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

[Sword of Spirit]

I came up with that factor by noting the game's math seemed to be centered around one monster against a party of four PCs, but it's possible the actual calculation uses something else that just happens to be close to 0.25. For example, if the actual calculation uses 0.65/2.5 = 0.26 then a base AC of 12 and a base AB of +4 fits the published XP values quite well. Why these numbers? Well, 0.65 is the base chance to hit, so our effective DPR would now include that factor. And 2.5 is the average number of rounds a monster tends to live for against a baseline party of four level appropriate PCs, so our effective HP is treated more like an effective HP per round.

I had a thought and wanted to share immediately in case anyone wants to make use of it before I get to it.

What if it's just x1/3, since combat is expected to last 3 rounds?

That might sound overly simple, but we know they oversimplify from the input form (they don't include initiative bonus at all, for example).

EDIT: That's not actually looking very promising.
@tomedunn do you have any other possibilities than 14/13 that might work for an exponential version? Playing around with some other things and realizing having more flexibility there might be useful.

 

[Steady Vane]

A couple other thoughts have just occurred to me after messing with the formulas as I was writing this. One is that stegosaurus stands out as a problem. The only formulas that can deal with it are your exponential one (which has a steeper slope, and is too high on the cyclops), and your linear one with a -1 rather than -2 (which somehow magically works for everything, even though, if I understand correctly, it relies on two approximations in its derivation). It fails on everything else. I'm starting to believe that maybe a mistake was made in the data entry for the stegosaurus when they were making Volo's Guide. In this kind of analysis, I'm loathe to dismiss something as an anomaly, as it could just as easily be evidence that the formulas are all wrong. But I'm at least considering the possibility. If the developer had entered a 36 instead of a 26, or a 9 instead of a 7, or a 15 instead of a 13 or a 96 instead of a 76, it would give us the listed CR 4. Going forward, I may flag the stegosaurus as a potential error in the published math and test out formulas that work on everything except the stegosaurus to see how they hold up with more complicated monsters.

One of the funny things about 5e is that it has come out how certain "iconic" spells do too much damage on purpose. They had a spell formula, and purposely ignored it for certain spells to make them more "fun" - fun meaning overpowered for their level.

If I recall correctly, this also applies to most Dragons in the CR calculations. They are flat out stronger than they should be for their CR level. Now this has not been stated, but presumably that choice would follow the same logic. They are iconic and should be more powerful to be "fun".

When it comes to spells, Fireball is the most notorious, but I think I recall people who did spell cleanups for 5e stating that there were one or two per spell level that were chosen as well, if simply not as well known.

All that to say, could the Stegosaurus be another such monster case, where it's simply more powerful than it should be, because it's an "iconic" monster?


Addendum: This is why I rely on averages when making 5e monsters, it tends to drown out the outliers. Tomedunn's blog has been a great source of such math crunching

 

[Ondath]

I've got a few questions for you two if that's alright: @Steady Vane and @tomedunn

I've been trying to understand the game's key assumptions about how combats are supposed to go, and I'm wondering if you also found the answers on some of these assumptions.

So from what I understand, we know that monsters are meant to survive for 2-3 rounds, that there is a hidden variable of average PC AC and average PC save bonus... But does this also give us a clearer picture of what the fabled "adventuring day" is supposed to look like? It's widely known that the ideal-type of an adventuring day contains 6-8 encounters of an appropriate challenge. But if we take the calculations you made into account, can we paint a clearer picture of what that adventuring day looks like?

How much HP are the players supposed to end the adventuring day? Someone had said in an earlier thread that the maximum amount of total damage balanced encounters can be expected deal at the end of an adventuring day are 1.5x the party's total HP, since you only regain half of your Hit Dice (and thus half of your HP recovery potential short rests) at each Long Rest, and if you use those to recover half HP during short rests, then get to a point where you're nearly at 0 HP at the end of the adventuring day, you'll make a full recovery with a Long Rest. Do your calculations confirm that? If so, this would be very interesting since it'd mean that WotC assumes that a "balanced" adventuring day beats the party nearly to a pulp, and I think many players would think that they are facing unfair challenges if every adventuring day ended with them at ropes.

Secondly (and this is probably very hard to analyse), do we know how many of your limited-use resources (things like spell slots and X/Short or Long Rest class abilities, not consumables or magic items) you're expected to expend at the end of the adventuring day? I'm guessing we could maybe guesstimate this number by looking at monsters' expected HP, get a total of the amount of HP 6-8 encounters' worth of monsters make, then see what amount of "feature use" would get an ideal-type party to get that amount of total damage. I know that @mearls mentioned in a Bluesky post that they assumed an adventuring day would last 20 rounds, and that they "spread" the additional damage from limited-use features to a class's "at will damage per round", so I'm wondering if this kind of "expected ability use in an ideal adventuring day" is also something we can reverse engineer. Again, the point would be to see how many of your spell slots/class features WotC assumed you'd have used up at the end of the day. And again, I'm guessing that many current 5e players would think that an adventuring where every single one of their spell slots/limited-use abilities are used up would be an unfair amount of challenge.

And a final thing, have you guys ever looked into including Lanchester's Laws in your calculations? There is a guy who argues that 5e CR could be used in a way that'd give us a score per monster that accounts both for that monster's overall quality, and how overbearing that monster would be when that monster is used in larger numbers. If such a calculation seems reliable to you as well, I think that could be one way to make calculating the balance of an encounter much more precise.

Anyway, I've been thinking about the deep fundamental math of 5e a lot lately, so I was very excited when I saw that this thread is ongoing and still active, so apologies if this was too many questions in one go!