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!