I can confirm the King's stats play a major part in the influence score.
Doesn't matter how much land you own, it's the stats that count.
Which sucks because in my current game I don't have time/cash to build way for heirs to get better...:(
And there's no way in hell I'm going to let crappy generals like my heirs command (at the moment) crucial battles between succes or failure in European history...:)
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