D&D 5E (2014) Tidbit for monster design

[Steady Vane]

The Grimlock is not a bag of hp - it's an ambush predator from the underdark, with stealth trait and capabilities. Assuming it gets Surprise, just multiply it's damage by 4/3 and see if it works then imo. Same for the Twig Blight, ambush trait means surprise round of damage. Needle Blight seems fine though, the hp and AC are a little low, but it has a ranged attack that does normal accuracy and slightly more damage than average.

 

[Charlaquin]

Oh, no, no, no! That's not what's going on at all (clever guess from my scanty info though!)

You probably already know this, but I'll briefly explain for anyone following. There are only 4 values that go into the equation that produces CR: HP, DPR, AC, and AB. That's it. There most definitely are many other factors that effect CR, but the way they do it is by altering those 4 values into the effective values that actually end up being plugged into the equation.

The DMG describes what, for purposes of the not terribly accurate DMG version of the monster building rules, those other values are that alter the basic 4 and what alterations they make. The official CR calculator spreadsheet's data entry page seems to show that at least some of those alterations are similar to the real monster math, but not all of them are.

Exactly how all of those alterations to the basic 4 values are done is unknown. In order to figure that out out, we need to first discover the correct equation, and then test--as far as is possible--each alteration independently.

Those 61 basic monsters are all of the monsters that I can be sure have no features that would affect their HP, DPR, AC, or AB. They just have the raw stats and nothing that might modify them. No saving throw bonuses. No damage resistances or immunities. No features that cause you to make a saving throw, or impose a condition. Etc. They are your "boring bags of hit points". Many of them are beasts. None of them have a CR above 7. Honestly, if there were as many monsters like that as people think there are this would be a lot easier to do! (It's actually likely that there are other monsters whose additional features have no effect on CR, but from the input form and info we do have, and lacking the full instructions of how to use that form, I can't be sure.)

So what's the importance of the basic monsters? Limiting initial trials of proposed equations to them is the only way to make sure the equation works right. The correct equation should work on 100% of basic monsters. Then I can move on to trying to discover how all the other variables actually adjust the 4 basic values, in order to fully reverse engineer the math.

However, I'm stuck at 95% of those monsters, and can't find any way to do better.

The 2 monsters that won't work with anything I can even think of are the twig blight and the needle blight. They both always come out weaker than the CR the MM gives them, regardless of what variant of what equation I use. Since they were in the original Starter Set that predated the MM by like half a year it's possible that they hadn't refined all the math (and, AFAIK, they never change the listed CR of a monster after publication), or even that they just decided to cheat, because they preferred that the CRs of the three blights ended up as the published 1/8, 1/4, and 1/2, rather than the 0, 1/8, and 1/2 they probably actually are by the official math. If it's the latter, it's quite possible they did that before they decided to stop doing that and be strict about using the results the equation gives them--which I think they have been doing since the MM

Oh! In that case, I have another guess what the problem might be. Blights have False Appearance. The most likely reason they aren’t lining up with your equation is that WotC assumed they would get a surprise round, so that’s messing up the functional damage output portion of the equation. Try adding an additional round worth of damage to their damage output, without adjusting their functional HP and see if that fits.

The other anomaly depends on which equation I use. I've developed several which end up with only 3 failures, but can't get it down to just those blights. The one I posted also fails on the grimlock--which is the most common one to take that honor. I have no explanation whatsoever for it. It just doesn't come up with enough XP to push it into the listed CR 1/4. Now, there are some equations that will get it there, but they are at least a little more complicated, and instead fail on different monsters. The one I'm most comfortable failing on is the myconid sprout, because there is an easy mistake that could have been made when entering its data that could cause it. But again, it just seems like the equation(s) that give us the grimlock as an inexplicable failure are more likely to be accurate.

Yeah, that checks out with my guess that they’re assuming a surprise round, because grimlocks, while they don’t have false appearance, do have stealth proficiency and advantage on stealth checks in rocky terrain. You’re treating these as “basic monsters” but WotC is treating their stealth features as a potential source of DPR. Though, in the Grimlock’s case I’m more inclined to assume that they’re factoring stealth into the attack bonus and ac rather than assuming a surprise round.

So that's what those 61 basic monsters are and why they are absolutely critical to everything--they are the ones that all have to work.

What are those monsters? I would not be surprised if the anomalies are likewise due to them not being as “basic” as you’re assuming.

 

[Ondath]

I couldn't tell you the relation between xp values and anything else, but I can tell you those assumptions are wrong.

PC accuracy is assumed to rise, it only starts at 65% at level 0 with a +0 weapon. Accuracy rises with every +X weapon, to 85% assumed PC accuracy, at least in the math. It is why both DMGs say explicitly you should use +4 weapons and armor.
DMG 2014 p284 and DMG 2024 p58 if you want to check

Monsters also grow more accurate, they go from hitting on ~13s (40% accuracy) to hitting on ~9s (60% accuracy). Your 50% works as an average of this. Both sides have the same increase of 20% accuracy as you level. If you are assuming XP relations based on accuracy, you need to start there.

When I ran the math, the levels where accuracy rises for PCs are assumed to be 2, and every 5 levels after. So 2, 7, 12, 17 for +1, +2, +3, and +4 weapons. That worked the best for PCs, but I couldn't say for monsters.

Hope this helps!

Does accuracy really rise? When I look at some reconstructions of existing monster math (like Blog of Holding's Monster Manual on a card), it seems like monsters' AC increase is in almost perfect lockstep with PC's ability score and proficiency bonus increases.

I don't have the exact calculations I ran before in front of me, but what I remember was that the to-hit probability for PCs was almost always 65%, only going up to 70% in some cases and then going back down the next level. This also seems in-line with the 2014 design team's explanation that they did not factor in magic items to encounter balance, so they're supposed to be pure bonuses that you can do without.

What I'm more interested in is reverse-engineering an "expected average PC health/DPR" chart based on these numbers, and I think we could do that if we knew a bit more about the designers' core assumptions about how an adventuring day was going to go. @Sword of Spirit says that monsters have baseline hit probability of 50%, and that makes sense to me (because people perceive equivalent losses worse than equivalent gains, monsters should probably hit less often than players do in order for a fight to "feel fair"). We could then multiply a monster's DPR and the number of rounds it's expected to survive with the monster's to-hit probability to calculate the amount of damage, then do this for a whole adventuring day's worth of encounters, and theoretically we'd get the amount of damage the PCs are expected to suffer from during an average adventuring day. And that might give us what the end of a full day of average encounters is supposed to feel like. Should all of the PCs be 1 HP away from death? Do they need to take a total amount of damage that would require them to spend half of their Hit Dice during Short Rests inbetween? All of their Hit Dice? If we know the amount of total HP monsters have throughout an adventuring day as well as the amount of damage an ideal-type "limited-use feature" for a PC is supposed to deal, can we calculate how many of their limited-use features are they expected to expend?

I'm honestly not fully equipped to do all of these calculations by myself, and the TTRPG people around me aren't so mathematically-minded either, so I feel like I'm ruminating by myself when I think about this stuff. So apologies if my post feels too convoluted or too much, I'm just really excited that other people are running the math in similar ways to the 5E chassis!

 

[Steady Vane]

Does accuracy really rise?

Yes. If accuracy is 65%, then with a +1 sword accuracy rises to 70%. Magic weapons are assumed in 5e, just not hard level-locked as they were in 4e.

What I'm more interested in is reverse-engineering an "expected average PC health/DPR" chart based on these numbers...

I'm honestly not fully equipped to do all of these calculations by myself, and the TTRPG people around me aren't so mathematically-minded either, so I feel like I'm ruminating by myself when I think about this stuff. So apologies if my post feels too convoluted or too much, I'm just really excited that other people are running the math in similar ways to the 5E chassis!

I have those numbers, at least on the PC side. That said, there are some hard assumptions in the numbers that 5e only somewhat supports RAW. After all, saying +4 items are assumed is nice, but WOTC never printed any, did they? It's hard for the numbers to ever match when the expected state of play is simply never supported. Maybe if more people made their own magic items with the extensive tables in the DMG and followed its instructions I suppose!

Average PC health is a d8 hit die with +2 Constitution. Simply because while there are d10 classes and d6 classes, on average the hit size of a party will be d8 in size.

Average PC damage is modeled quite closely by spell damage for AoE spells. Or more specifically, in 5e, Aoe save-for-half spell damage is modeled on the average damage a weapon character deals in a round against a monster of the same CR as the character's level.

This is important: every class in the game does the same damage on average, and that damage matches spell damage.

Part of the reason I am so adamant about magic weapons, and their accuracy increases, being assumed, is the math doesn't work unless they are there.


To prove this, simply try four different regular 5e (2014) classes at level 5 with +1 weapons:
a fighter with a polearm and the polearm master feat (or any weapon feat and its associated fighting style, they all work)
a dual-wielding rogue who gets advantage and sneak attack, but has no weapon feat until level 10
a ranger using a longbow and hunter's mark, no weapon feat
a monk with a staff, who flurry of blows once per three rounds of combat and has the damage averaged

Really, go try it.

DnD 5e DPR Calculator

Damage Per Round or "DPR" is a helpful way to approximate your character's damage output, allowing you to more easily weigh build choices.

rpgbot.net

No way they all deal the same damage, right? Turns out they do! At level 5, they all do an average of 21 damage per turn. At level 11 with a +2 weapon, they all deal 38.5 damage. (Ranger and Monk match at 5, but don't at 11 without a 3rd attack. WOTC screwed up the attack progression on them)
Spells you get at 5th level deal 21 damage, and spells at 11th level 38.5 damage. Barring the "outlier" spells such as Fireball.

The expected damage, after accounting for accuracy, weapon feats, and +1 to +4 magic weapons at levels 2, 7, 12, and 17, matches spell damage pretty much exactly. (Spell damage gets squirrely above spell level ~6, because there are simply fewer AoE for half spells at all printed at those levels)

Character level REAL DPS based on fighting against average equivalent CR monster. +X items at 2, 7, 12, 17

lvl 1- 7 (10)
lvl 3- 14 (+1)
lvl 5- 21
lvl 7- 24.5 (+2)
lvl 9- 28
lvl 11- 38.5
lvl 13- 45.5 (+3)
lvl 15- 52.5 (2nd Feat)
lvl 17- 59.5 (+4)
lvl 19- 66.5

Spell AoE/half damage by character level, from the DMG
lvl 1- 7 (10)
lvl 3- 14
lvl 5- 21
lvl 7- 24.5
lvl 9- 28
lvl 11- 38.5
lvl 13- 45.5 (42) --> spell damage chart in DMG starts being wrong this level, parentheses is DMG value, Actual value is 4.285 TTK as the other levels are. DMG value is with only one Feat and only +2 magic weapons.
lvl 15- 52.5 (45.5)
lvl 17- 59.5 (49)
lvl 19- 66.5 (-)
lvl 20- 70


Side note, the spell damage charts in both DMGs are mostly correct but also lie for no reason. 1st level spell damage is average 10, not 7. PCs with weapons do about 7, unless they have a Bonus Action attack, in which case at level 1 they do about 10 average damage per round. Also, the 2024 DMG lies about level 2 spell damage, claiming it is lowered when not a single spell actually got its damage nerfed. I just assume it's policy at this point.

The average time to kill (TTK) of a PC against an on-level CR monster in 5e is ~4.285 to 4.6 turns

 

[Steady Vane]

That said, these assumptions have some problems:

Firstly, many classes do not scale attacks per turn past 2, which trashcans their DPR at higher levels. 5e was not designed for high level play for many classes. Ranger and Monk should have attacks scale as Fighter. Barbarian should get a third attack at 11, but their level 20 feature makes up for a fourth attack. Paladins do not need a third attack at 11, but do need a third attack at level 17/20. I don't consider a Warlock a weapon user, but the pact of the blade probably needs some scaling as well.

Feats are technically optional rules, but are hard assumed in this math.

Magic item guidance by level is sparse at best. Magic items are not an optional rule, but the advice is pretty much "do whatever you want". In 2024, they printed a magic item by level chart for the party that does not scale with party size.

Spell outliers like Fireball and Meteor Swarm make this relationship in actual play tepid at best. 70 damage at 20? Meteor Swarm deals 140.

Why should a monster last 4+ turns against a PC? if you halve monster hp, they last just over 2 turns, meaning you can simply slot one monster per PC and have a working combat. Much simpler. 4e doubled monster hp, did 5e do that too?

 

[Sword of Spirit]

Great info. I would really like to get into a thorough discussion of all of this stuff, but I don't currently have the time. I want to drop a few bits of info at least though.

WotC may have used different assumptions which appear contradictory to accomplish different things. Example: The CR calculations assume no magic items and a 65% chance to hit a monster. The monsters in the MM better fit a 65% chance to hit with magic items. They have less HP to balance that.

The idea that grimlocks and blights have their base stats altered to account for their surprise capabilities has merit. To make it work, there has to be a way to include the alterations in one of the fields of the CR calculator input form I've attached. They use this form to enter data, and it spits out the correct CR at the bottom.