You have four basic grades of troops, Professional, Semi-Professional, Militia, Levy. There is a fifth, but Elite forces are absurdly rare and expensive, and are basically the province of Spellknights and Capo's Chimaeras, so for practical concerns, just worry about the other four. The difference between them lies in their combat dice pool size, and their base morale; i.e., they fight better and withstand reversals more readily. Professional and Semi-Professional both roll 5 d20s in battle and pick the best three. Militia rolls 4 and picks the best three, and levies just start with three. As units lose combats or suffer casualties, they lose dice from their pool. By and large, against most opponents when you are reduced to two dice you are nearly combat ineffective, and anything below that is useless for combat and the disorganisation penalties to morale have almost certainly seen you rout by now. The dice pools can also be affected by some character bodyguard types, song types, elevation scenarios, etc.
- The number of Professional Troops is a matter of treaty between the Houses: 5 Regiments Max for the Great Houses, 3 for the Vassal Houses, 0 for the Minor Houses and any estates below them.
- The number of Semi-Professional Troops is a matter of how wealthy your populace is, since they are basically drawn from your landowning gentry to cover a lot of their own costs (hence their upkeep is half that of professional troops, but they fight on a similar level). The more well off your province (higher your Gentry Level) the more regiments can be sustained. There are a few other modifiers as well, such as certain House traits, what tier of House you are, etc. Also, Castle Districts (like Minor House Tsu's Mastiff) get +1 to their cap to reflect the Martial focus of the district.
- The number of Militia and Levy Troops is not hard-capped, but does have a soft-cap in that the closer you get to your militia and levy making up 30% of your district population (30% of 160,000 for Tellar, or a total of 96 regiments), the more I start imposing additional cost and quality penalties.
Because of how combat works, expect a higher tier troop to beat the lower tier on
most occasions, but in practical terms there are very few pure head-to-head fights without morale modifiers, characters, Songs, etc.
- Professional and Semi-Professional Troops are your standing forces, always available, you only have a few, but they're very solid, and they are the most likely to be able to travel a long way to respond to travel.
- Militia are forces that can respond quickly and competently to local crisis. Their upkeep is very cheap as long as they are not forced to be called up. Each regiment is entitled to a certain battle pay bonus, and keeping a Militia regiment raised for a six-month block requires 1,000g*, which is why there are references to the Lumen family getting drunk upon tallying up the expenses of your stand-off with the Sonissimmo.
- Levies are forces that don't really appear unless their home town is being attacked directly, or if you have summoned all your banners. Keeping one of their regiments raised requires 500g*.
As a rule of thumb, when it comes to responding to provocations from other Houses/Raiding:
Standing Forces to make a point.
Militia to show you're mad.
Levies if you're going to the Triarii on this.
Part of what makes Dale and Vincennes dangerous is not their own Household Troops, but the fact they can also call upon their own six Minor Houses, who are each running full complements of troops. It also makes them rather poor, mind you, and the Turn 0 standoff actually required Vincennes to financially bail out a number of their vassals.
* = Minus Military Upkeep Bonus, the current value of which Tellar can't compute, because Tellar cannot into economics.