I don't think it's auto-calc. In another thread I did an experiment where I swapped the troops so that Sturgia had Khuzait troops, and Khuzaits had Sturgian troops. It made no difference in the long run. It might make a difference at the start, Sturgia seems to lose the opening battles with Vlandia more often than not.
I'm pretty convinced the main problem is geographical, it's only a matter of time before Sturgia is busy at the other end of the map when this happens:
They are too far away and cannot react in time. Then while they are busy losing their armies trying to retake Tyal, Battania or Vlandia takes Varcheg, and it's all downhill from there. Tyal is just a juicy fruit waiting to be plucked.
I have seen Sturgia do reasonably well up to the mid game, but it wasn't because they were able to defend their lands with their armies. It was because the Khuzaits decided to mostly leave them alone.
I don't think buffing Sturgians will make much difference honestly, it doesn't matter how strong the army is, if it is 15 days travel away then it can't even contest the fight.
Aserai have the exact same problem and get seem to lose Quyaz and Husn Falq in every game, and I've seen them wiped out after only three years. Sometimes they make some gains into the Southern or Western Empires but they never seem to hold them for long. Same goes for Sturgia, they seem to take Amprela quite often but it's only a matter of time before they lose it, usually to the Khuzaits.
But the faction that gets crushed most consistently in my experience is Northern Empire. Their empire isn't spread out, but they are surrounded on all sides and often end up at war with three factions at once. It's just too much and they get picked apart in pretty much every game.