Well, I have good news, and I have bad news. Kind of a lot, so it's probably more than I should squeeze into a "tidbit" topic. I'll try to hit just some big points.
I found an
old Livestream of Mike Mearls doing monster design, where he is showing you the spreadsheet they use. You're only seeing the user input part, so it doesn't give us the actual formulas, but we can guess a lot of things from it. I took a bunch of screenshots and pasted them together into an ugly mess that can be used to look at it all together. It seems complete, other than some monster features that were never on-screen, but I expect they are similar to the ones in the DMG. I'm attaching the ugly mess of an image in case anyone else is interested.
That's good news...but it's somewhat bad news, because I was very disappointed in their spreadsheet. I figured that, for example, the +2 AC for creatures that can fly and attack from range if under CR 10 was a simplification of a system that probably had +1 at some ranges, maybe +3 at others, rather than CR 10 = +2; CR 11= nothing. Apparently not.
So there is some just bad design apparently in the official one. (There is no good reason they can't make it more granular than that.)
On the bright side, I have no reason to believe that the formula I previously mentioned about attack bonus and hit points isn't what they're using. And if it isn't, then that's them doing it wrong, because it's what their math says they should be doing.
The next tidbit I was going to share, was only slightly speculative, because it follows by analogy from the first tidbit. The spreadsheet may be expecting it also, because it says "saving throw bonus" rather than saving throw proficiencies.
I am assuming that for every total +6 to saving throws gained from proficiencies (so, one saving throw at CR 1 is worth a +2, that can be ignored, while six saving throws at CR 20 is worth +36) you increase the effective AC by 1. Most likely it's round down. If you look at it across the various CRs, that makes sense of the rule of +2 effective AC for 3-4 saves, and +4 for 5-6. So just apply any bonus from that to the effective AC before doing the calculation with the hp to get their Defensive CR line.
The good news about the Offensive line, is that if you are only using Attack Bonus and Damage and things that alter your effective attack bonus or damage output, it should work exactly like the AC and Hit Points.
The bad news, and what I've been stuck on for a long time, is what's going on with Saving Throw DC based damage.
See, here I have to digress a bit for background info. On both PC and Monster sides, for both attack rolls and saving throws, the baseline assumption is a 65% hit rate. The relevant issue though, is that save for half effects (which is what most non-cantrip damage sources that rely on a saving throw are) do significantly more actual damage with that 65% hit rate.
25% more damage in fact. So, when you are entering the damage value of monsters into the formula, whether an effect deals half damage on a successful save or not has a real effect! Neither the DMG, nor the spreadsheet mentions that.
This, hopefully in some way, ties into the other major problem I was running into (that might be the solution in disguise). The Saving Throw DCs on that table and the Attack Bonuses...don't make obvious sense. We have 4 numbers: Save DC, Attack Bonus, PC Average Save Bonus (hidden), and PC average AC (also hidden). We can derive the hidden values from the known ones by assuming that 65% chance. And those values are weird. Assumed AC for 1st level characters is 11? Assumed saving throw bonus is -1? At 20th level those numbers are 18 and +5. The 18 could make sense, but the +5 is real hard to find a source for.
I don't want to go into an entire unpacking of the mess that is the interaction between those 4 numbers, but there is one other point that has to be brought up. If you subtract the proficiency bonus for the CR from the Attack Bonus and the Save DCs...the remaining ability scores don't match. And they don't match in the
wrong direction. For those who've spent time plugging the stats of existing monsters into the DMG chart, you realize that you usually have a higher attack bonus than the damage line for attacks, and a lower save DC than the damage line for save based damage (which makes sense, because monster Strength tends to increase faster and further than mental stats). Well that's the exact opposite of what's going on. The ability modifier than can be extracted from the chart for Save DCs is consistently 1 or 2 points higher than the one that can be extracted for the Attack Bonus.
Believe me when I say I spent endless hours and thousands of lines of spreadsheets trying to make sense of it. I came to the speculation that this must have been intentionally designed to deal with a combination of the 25% extra damage from save for half effects, and the fact that you assume 2 targets for multi-target damage effects (which are almost exclusively save for half effects). Basically, if you have a 5th-level wizard sort of monster that can throw fireballs, their Save DC is most likely going to be 13 (8+proficiency bonus (2, since they will be lower CR than their PC level would be)+3 casting stat). Their damage output, however is going to be 56 (28x2). So you are on offensive line 8, but that DC 13 will drag it down to a lower line. Which means, based on the appropriate DCs for single target damage, you can actually connect a Save DC that is lower than the listed one to the DPR lines. I found that ability mods in the the save DCs for levels 1-20 aligned almost (or exactly, depending on how you interpret the trendline) with the ability mods in the attack bonuses if you multiplied damage by 1.75 (rather than by 2). I tried a variety multipliers for a variety of reasons, and that one came out the best. That being said, 2x, which is what they apparently actually do use, also works, and it is "off" in the
right direction to work this time, so it's not a big deal.
Except that it completely ignores the 25% damage increase. It should be x2.5, not x2. Or some other value, if you aren't actually assuming hitting 2. But just multiplying it by 2, given this is save for half territory, is the equivalent of assuming you are hitting 1.6 targets...which doesn't really fit anywhere.
Anyway, one thing that is certain is that the Save DC cannot work for your four different save for damage situations (single target save for none, multi-target save for none, single target save for half, multi-target save for half). It can only apply to one of those, and you must use a different number for any of the other three.
I'm restraining myself from going on about several other things, but yeah, it's tough. I'm actually glad I learned what I did, but I'm disappointed that, even if I can figure out what I want to, there are fundamental flaws with the way they implemented their own design. Not the design itself--that's a matter of opinion. But, things where they knew how it worked, and just messed up. Like, for instance, attacks where you have to save or take poison damage. I am 99% certain that they would just plug in the poison damage along with the damage from the attack and not even worry about the Save DC (which is likely statistically quite a bit different than the attack bonus). And they also won't make the important calculation of multiplying the poison damage by the assumed chance of failing the save--which you have to do because the rules only take account of the initial chance to hit. That added save for the brunt of the damage significantly reduces the overall damage, and if not calculated for will not give correct amounts. Take the wyvern's sting for an example. That 24 poison damage needs to be multiplied by some percentage before adding it to the 11 from the stinger. A better spreadsheet would have places to enter all of this stuff, including the saving throw against the poison.
And this is all totally doable! I can do it! Those of you reading this can do it! Ugh. Anyway. If I completely steer clear of monsters with save based damage output, I might be able to reverse engineer more of those additional consideration formulas--the things that change effective AC, HP, Attack Bonus, and Damage output. However, I wonder how well designed some of that stuff actually is. For example, the given multipliers for damage resistances and immunities have serious issues when you try to analyze monsters. Because they make giant jumps in effective HP multipliers if you shift over a threshold (from CR 4 to 5 for example), you can end up with CRs that are quite a bit off by applying them. That was an issue I had when I was using the DMG formulas on the MM monsters. Again, I need to stop. This is not a full analysis, just a progress report.
A little while back I derived a formula for
calculating monster XP values based on their effective offensive and defensive stats.
View attachment 405801
It may look arbitrary, but it was derived from a basic calculation of how much damage the monsters can be expected to do during an encounter against four generic PCs. You can find the full derivation
here.
Once a monster's XP has been calculated, it can be converted to a CR by simply finding the CR with the closest corresponding XP value.
It works best for monsters that don't have special traits and don't apply conditions to the PCs, but it can also be applied to more complicated monsters by converting those things into bonuses/penalties to their base stats. For example, a monster that has a consistent way of gaining advantage might have an effective bonus to their AB of +4 to represent their increased chance to hit.
Edit: made equation less obnoxiously large.
I took a look at your website and really like your work! I have some questions about it I might bring up when I get back to things, but you might be interested in watching that livestream if you don't mind finding out disappointing things like they are actually rounding damage down for each individual attack (so two attacks for 1d6+3 each, gets entered as 12, rather than 13) and completely and utterly ignoring the existence of critical hits.
