More on 5E Mass Combat

Contrary to what I'd previously believed, the CR table is surprisingly linear. Between 1st and 20th level, 1 point of CR pretty much gains you 15 HP and 6 points of damage. Between 21st and 30th levels (inclusive), the rate of gain triples: 45 HP and 18 points of damage. CR 1 has about 5x the HP and 2x the offensive power of a typical CR "step" (but of course, most CR 1 creatures in the MM are not actually as tough as that table predicts). That means that all of the non-linearity after CR 1 comes from gains to-hit and AC, which kind of offsets the early stat HP/damage boost that comes before CR 1. Linear is good for mass combat because if you sum a linear measure, you can be pretty sure the result will come out close to your actual result.

I'm still running sims to find a BR measure that is plausible to me. So far, it seems roughly plausible to assign BR = CR for CR between 1 and 20.

Data points: purely by the numbers, a Marilith can take on 20 orcs, just barely, but loses pretty badly to 21. A Githyanki Knight can take on 6 orcs, about 70% of the time, but loses about 60% of the time to 7, and it's hopeless against 8. (In a real fight these differences would be less extreme because terrain and tactics come into play, but we're just talking pure numbers here, which is what mass combat is all about.) A pit fiend handily beats 30 orcs reliably (10/10) but loses reliably to 35 (9/10); the tipping point seems to be about 32. (Pit fiend winds 50% of the time against 32 orcs.)

So, I think you wouldn't go far wrong to start off saying that BR = CR (in conjunction with some set of rules that's better than the UA rules, e.g. http://bluishcertainty.blogspot.com/2017/02/mass-combat-rules-revision-to-unearthed.html), with CR 1/2 counting as BR 2/3 and CR 1/4 counting as BR 1/3, and anything over CR 20 counting as perhaps BR 20 + 3 * (amount over 20), so CR 30 is BR 50. Then the DM can adjust things on the fly as needed, e.g. he can say that an ancient red dragon (BR 32) against 300 orcs (BR 200) counts as BR 320 for offensive purposes because its breath weapon scales so well against massed targets--so the ancient red's commander just needs to find some kobold or goblin meat shields to soak up orc javelins while the ancient red annihilates the orcs, and he'll be able to win. Similarly, a DM might reasonably rule that Ogres are not BR 2, they are only BR 1, barely better than orcs. (He might also downgrade them to CR 1 as well, but that's a separate conversation.)

--
If I esteem mankind to be in error, shall I bear them down? No. I will lift them up, and in their own way too, if I cannot persuade them my way is better; and I will not seek to compel any man to believe as I do, only by the force of reasoning, for truth will cut its own way.

"Thou shalt love thy wife with all thy heart, and shalt cleave unto her and none else."

Mass Combat rules (revision to Unearthed Arcana system)

Here's my attempt at revising the rules from http://media.wizards.com/2017/dnd/downloads/2017_UAMassCombat_MCUA_v1.pdf:

(1) Every mass combat turn takes 10 minutes, not 1 minute. (This is an aesthetic choice to make battles feel right; choose a different timeframe if you prefer.)

(2) Use everybody declares/everybody acts resolution, like BattleTech or AD&D, instead of turn-by-turn resolution. This is important for resolving battles.

(3) There is no Attack action, only a Fight action. When a unit Fights another unit, both of them are fighting and either one can take damage. See below.

(4) Resolve movement before resolving Fights. You don't need to Disengage unless you were already adjacent to the enemy at the beginning of your turn (during action declaration).

(5) When a fight occurs, you total up the BR of all allies involved in the Fight on each side, and roll [B]3d6 * (BR/100[/B], not rounded). The enemy units in the fight must lose that many BR--the enemy commander(s)/players can allocate the losses wherever they chose. Whoever loses the most BR is the loser and must make a morale check or disband and be destroyed. There is a cumulative -1 penalty to the morale check for every 5% casualties the unit has taken. 

Example: If 200 BR of dwarves are Fighting 300 BR of Yetis while 150 BR of elven archers fires arrows at the Yetis, the dwarves and the elves roll 3d6 * 350 and the Yetis roll 3d6 * 300. If the elves and dwarves roll 11 and the Yetis roll a 12, then Yetis lose (11 * 3.5) = 38.5 BR, rounded down per usual 5E rules to 38. The elves and the dwarves lose 12 * 3 = 36 BR, which the dwarven commander allocates to the dwarves (because that makes sense, since the elves aren't in the melee and Yetis don't have spears). The DM is playing the Yeti commander and allocates all 38 BR to the Yetis. Since the Yetis took more BR damage, the elves and the dwarves win the field, and the Yetis must make a DC 10 morale check at -2 (they've taken 12% casualties) or be disbanded. The DM rules that the Yetis are normally Stalwart (+4), so the Yetis roll at +2 total. They roll a natural 14, for a total of 16, and remain intact. The Yetis and the dwarves will continue to fight next turn.

--

If I esteem mankind to be in error, shall I bear them down? No. I will lift them up, and in their own way too, if I cannot persuade them my way is better; and I will not seek to compel any man to believe as I do, only by the force of reasoning, for truth will cut its own way.

"Thou shalt love thy wife with all thy heart, and shalt cleave unto her and none else."