The way auto-calc seems to work is heavily based on the strength of the first unit in your stack. Generals very rarely die in battle, have excellent stats and armor, and add their attributes to battle stats. So a stack that might have taken large casualties in each battle, especially against other captain led stacks, is suddenly taking very small casualties in battle and is able to fight again and again without reinforcement.
Additionally during a crusade each region (Not province) has it's own set of mercenaries which a general can hire on. It's possible still, even without many generals, to abuse this system but having a lot of generals with huge movement rates under crusade effectively means that each of them can generate a decent stack of mercenaries at the drop of a hat.
In my case I Caesarea would still be under siege, and about 6 companies of mercenaries would not have fit in the stacks I had in the area, and a few more would have required some manipulation to get that might have left me unable to even lay siege. Adana almost certainly would've gone to the Sicilians, and it snowballs from there as I can reach Yerevan, Tblisi, Trebizond, and etc. much faster and hire mercs there as well.
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