So, hundreds of [INSERT MONSTER NAME HERE] pose a threat to a peaceful village? And your party is like, "Yep, let's go head-to-head and defend the people"... I hope you have tons of minis or The Lord of the Rings game lying around. Also, a Deus-Ex Machina is pre-planned if your balance calculations are way off.
There is a way to simplify things without breaking or changing the balance. Let's say 50 goblins are walking your way. Goblins have 7 HP on average. If your characters gain a few levels, they will be killing those boys in 1 or 2 hits 95% of the time. So, if the Goblin takes four damage - he isn't killed. But instead of writing in a notepad that he has 3 HP left, I mark him as injured - put some plastic circles from used water bottles onto him - the filthy way of Mat Mercer. Now, if the wounded Goblin takes another hit, he is done.
Sometimes a goblin could take three damage and then two more and die, while he should have had 2 HP left. But this is just too rare when players are of a sufficient level.
Cut in half
DM Guide contains Cleave optional rule, and I like to combine it with the variant rule above (The HP tracking). But players can only Cleave weak minions.
If you deal 14 damage with a spear and another goblin behind the one you killed, then you impale both of them. If you end someone with a short sword and another one next to the target, you can take a few more heads. A Warlock may want to find an excellent line of fools to blast while a rogue gets himself in the middle of the crowd before starting his dance of death.
You need to deal enemy's Max Hp worth of damage to the target to hit the next one. It makes it easy to calculate: Just divide Damage by Max HP to get the number of enemies you will hit. Round up if any of them were injured, and round down if none of them is.
Example: Lineup of Goblins (7 hp each).
14 damage will kill 2, and it doesn't matter if any of them are injured.
15 damage will kill 2 and injure 1 if none of them is injured. Will kill 3 if any of the first 3 are injured.
13 damage will kill 1 and injure 1 if none of them is injured. Kill 2 if any of the first 2 are injured.
A few limitations worth mentioning:
Damage can carry over only if the next creature has the same or lower CR rating, AC and conditions (Advantage/Disadvantage). This way, killing a goblin wouldn't allow you to damage their boss.
Damage can only spill in one direction from the defeated creature (clockwise, counter-clockwise or in a line from nearest, based on an attack-type) and can't skip enemies, but can skip empty cells. If someone has two weapons, they can negate this rule.
Combat is not Fencing.
A juicy fight needs your total concentration on the Epicness, so it is essential to know that all the rules represent probabilities rather than a direct conversion of Actions into mechanics. For Example:
"Barbarian is attacking with his Axe."
It doesn't necessarily mean that he is doing the same old Axe swing every time. Maybe Goblin is focused on the weapon while the barbarian bites off Goblin ear with his mouth before punching another Goblin's ribs with a shield.
Or, if I were to stretch the definition to its limits, In a bar fight: 4 unarmed damage doesn't need to translate into a punch to a face. Maybe the character points at the nearby table where the other player's Bard is romancing the opponent's mother. That is 4 points of Moral damage. Yes, it is still physical and not psychic damage in the interest of rules. Unless DM makes a ruling...
The damage of any weapon represents an average output someone would have with it. And while your character may be an expert swordsman - you don't have to be. Game rules imply that your fighter decides when to Lunge, Remise, Parry, Passata Sotto, or kick someone in the nuts while you roll an Attack action.
Also: A good warrior wouldn't miss when allowed to deal a fatal blow. So when Attack action fails, it could also mean that there was no opportunity to perform a hit, and the warrior didn't swing his sword at all. If he hits and deals two damage, he pushes the enemy with his shield to throw them off-balance.
Also, a fighter making four attacks during his Action can mean that he is doing one mighty hit with 4-times the damage he could 20 Levels earlier. True, fighter rolls for each one, but he is less likely to miss during his turn because he is powerful).
Suppose there is a system with unique rules for each of the abovementioned actions. In that case, that will imply that unless you are using that rule, you are not performing any interesting Actions and just doing traditional combat, but that would be very boring, Barbarian or Bard.
As a DM, I don't talk about this stuff directly, but now and then, try to show that if something makes more sense in the given situation and doesn't affect the numbers, it is happening.
Storytelling through combat
DMG has some easy to overlook suggestions, one of which is to sometimes allow players to succeed on a throw they missed by 1 or 2. The player rolled 11 when the AC was 12. This could be an opportunity to introduce some story building. Maybe the enemy wants to break through the ranks, you could offer a hit if the player moves 1 cell back (with the monster).
Epic encounter balance
Does cutting through break the balance, and should you account for it? It depends on how critical balancing and XP are to your game. If you level up by milestones then I'd say go for this rule. Also, how powerful the characters should feel in your story? Too much power and you may lose some of the tension. I can offer a few counters to swing the balance back into the Goblin's side.
If a character is surrounded, the attacker gets +2/+5 to hit instead of Advantage. That will be +2 if two enemies are on opposite sides and +5 if three are attacking one creature from relatively different sides. Advantage may seem better than +2, but if enemies have Pack Tactics or any other Advantage source, you'll get benefits stacked and players overwhelmed. Also, in our campaign, encounters often end with everyone surrounding the boss who has his abilities lowered by spells. While everyone realizes there is no reason to wait for the previous player to finish his turn before rolling your attack, DM is playing this:
Anything else you can do?
Yes, here is a list of ingredients to spice up your encounter:
High ground/Tight passages - players would welcome any opportunity to ration the flow of enemies to create choke points.
Legendary Actions - something I didn't appreciate at first, but
Civilians/Structures - if the environment demands things to be protected or destroyed, the opponents themselves are no longer the main point, which is a great thing. You can say that the flow of zombies isn't meant to be defeated but stopped or held back for long enough for the people to evacuate.
A Boss - Yeah, the only thing more intimidating than a swarm is a queen in charge of it.
Timer - Holding the line until the mage arrives with a backup or blasting forward to stop the doom mechanism instantly scales the epic-ness of a horde slashing exercise.
Decision - It is infinitely better when a fight starts with the player's choice to start it, instead of DM's "Surprise, we'll be throwing lots of dice today."