Understanding CR calculations of these monsters from the Monster Manual

Question

I've been working on a tool to help me design monsters, specifically doing CR calculations as described in the DMG. In order to test it, I've tried it out on some monsters in the Monster Manual, which of course are giving me different results.

I just want to say up front that I'm fully aware that the DMG method doesn't align with what's actually in the MM, and that a different calculation was used for it. And for my purposes that's ok, but it does make testing it rather difficult. I also understand that playtesting can influence the CR.

So what I want to check is: For these 3 test monsters, is my calculation correct, or have I overlooked something? And if it is correct, is there any widely accepted or documented reason for these monsters specifically to have different CRs?

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Wolf (MM CR: 1/4, calculated CR: 1/2)

HP: 11
AC: 13
Damage per round: 7
Attack bonus: 4 + 1 (for Pack Tactics) = 5

Defensive CR: 1/8
Offensive CR: 1
Average CR: 0.625 rounded = 1/2

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Wight (MM CR: 3, calculated CR: 2)

HP: 45 x 2 (for damage resistances) = 90
AC: 14
Damage per round: 2 x 6 (longsword) = 12
Attack bonus: 4

Defensive CR: 2
Offensive CR: 1
Average CR: 1.5 rounded = 2

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Planetar (MM CR: 16, calculated CR: 15)

HP: 200 x 1.25 (for damage resistances) = 250
AC: 19 + 2 (magic resistance) + 2 (3 saving throws) = 23
Damage per round: 2 x 43 (angelic greatsword) = 86
Attack bonus: 12

Defensive CR: 12 + 3 (adjust for AC) = 15
Offensive CR: 13 + 2 (adjust for attack) = 15
Average CR: 15

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The advice related to challenge ratings in this article can be used to explain the Planetar and Wight. Both of those monsters can drop a PC in one round, so refining and applying the approach referred to for Ogres (i.e. increase it's CR by one if it can drop a PC in one round) results is CRs of 3 and 16 respectively. Statistically there are a few things that don't make sense with that approach, but then again there is quite a lot about the CR system that is statistically questionable.

None of that explains the wolf though.

Answer 1

To "explain" the wolf, take a look at the Ranger class in the PHB

The Beast Master ranger (PHB, p. 93) gets to attract a CR 1/4 creature, not a CR 1/2 creature.

At 3rd level, you gain a beast companion that accompanies you on your adventures and is trained to fight alongside you. Choose a beast that is no larger than Medium and that has a challenge rating of 1/4 or lower (the hawk, mastiff, and panther are examples).

It is reasonable to estimate that a design desire for a Ranger to be able to have the wolf as a companion may have informed that decision.

Don't look for precision in the CR tool: it isn't that precise

As you mentioned, the CR rating method is soft around the edges, but that isn't a problem when you realize that a given party composition will experience a greater, or lesser, difficulty in dealing with a given monster or group of monsters.

There are 12 PC classes. There are dozens of subclasses.

There are 4 or 5 PCs in most parties, and the CR budgets in the DMG are complementary to a 4-person party.

To make the leap that a monster with a CR of 2 or 1 is an identical challenge to all parties, regardless of party composition and skill mix, is to overlook the wide variety of party make up that a given monster faces. I have watched this in play and seen different results based on the mix of class features, and spells, that the monsters face.

Party composition can swing encounter difficulty (rendering CR moot)

As an example, in a party with a 2nd-level Ranger (ranged attack, longbow) and a 2nd-level Warlock (eldritch blast and Repelling Blast invocation) the party can do a much better job of kiting an ogre - avoiding the ogre's lethal attack with some frequency - thanks to it being knocked back frequently.

Toss in any other spellcaster, or a character with Magic Initiate feat, who has ray of frost, and they can do an even better job of kiting that particular monster by both knocking it back and slowing it down.

Against 3 Orcs with the Aggressive feature (MM, p. 246) ...

Aggressive. As a bonus action, the orc can move up to its speed toward a hostile creature that it can see.

... that same party isn't kiting anyone.

CR formulation: it's a rough approximation, at best, and is workable. You are asking for more than it has to offer.

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In the interests of clarity, the term 'kiting' is explained here. Thank you, @Kirt.

Answer 2

The thing about CR is that is very difficult to take into account the major variables involved in encounters.

So if is stated that the CR's on MM are calculated considering "four member groups with optimized abilities" but there is so many ways that those calculations could be wrong. Environment, multiclass, player's abilities with the PC class or position in the party, monsters intelligence, battle strategy, dice rolls just to name a few.

I don't think such documentation you are looking for exists, at the very least not one that can be used in a very broad way...