Challenge rating is an attempt to boil down a complex and nuanced quality (the difficulty of facing a particular creature in combat) to a single numeric value.
A lot of old-school D&D DMs will often tell you to just ignore CR, finding it useless.
But I think that might be going too far. I do think it is useful to have CR as a quick reference - you don't want to make the mistake of sending an adult dragon against a group of 3rd level adventurers. It wouldn't really be fun for these bright and exciting new characters to just get instantly roasted, maybe even dying despite succeeding on their saving throws against the breath.
There are a few changes I would make to the guidance surrounding CR, and also to the way that it's implemented.
The first change I would make is to use the Xanathar's Guide to Everything guidance on encounter building in place of the DMG's. In the DMG, there's way more complicated math, combining the XP the monsters grant and then adding multipliers as you add more monsters to the encounter. As a new DM, I often struggled with this system, in part because it seemed extraordinarily punishing to add additional monsters to an encounter. So, in my early days, I'd typically have just one or two creatures for them to fight, and with a party of heavy damage-dealers (a Fighter, Rogue, Paladin, and Wizard) it was basically up to the initiative rolls to see if the monster even got to do anything.
The Xanathar system has a simple chart for "solo monsters" (which I still think is often a little undertuned) but, far better, it has a set of tables that show, essentially, how many monsters of a given challenge rating each party member affords you. So, for example, a 5th level character affords you one CR 2 monster, or it could give you two CR 1 monsters, or 12 CR 1/8 monsters. Or, it can go the other way. A single level 5 party member can account for half of one CR 3 monster.
So, using this to build encounters, I'll think of a type of monster I want - say, I want have the party fight a band of orcs. I've got five level 5 characters. So, one of those characters can account for 4 standard issue orcs. I've got four characters' worth of monsters left to add more interesting creatures. Say I want to give them a nice boss to be the toughest foe they face in this band, so I'll see that three characters will afford me a single CR 4 monster, and I'll get a big, scary Blade of Ilneval (a creature that also happens to have an ability that relies on having allies nearby). So, now, I have one character's worth of monsters left. So far, the orc band is the same number of creatures as the party. Orcs are generally scarier in big numbers, so I'm going to go for something where I can afford more. I could just do four more standard orcs, but then I might get bogged down running 9 monsters - a bit much for me. So I'll instead see that a 5th level character can give me 2 CR 1 monsters - these could be the Blade of Ilneval's lieutenants. Turns out there aren't any CR 1 orcs, and I don't want to homebrew one, but maybe there are some Warforged Soldiers - perhaps this raider leader doesn't actually trust other orcs to strategize with, and thinks that the Warforged with their constructed nature will be less ruled by ambitions and passions.
So, that gives us our foes for the party to fight: a Blade of Ilneval, two Warforged Soldiers, and four Orcs.
Pretty simple and quick. Indeed, for a very quick fight, you can just see what CR has a 1:1 ratio with the party's level and just pick a monster with that CR and throw one of them for each party member.
But there are nuances, because not all stat blocks are built to do the same thing.
Consider these two:
An Orog is an unusually intelligent orc (this very concept might feel a bit dated given recent efforts to untie things like intelligence to humanoid races). The Orog stat block is very simple - it's got two attacks, armed with a Greataxe and some javelins, and it has the standard Aggressive trait that orcs tend to get.
The Orog does have pretty high AC (18) but overall, it will not add a ton of complexity to a fight to have multiples of these guys. Essentially, you could have it be a significant threat to a low-level party, but it would also serve very well as a minion for a higher-level foe. If the party fights a single one of these at level 2 or 3, they'll probably do just fine. And if a party fights fifteen of them at level 12, they're also, probably, going to be fine.
By contrast, a black dragon wyrmling is also CR 2. Now, I had to adjust a fight in real-time when I tried to treat these as minions. My party was around level 7, and had expanded to five players (they added a second wizard). So, I had an encounter with 5 black shadow dragon wyrmlings (they were in the Shadowfell).
Thing is, dragons are not built to be minions. Dragons have a breath weapon.
In a typical dragon fight, the breath is a horrifyingly powerful opening move, but there's only a 33% chance that the dragon will be able to use it on each subsequent turn. The damage of the breath is thus adjusted to be way more powerful than what it's supposed to be able to do in an average turn. The black wyrmling only does about 9 damage on a hit with its bite, but its breath does 22 damage on a failed save against its breath, meaning that it's doing over twice as much damage on its first turn (and any time it recharges its breath.)
So when you have five of these things, the damage is... too much. It's 20d8, which comes to 99 average damage. Even an adult black dragon does 12d8 (54) damage with its breath. So, even if the party succeeds on all its saves, it's taking nearly as much damage as if they failed against an adult black dragon, which is CR 14, and thus would be considered balanced according to Xanathar's for 11th level characters in a 5-player party.
So, what is the ultimate upshot of all of this?
D&D does have mechanics for "legendary" monsters. This typically means legendary resistance (allowing them to turn failed saves into successes) as well as legendary actions (giving them more action economy and prevent a party from feeling they are safe outside of the monster's turn) and often lair actions (which fill a similar role to legendary actions.)
A legendary monster, in theory, should be able to pose a significant challenge to a party without any other monsters. Generally, I think DMs need to do a bit of tweaking to make the fight a little scarier (I often maximize the monster's HP to make them last longer) but it's a good general rule.
But I think that there's an intermediary step that would be good to specify: a different between Premiere monsters and Minion monsters.
One of the things that makes this tough is the very low levels. A zombie, for instance, is a monster that I think is intended (and usually works) for the party to fight starting at level 1. It does low damage and has a low hit bonus, and a minuscule AC. Really, the only thing that makes it a challenge is its relatively high HP pool (22, which is a whole lot more than, say, a Goblin's 7) and its Undead Fortitude trait.
Even at level 1, I've treated zombies as "minion" monsters, and it's worked out fine. But 1d6+1, despite being a pretty low amount of damage, can still potentially take down a level 1 character... if its crits. (Or if you have a Wizard or Sorcerer with a +1 to Con or less).
Still, the reason I think that a zombie really works best as a minion is that it's just not doing all that much interesting. It's never much of a threat on its own when outnumbered. But it works pretty well as a hazard and obstacle when fighting a more exciting foe. Indeed, in Descent into Avernus, when we were fighting a demon lord at level 12 or so, I used Danse Macabre to make a staggered wall of zombies that prevented the demon lord from getting to the ranged players, and that Undead Fortitude even allowed one of them to survive one of the demon lord's attacks, keeping him on one side of the battlefield while we pelted him with spells and arrows. (Sometimes the monstrous minions can be your friends!)
You can send absurdly large numbers of "minion" style monsters against a party and they won't become an unbalanced threat.
But I do think that there is a point where you encounter opposite issues.
Last night, I was running a session of my regular campaign, but only two players could make it, so I came up with a kind of side-story that provided hints to an ongoing narrative. The players were sent over 10,000 years into the past of Ravnica, back to when the plane was not entirely covered in city and before the guilds took on their codified form. The players are level 13, but with only two of them, I couldn't go super high CR when it came to the big bad they had to face.
They wound up fighting a Priest of Osybus, who I used to represent one of the heretics who would eventually corrupt the Orzhov Church into the cynical, exploitative thing that it is in modern Ravnica.
Priests of Osybus are a cool stat block - each time they die, you roll on a table and have them revive with a new ability, but only if they don't roll on the same ability twice. They're CR 6. They aren't legendary, but they have some nasty abilities - they can summon Shadows as a recharge ability, and their dagger automatically paralyzes those it hits.
But that dagger only has a +4 to hit. Against a level 13 Artificer and an level 13 Barbarian, I didn't land a single one of those dagger hits.
Now, ultimately, especially given how pressed for time we were, the fact that the fight went so smoothly, and that the priest only revived once (becoming a flameskull that kept its revival ability and made all its fire damage deal necrotic) worked out for our purposes. But it struck me that I think that this stat block is designed to be a premiere threat, likely with minions, but for a lower-level party (granted, I just happened to have two classes that can have pretty high AC, so maybe it would have been scarier if, say, the party's Bard had been there).
I think this is one of the major challenges of CR: that there's a multidimensional value to consider. Two monsters can have the same CR, but be intended for different level players.
There's also a whole thing to get into vis a vis how different classes are better at dealing with different types of foes - like how a wizard or sorcerer can destroy a swarm of skeletons with a single spell but struggle against a hulking monstrosity that resists its crowd control spells, while a fighter will carve that monster to pieces and easily deflect its attacks but take many turns to get through the dozen skeletons that are swarming it.
Still, I think CR is a good thing to have. But perhaps it could have a couple more dimensions.
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