In the "Without the action economy" thread, @Deliverator
gave a method for simply spending HP & other resources
to resolve minor fights. @Eero_Tuovinen
responded with his thoughts on resolving large skirmishes
, predicated on D&D's core conceit that for each HD of each combatant, there's about a 50% chance of dealing 1HD's worth of damage per round:
At the start of the combat round talk about the fictional positioning however much you need to. Figure out which parts of the forces engage which other parts [...]. If you just want a result, then assume that all forces on both sides engage effectively, tactics be damned.
For each combat-participant who manages to engage this round roll a d6. The default hit probability is 50% [...] Similarly, if the forces are too large to roll all the dice, scale the dice proportionally [...]
Because 50% casualties per round is a tad too quick [...] do a "damage soak" stage next: for each hit of damage caused, roll the die again and discard the hit on a 1-3; this signifies a hit that was too minor to down a combatant. [...]
After deducting casualties you're ready for another round! Do some more maneuvering to shift forces around and represent the tactical consequences of the round you just resolved, then continue on to dicing the second round. Don't forget morale checks where applicable. [...]
This is great! The meat of the thing seems to be in the "establish fictional positioning" and "do some maneuvering to shift forces around" bits that Eero kinda breezes past.
I'm not a medieval warfare history buff, but I'm pretty sure the whole point of things like shield walls, pike squares, archers, skirmish lines, light horse, cavalry charges, and all that jazz is maximizing the number of your dudes who can engage effectively while minimizing the number of their dudes who can engage effectively, ie, fictional positioning, do some maneuvering.
To actually run
a big battle, you'll probably have to think about all that stuff a lot more deeply.
The crux of it is, though, that while formations remain... in formation, you'll have relatively small "surface areas" of combatants coming into contact with one another. When formations break, you'll get actual melees, where everyone gets to hack at everyone. A broken formation is probably quickly followed by broken morale and disorderly withdrawal from the field; if it's not, you get slaughter.
So a fight might look like this: a wedge of knights charges a shield-wall of infantry backed by pikeman, with a formation of longbowmen behind.
First we resolve a round where all of the bowmen apply themselves against the knights.
We check damage and morale. Is it enough to stagger the charge and turn back the knights, or break the formation so that they arrive at the shield wall as a ragged lone horsemen rather than a tight, driving wedge?
Then maybe we resolve a round where a small number of knights—the tip of the wedge—match up against a small number of shield-men and pike-men—the point in the shield wall that they are trying to breach.
We check damage and morale. Does the wall hold, or buckle and give?
Then we maybe resolve a round where knights take on shield- and pike-men one for one, ish, as they pierce the wall and charge through the line. Does the morale of the line hold, allowing it to re-group, or does the formation dissolve?
Then maybe we resolve a line where knights take on archers one-for-one in close combat, as they break through the other side of the enemy's main line of battle and reach the unit of longbowmen. Or maybe by this time the longbowmen have had the wherewithal to retreat, and the enemy's reserve horse have been rallied in time to engage the knights, or whatever.
That's a lot hidden in "talk about the fictional positioning" and "do some maneuvering"!