I learned something new, thanks!
After reading though since the armaments are on melee range (and their deployment reflects that), won’t the Lanchester’s Linear Law apply instead? In that case then, the logic would be a simple attrition. As an extreme hypothetical case, all they need to deploy is 5001 troops to win (=annihilate) based on the Linear Law. Of course this ignores the fact that routing usually means losing 20-30% of the total number. Hence won’t this point towards the lack of necessity to vacate the fort as realistically 6-7k would be more than sufficient?
In addition, if Ars’ other 5k suddenly appears(from their POV) their 10k is now pincered, or their fort sieged with no troops. By leaving 2-3k back at the fort they can prevent this case and be able to provide an escape back to the fort in an emergency.
I would also argue that them knowing that the opposition has a spellcaster that can cast AoE akin to a mortar, they should minimize the infantry on an open plain to reduce their excess density and leave them to guard the fort. On this point, the following chapter does show that the main action is done by the cavalry.
That said, I do notice that in the previous chapters, in their world sieges are focused on maintaining a barrier against the opposition’s spell barrage and not people climbing up the walls. If that’s their logic.... I guess that could explain why they willingly vacate the fortress to fight. Still kind of silly especially for people judged to be competent and intelligent not thinking the different possibilities......
These are all perhaps too serious for a series like this...