Right; it doesn't go into the sub-6m hex scale. But, it's not so much the frequency, though, as the amplitude? I'm not necessarily starting a debate; I was taking the system apart as I'm about to "enable" it for my party, and this seemed interesting enough to comment.
With Axioms 3, take a Woods domain at 1, 8, and 16 hexes in size; the periodic frequency expecation is every 55, 6, and 3 time periods, be that months, weeks, or days. While one could take the expected BR of a Woods hex encounter (~2.1) and average the expectation of an encounter over a 30 day month, they're each discrete encounter events, and the garrison needs to match that full BR for each one.
The civiilized domain has it a lot easier, in they only expect an encounter every 55/6/3 months; and the effect on the standing garrison is a lot less, whereas the wilderness garrison is getting hit once every 55/6/3 days. The wilderness garrison would either have some cost overhead based on attrition from violent encounters, or, more likely, consume much more of the character's (and henchmen's) time helping out the garrison, which does make a good deal of sense.
Taking tire_ak's Imperial troops; they average $26 per troop, have an averaged individual BR of 0.0341, and an averaged "Troop Size" of 1.2 (so a platoon is 25 averaged troops in size, where troop size 1 == man-sized) - that gives us a full platoon BR of (0.0341*25*4)==3.41.
Assuming I didn't mess that or this next thing up, then, for a starting domain of average starting population, at $26 per individual averaged troop:
||Avg. Starting Fam
The wilderness and borderland garrisons would need some help. That being said, if we're assuming this was a 9th level character that's just established this domain, that character's effective BR for platoon-scale engagements is probably in the double digits at least, which more than makes up for the size of the garrison. It may indicate the starting domain gets a lot of hand-holding from the character or his/her henchmen during domain encounters. It also kinda supports the old OD&D trope of having the lord of the castle come out and meet a passing party.
All this still ignores domain encounter reaction rolls as well as the lingering/migrating chances, etc; and I haven't yet integrated what NPC party encounters look like on the average, nor the limitations of mindless or animal encounters. Kinda one of those things I dig into when I think about doing ACKS as a computerized world simulation; or I guess just averaging the whole game to "roll 1d6, on 5+ you win".