get that good at it, this is a fallacy. When you analyse savantism within games, suddenly it becomes far clearer.
In League of Legends, you have basically got 3 types of highly skilled players and one is the savant. Yet all of them may be good at LoL to a point where they seem to only be a LoL savant.
There are people who are so insanely skilled at 1 or 2 characters (called Champions) or alternatively play quite a few champions but only really understand 1 role. They are so extremely good at that 1 role with the small champion pool that they make it work. These people tended to be naturally gifted at the playstyle required for their niche and then refined it.
Then you have the hybrids, the people who are good (maybe mindblowingly maybe not, usually just good) at a small champion pool but who easily are above average at most. They are also balanced between mechanics and macro, they have this innate 'voice' in their head that surpasses raw instinct, great map awareness etc they even outrank the third type often on the leaderboards and career output, they are natural talent meeting practise.
The third type are people who in some ways are terrible at LoL. They often think too much and have slower reaction times, they compensate a lot with studying the game, theory-crafting, using builds that will blow your mind yet unlike savants not only doing that for 1 character/champion. Rather than know and do so much with a few characters for 1-2 positions, they know so much about every single character and item in the game. Their brains are databases, they study the game like their life depends on it. These people can often make better coaches than players in the long run as often because they are such deep and long thinkers that they keep failing to perform at apex levels when the crunch times comes to 'pull off' their mechanical skill in a situation. They will do very well but not extremely brilliant, they lack the talent but have the brain.
Each of these is extremely phenomenal in their own way and flawed in their own way. While the hybrid instinctive type tends to perform best, as soon as they retire or need to help others get good, they realise where the issue is. They are the type that aced all their exams at school but couldn't teach anyone much at all and refused to help their buddies with revision.