The 5e DMG has a short section on “handling mobs:” it has a chart for approximating, out of a group of attacking monsters, how many monsters hit.

• Corruption Point 5e
• Dnd 5e Dmg
• Dnd Corruption Rules

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It’s pretty simple: subtract attacker’s hit bonus from the target’s AC. Cross-index that number on the chart. If the number is 1-5, all the attackers hit; if it’s 6-12, 1/2 of them hit; etc., up to 1 in 20 of the attackers hitting on a 20.

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I ran a big set-piece battle yesterday: 8 mid-level PCs and 10 gnomes against 20+ drow and other assorted creatures, including a drow spider chariot and a sinister angel. With a wizard and a sorcerer PC and two drow wizards, all slinging fireballs, the mob attacks weren’t much of a factor. With all those fireballs, what I COULD have used was rules for mob saving throws.

If I’d thought about it, I’d have realized that the same chart can be used for saving throws. Instead of subtracting attack bonus from AC, subtract saving throw bonus from DC, and use the chart as normal. For instance, a fireball save DC of 15, minus the drow dex save (+2) is 13, which, according to the chart, means that 1/3 of the drow succeed on their saving throw (and probably survive with 1 or 2 HP left).

In fact, this same chart can be used for ability/skill checks (how many orcs managed to climb the wall? DC minus skill bonus) or any other d20 roll.

To me, it seems this is all you need to run fairly simple battles with dozens or hundreds of creatures per side. The amount of HP tracking is not excessive: for instance, in this unit of 50 ogres, 24 have 15 damage and the other 25 have 30 damage. (For ease of bookkeeping, assume that melee attacks always target the most-damaged creature.)

You might also care about the base size of big units. I assumed that a close-packed formation of 10 Medium troops took up the size of one Large creature. I’d say that 25 troops are Huge and 50 are Gargantuan.

If we do any bigger-scale battles, I might find other rules that I need (after all, the Chain Mail rules are much longer than this blog post) but right now, this is looking pretty good for running big D&D skirmishes.

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In response to your request from another thread. I'll edit in from the other books once I get around to it, right now it's just the PHB and DMG. The DMG is practically all a discussion of different ways a campaign can be constructed or the game can be run, so there's a substantial number of optional rules and variant rules in there.
Variant/Optional Rule Name (Book Page Number)
PHB:
Customizing Ability Scores (PHB 13)
Human Traits (PHB 31)
Criminal: Spy (PHB 130)
Entertainer: Gladiator (PHB 131)
Guild Artisan: Guild Merchant (PHB 133)
Noble: Knight (PHB 136)
Retainers (PHB 136)
Sailor: Pirate (PHB 139)
Feature: Bad Reputation (PHB 139)
Equipment Sizes (PHB 144)
Multiclassing and Feats (PHB Chapter 6, pg 163-170)
Skills with Different Abilities (PHB 175)
Encumberance (176)
Playing on a Grid (PHB 192)
Warhorse Armor (PHB 310)
DMG:
Feywild Magic (DMG 50)
Shadowfell Despair (DMG 52)
Psychic Dissonance (DMG 59)
Blessed Beneficence (DMG 59)
Pervasive Goodwill (DMG 59)
Overwhelming Joy (DMG 60)
Hunter's Paradise (DMG 60)
Beast Transformation (DMG 60)
Intense Yearning (DMG 61)
Immortal Wrath (DMG 61)
Power of the Mind (DMG 61)
Mad Winds (DMG 62)
Abyssal Corruption (DMG 62)
Prison Plane (DMG 63)
Vile Transformation (DMG 63)
Cruel Hindrance (DMG 63)
Pervasive Evil (DMG 64)
Bloodlust (DMG 66)
Law of Averages (DMG 66)
Imposing Order (DMG 66)
Planar Vitality (DMG 67)
Loyalty (DMG 93)
Training to Gain Levels (DMG 131)
More Difficult Identification (DMG 136)
Mixing Potions (DMG 140)
Scroll Mishaps (DMG 140)
Wands that Don't Recharge (DMG 141)
Flanking (DMG 251)
Diagonals (DMG 252)
Facing (DMG 252)
Proficiency Dice (DMG 263)
Ability Check Proficiency (DMG 263)
Background Proficiency (DMG 264)
Personality Trait Proficiency (DMG 264)
Hero Points (DMG 264)
New Ability Scores: Honor and Sanity (DMG 264)
Fear and Horror (DMG 266)
Healer's Kit Dependency (DMG 266)
Healing Surges (DMG 266)
Slow Natural Healing (DMG 267)

Corruption Point 5e

Epic Heroism (DMG 267)
Gritty Realism (DMG 267)
Firearms (DMG 267)
Explosives (DMG 267)
Alien Technology (DMG 268)
Plot Points (DMG 269)
Initiative Score (DMG 270)
Side Initiative (DMG 270)
Speed Factor (DMG 270-271)
Action Options (DMG 271-272)
Hitting Cover (DMG 272)
Cleaving Through Creatures (DMG 272)
Injuries (DMG 272)
Massive Damage (DMG 273)
Morale (DMG 273)

Dnd 5e Dmg

Spell Points (DMG 288)
SCAG:
Human Languages (SCAG, 112)

Dnd Corruption Rules

Svirfneblin Magic (SCAG, 115)
Half-Elf Variants (SCAG, 116)
Tiefling Variants (SCAG, 118)
City Watch: Investigator (SCAG 145)