I know it sounds counter-intuitive but I think the limited gene pool during the War of the Roses produced some extremely bright people. Richard, himself, was a Latin scholar, bookish, highly knowledgable about music, an able administrator and a military powerhouse. His brother, King Edward IV was no dope either. Henry VI might have been a little slow, though...
I think that makes sense, actually. Look at the Lees ... some of the most brilliant people of their time, even the ones who were moonbat crazy.