D&D 5E Tidbit for monster design

[Sword of Spirit]

Something else I think might help you along this path is that the baseline monster stats by CR in the 2014 DMG don't match values used by WotC. This is a point the designers have brought up a few times over the years, but you can see it pretty clearly in my analysis of published monsters from the 2014 era. This is especially evident when comparing monster attack bonuses and save DCs. As you pointed out, if compare the two, as listed in the 2014 DMG, they imply different underlying stats, which isn't the case when looking at actual monsters.

I still question exactly how it differs. I assume it primarily differs due to most likely doing what I mentioned in the first post--adjusting CR based on actual changes in effective hp and damage from the changed percentages to be hit / hit, rather than using the +2 change = +1 level on the chart. Statistically, that checks out as a simplification of what the actual math does.

I assumed there were other non-simplified versions of calculations, but from the data entry points of that spreadsheet there don't appear to be as many as I hoped there might--although without the calculation portions of the sheet, we can't see what there actually is. For instance, they may still have a calculation for damage resistances that is more granular. And certainly Aggressive must be based on the creature's actual damage output, rather than a flat +2 damage per round (it honestly looks like a straight up mistake in the DMG, but maybe they were just assuming you'd only use it on something with a similar damage output to a basic orc). And it's interesting that there was no line for Save DCs at all, which makes me wonder if there is a separate sheet for monsters that "relies more on effects with saving throws than on attacks" (whatever the criteria for that is).

I don't see any benefit for them to make up different values for the chart in the DMG than the values in the spreadsheet, given the similarities, which makes me believe the differences are in how those values are manipulated, not in what the baseline is. I'd be interested if you have the exact statements for me to review though--maybe they were more clear than I'm assuming.

So far, I've mostly examined the stats in the 2014 MM, in case they made changes afterwards. Actual monsters have higher ACs and Attack Bonuses than the chart gives for the CR. However, this still fits the chart, because they have correspondingly lower hit points and damage output than the chart. So they just set some of the chart assumptions oddly. In the case of AC, it actually makes perfect sense since the chart gives the monster's AC assuming a 65% hit rate, and we can determine exactly what that is for a typical PC using easily established assumptions.

It's much murkier how they came up with the numbers on the Offensive side, though I can at least understand the difficulty, given that the average saving throw of a PC varies only by 2.167 to 2.333 from level 1 to 20. Average PC AC also doesn't vary by many points, though that one is difficult for me to pin down. I assume they wanted the amount of variation over the levels closer to the AC variation in their monster numbers over those levels (though it's odd that the variation in Save DCs is the same 7 points as monster AC, while the variations in Attack Bonuses is 8).

Actual MM Save DCs start a little lower than the ones in the DMG, are the same around 12-15, and then start climbing higher. Actual Attack Bonuses on the other hand, are higher pretty much the whole way, and by a larger amount than the Save DCs.

I'd like to assume those Attack Bonuses and Save DCs workout somehow, given how, as you mentioned, the simplified DMG guidelines do get pretty close results. I'm just not sure where they are getting their numbers. If we ignore the discrepancies between Attack Bonus and Save DC, it doesn't matter too much where they set the numbers, as long as the percentage hit chance multiplied by the given damage number adds up to the amount that deals the appropriate damage to the PCs. They could set it at 95% hit chance, adjusted the damage accordingly, and then we'd just find the actual monsters have much lower Attack Bonuses and higher Damage values than the chart indicates, but it would still work out to the same end result.

Now, some people mistakenly take this to mean the method used in the 2014 DMG is entirely wrong, but, having calculated CRs for over 2,000 monsters using it and seeing how well it holds up, I think a better way of looking at it is as just a different reference point along the same power curve. It's not a good representation of the baseline WotC follows, but you can still use it to calculate monster CRs accurately enough.

When I first started out analyzing official monsters, I stuck pretty close to what WotC described in the DMG. Over time, as I've developed my theoretical model, I've deviated from it more and more. However, despite that, my results still don't differ all that much from what the 2014 DMG gives. I don't think their method for calculating monster CRs is perfect, but I think it does a good enough job to be practically useful in most circumstances.

I'm hoping to test out the formulas I'm coming up with to see if they work where the simplifications in the DMG don't. By limiting my tests to creatures that don't have any of the complications in their statblock to determine what happens, and then add in individual complications, I'm hoping to be able to determine what each does. Unfortunately for this exercise (but fortunately for play experience) there aren't many monsters that have nothing going on but AC, HP, AB, and Damage, which are the values I can test the formulas for. I tried it on all the ones that were limited to values. 14 of those don't get the right CR with the DMG values, and 12 don't get the right values with these formulas. (Including, in both case, the humble ogre. It's really only CR 1, no matter how you do it. I don't know why it's listed as CR 2. It makes me wonder if they initially gave it 2 attacks, and then dropped it to 1 attack without adjusting the CR.)

With there still being 12 (mostly the same ones, though a couple of them were different) extremely simple monsters that don't work, I need to know why they don't work before I can continue. One question I have is if they ever actually ignore what their spreadsheet says and give a monster a different CR than it says. Statements are unclear. I could interpret Mike Mearls as saying that, but I could also interpret him as meaning that if it isn't working quite right, he adjusts the numbers in the spreadsheet until it spits out the CR he wants. And Jeremy Crawford talked about doing exactly the latter with increasing hit points by small amounts.

The thing is, my end goal is actually to adjust the formulas to better fit the assumptions I want to bring to the game. For example, we always play with at least the standard amount of magic items, so I intend to adjust the math to assume the standard magic item allotment. I also find that the DMG vastly overrates the effect of damage resistances and immunities (I stick with the 2014 rules), and intend to change how it handles it to get numbers that make more sense to me (I'm also making more nuanced damage resistances, similar to what 3.5e did, so I'll be adjusting it differently than I would with the standard way of overcoming damage resistances). But before I change the rules, I prefer to understand why they are the way they are as fully as possible.

 

[Sword of Spirit]

Here's some numbers I'm putting up to see if I can get some other sets of eyes on them.

I selected the simplest monsters in the Monster Manual, that should derive their CR purely from AC, Hit Points, Attack Bonus, and Damage output. I left out creatures that had anything I knew could affect CR (such as saving throw proficiencies, imposing conditions, effects relying on saves, damage resistances, etc), and even anything I previously suspected might affect CR (like a fly speed, even without ranged attacks). These are all basically just your "bags of hit points".

In other words, these are the creatures that the spreadsheet WotC used should work for perfectly. I re-did my calculations today, since I now know that they base damage output on fixed values, and my proposed formulas hold up better than I thought. There is only one case where the DMG rules give you the MM CR and my formulas fail to do so (the veteran), while there are 5 where the DMG CR doesn't match the MM but the proposed formula does. For the remaining 10 discrepancies, neither the DMG nor the proposed formula agrees with the MM.

Blue is used to indicate that the formula gave a higher value than the MM CR, while orange indicates the opposite.

And here's an expanded one with the Defensive and Offensive CRs.

Here are the two most likely theories of what's going on here.

1) The designers sometimes ignored their own CR formulas and assigned a different CR. I know a lot of people assume this is what happened, but I'm really trying to see if I can falsify this claim before I accept it. Now to be fair, we were told that dragons are intentionally under-CR'd to make them more dangerous than their CR would indicate: because Dragons! So there is already precedent that they have done this in the past. However, in both listening to how Jeremy talked about adjusting hp in small increments to get a desired CR, and how Mike played around with the numbers on the video I linked, it seems like that wasn't standard procedure, and standard procedure was to instead tweak your monster's numbers to make it work with the formula, rather than to ignore the formula and just assign whatever old CR they wanted to.

2) Their internal formula (as implemented in the spreadsheet Mike Mearls was using) does produce the formulas in the MM, and my proposed formula isn't exactly right.

In order to accomplish anything else, it's pretty vital that I'm able to find out which of these is the case, so any analysis of those tables, or just random ideas, is appreciated.

The biggest problem here, is that those formulas I derived are right. They aren't guesses. They are literally how the math works. We know various assumptions, we know how the math fits those assumptions, and we know how that can change by altering the percentages. It's really, really solid with the Defensive CR, as I explained in the first post. Now, it's theoretically possible that something different is going on with the Offensive CR. Or it's possible that there are additional considerations beyond the strict percentage system going on in their formulas.

For example, maybe they have something slightly different going on under the hood with fractional CRs? As you can see, almost all of the discrepancies involve a fractional defensive and/or offensive CR. However, the Giant Ape is a standout that doesn't work right, even though it has no fractional CRs, which means if that is the case, there must also be something else going on that explains the giant ape. (Now, if we can get everything but 1 or 2 monsters figured out in the whole MM, we can probably assume that someone just made a mistake somewhere, but at this point that giant ape is still significant.)

Now, remembering that we can look at the entry forms of the spreadsheet they themselves used to see what data can be included, do you all have any ideas about what might possibly be going on with the invisible calculations on that sheet to cause it to give us the MM CRs rather than the ones from the proposed formula I derived?

 

[dave2008]

Here's some numbers I'm putting up to see if I can get some other sets of eyes on them.

I selected the simplest monsters in the Monster Manual, that should derive their CR purely from AC, Hit Points, Attack Bonus, and Damage output. I left out creatures that had anything I knew could affect CR (such as saving throw proficiencies, imposing conditions, effects relying on saves, damage resistances, etc), and even anything I previously suspected might affect CR (like a fly speed, even without ranged attacks). These are all basically just your "bags of hit points".

In other words, these are the creatures that the spreadsheet WotC used should work for perfectly. I re-did my calculations today, since I now know that they base damage output on fixed values, and my proposed formulas hold up better than I thought. There is only one case where the DMG rules give you the MM CR and my formulas fail to do so (the veteran), while there are 5 where the DMG CR doesn't match the MM but the proposed formula does. For the remaining 10 discrepancies, neither the DMG nor the proposed formula agrees with the MM.

Blue is used to indicate that the formula gave a higher value than the MM CR, while orange indicates the opposite.

View attachment 406725
And here's an expanded one with the Defensive and Offensive CRs.

View attachment 406726

Here are the two most likely theories of what's going on here.

1) The designers sometimes ignored their own CR formulas and assigned a different CR. I know a lot of people assume this is what happened, but I'm really trying to see if I can falsify this claim before I accept it. Now to be fair, we were told that dragons are intentionally under-CR'd to make them more dangerous than their CR would indicate: because Dragons! So there is already precedent that they have done this in the past. However, in both listening to how Jeremy talked about adjusting hp in small increments to get a desired CR, and how Mike played around with the numbers on the video I linked, it seems like that wasn't standard procedure, and standard procedure was to instead tweak your monster's numbers to make it work with the formula, rather than to ignore the formula and just assign whatever old CR they wanted to.

2) Their internal formula (as implemented in the spreadsheet Mike Mearls was using) does produce the formulas in the MM, and my proposed formula isn't exactly right.

In order to accomplish anything else, it's pretty vital that I'm able to find out which of these is the case, so any analysis of those tables, or just random ideas, is appreciated.

The biggest problem here, is that those formulas I derived are right. They aren't guesses. They are literally how the math works. We know various assumptions, we know how the math fits those assumptions, and we know how that can change by altering the percentages. It's really, really solid with the Defensive CR, as I explained in the first post. Now, it's theoretically possible that something different is going on with the Offensive CR. Or it's possible that there are additional considerations beyond the strict percentage system going on in their formulas.

For example, maybe they have something slightly different going on under the hood with fractional CRs? As you can see, almost all of the discrepancies involve a fractional defensive and/or offensive CR. However, the Giant Ape is a standout that doesn't work right, even though it has no fractional CRs, which means if that is the case, there must also be something else going on that explains the giant ape. (Now, if we can get everything but 1 or 2 monsters figured out in the whole MM, we can probably assume that someone just made a mistake somewhere, but at this point that giant ape is still significant.)

Now, remembering that we can look at the entry forms of the spreadsheet they themselves used to see what data can be included, do you all have any ideas about what might possibly be going on with the invisible calculations on that sheet to cause it to give us the MM CRs rather than the ones from the proposed formula I derived?

Perhaps you said and I missed it, but are the tables above using the 2014 or the 2024 MM?

 

[dave2008]

OK, I have done a deep dive yet, but I just take a look at the monsters the 2014 DMG and your formula are in agreement, but disagree with the 2014 MM to see if revisions in 2024 versions change the result.

Giant Ape CR 7
Using the 2014 DMG calculator I get the following:

2014: CR 6
2024: CR 7 (6.5) - CR increase do to increase in HP (168 vs 157)

Owlbear CR 3
Using the 2014 DMG calculator I get the following:

2014: CR 2
2024: CR 3 (2.5) - CR increase do to increase in DPR (28 vs 24)

Ogre CR 2
Using the 2014 DMG calculator I get the following:

2014: CR 1
2024: CR 1 - however it gets a 15% boost in HP (68 vs 59) which almost justifies the CR. If they had bumped it to 71 HP, then it would be CR 2 per the 2014 DMG

Plesiosaurus CR 2
Using the 2014 DMG calculator I get the following:

2014: CR 1
2024: CR 1 - oddly the DPR is actually lower (11 vs 14)

It seems likely to me that both the 2014 DMG and your math are mostly correct for these monsters, it was just an error in the 2014 MM version of the monster that leads to the CRs not matching. However, both the 2024 Ogre and Plesiousaurus lead me to believe their CR calculator was revised down a bit a low CRs.

 

[dave2008]

1) The designers sometimes ignored their own CR formulas and assigned a different CR. I know a lot of people assume this is what happened, but I'm really trying to see if I can falsify this claim before I accept it. Now to be fair, we were told that dragons are intentionally under-CR'd to make them more dangerous than their CR would indicate: because Dragons! So there is already precedent that they have done this in the past. However, in both listening to how Jeremy talked about adjusting hp in small increments to get a desired CR, and how Mike played around with the numbers on the video I linked, it seems like that wasn't standard procedure, and standard procedure was to instead tweak your monster's numbers to make it work with the formula, rather than to ignore the formula and just assign whatever old CR they wanted to.

It the video you posted Mike made it very clear that the spreadsheet calculation was just a starting point. That playtesting could cause a revision in the CR up or down. So I think it is likely you can only get so close with a spreadsheet style calculator. Get 100% accuracy with the MM just isn't possible.

 

[Sword of Spirit]

Quick Note: Ignore the blink dog in that chart. I don't know how I missed that is has that teleport + bite feature, which likely affects CR.

Perhaps you said and I missed it, but are the tables above using the 2014 or the 2024 MM?

I'm sticking with 2014. Once that's figured out, it shouldn't be too much trouble to see what they changed for 2024. I'm particularly interested in knowing how they are valuing the proficiency/expertise in initiative, since that's something I'll be using in my 2014 based game.

It the video you posted Mike made it very clear that the spreadsheet calculation was just a starting point. That playtesting could cause a revision in the CR up or down. So I think it is likely you can only get so close with a spreadsheet style calculator. Get 100% accuracy with the MM just isn't possible.

You are very likely to be correct. But I think there is still room to interpret it differently--and we know that sometimes our widespread interpretations of designer intent have been mistaken.

Instead of interpreting it as:

"The monster may not feel like it's working as expected for its CR after playtesting. If that happens, just raise or lower the CR in the monster's statblock to what feels more accurate to you."

Try on this interpretation:

"The monster may not feel like it's working as expected for its CR after playtesting. If that happens, adjust the monsters stats, such as hit points and attacks, until it feels right for the CR the tool gives you. You may even decide you prefer the monster to be a higher or lower CR, and the tool will help you get the right stats for it either way."

The reason I'm investigating the latter option, is because that fits the actual examples Mike and Jeremy have given us. Other than the dragons, I've never heard them actually say, "The tool tells us this monster I made is CR 3. That doesn't feel right to me, so I'm just changing that line to say 'CR 4'." Mike talked about tweaking what he was using for damage dice, and switching from a weapon attack to a spell attack to get the numbers he wanted, and kept checking things to see if the CR changed. Jeremy talked about incrementally adding a few hit points (probably 1 HD at a time) until the monster ended up the intended CR.

Also, even if they do sometimes have to make judgment calls, it makes very little sense that they would feel a need to fudge the CR on these basic "bag of hit points" monsters. It makes a lot more sense to need to do that if you are adding a feature that is combat relevant but doesn't have a clear way to input it on the form. Like what does the banshees wail count as? But when we are dealing with monsters that are nothing but AC+Hit Points+Attack Bonus+Damage Output the formula ought to just work. I mean, with all the behind the scenes data and assumptions, it would almost take more skill to design one that doesn't work for that! It's basically a pure question of math with these basic critters.

To move outside of the bounds of what they may or may not have done into the realm of what they probably should have done... Even when they are dealing with things that are harder to quantify they could have a set of guidelines--it doesn't have to be completely freeform. For example, when I get to the point that everything quantifiable has been, and I need a way to value other factors, I would probably create statistical values at each CR for "Average Defensive Feature", "Strong Defensive Feature", and "Very Strong Defensive Feature", distilled from the math of existing features that seem to fit those categories (as well as the offensive equivalents). Then if I'm creating a feature and there is no clear method of entering its stats in my own tool, I can check the box for it having a "Strong Defensive Feature" and that will do whatever that should do (probably treat its AC as 4 higher or something).

Moving on again...
After looking over those charts I posted again, it occurs to me that the lower CR creatures tend to be higher CR in the proposed formula than the MM, and the higher CR creatures tend to be lower. Now, there are really not many ways to get those results if we stick with the percentages. However, it occurred to me that if the percentage chance to hit in the Offensive CR is not consistent at 65%--if it varies by Offensive CR line, that might solve the issue, if I could derive the values. I'm still looking into that...and there are places where it helps, but I'm doubting it will actually solve the problem. Ponys and Veterans are particularly stubborn in refusing to play with the math.

Ogres and Plesiosaurs, however, take the cake. They don't work for any hit chance I've tried (30%-95%). I also discovered the reason. Since actual hit chances never go above 95%, it sets a ceiling of how much attack bonus can matter for offensive CRs. If your average damage is 13 (like the ogre), you can't go above the CR 2 offensive line, no matter how high your attack bonus is, because chance to hit can't go beyond 95%, and 95% gives them an adjusted effective DPR of 19, while the threshold for CR 3 is 21. With that damage, the ogre would have to raise their Defensive CR 1/2 up to 1 to get the listed 2.

 

[dave2008]

"The monster may not feel like it's working as expected for its CR after playtesting. If that happens, adjust the monsters stats, such as hit points and attacks, until it feels right for the CR the tool gives you. You may even decide you prefer the monster to be a higher or lower CR, and the tool will help you get the right stats for it either way."

That would definitely make sense and I hope that is how it works.

 

[Sword of Spirit]

Well, I'm really stumped here. I created a spread of results for those monsters with different hit chances (instead of just 65%) in case it varies over CR. I couldn't come up with any functional curve from that--too little consistency.

I did find an error in my spreadsheet, and corrected it. Unfortunately the only result with these sample monsters was to make brown bear not work again, lol.

I considered maybe the rule of rounding off the average of the defensive and offensive CRs was a simplification. Maybe the real rounding formula varies by CR. Always rounding down if CR 1 or lower, and up if CR 2 or higher would fix several monsters, but it doesn't fix everything. It's also rather odd for it to switch immediately from down to up without an off stretch in the middle, but that could be a thing.

I finally decided that when I continue my investigation I'm going to find similar simple "bag of hit points" monsters from VGtM and see how they respond to my formula. I'm doing this because, while I couldn't find a completely consistent pattern, for most of the monsters that don't map CR properly, I could find potential errors that might have been made. For example, maybe someone had the owlbear attack once with their bite and twice with their claws. The veteran may have had a shield option. Those sort of things would get those guys to CR 3 where they are supposed to be. It's also possible that having a secondary ranged attack is supposed to count for something, etc. And some of those rules might have changed as they were working on it, leaving us with incorrect values. Or maybe they hadn't decided exactly how it was going to work when some of these monsters (like the ogre) came out in the starter set prior to the core books, and they just left them where they were because they had already established ogres as being CR 2, even if the math didn't end up backing that up.

In any case, if I examine more monsters in Volos (assuming there is a reasonable number of super-simple monsters, which there may not be) and they all just work, that's reason to further pursue the theory that they may just have made errors when CRing some monsters and decided not to fix them afterwards. I glanced over the errata of the MM (plus VGtMs and MToF) and couldn't see that CR was ever changed.

I did, however, notice that some of the ancient dragons had non-standard XP values before errata. This makes me wonder if they actually use something like @tomedunn 's XP-based formula and just round the XP to fit the defined CR value. There must be some explanation for why someone typed in all of those different and incorrect/non-standard XP values. I did test the XP-based formula briefly, and it wasn't working out with the real low CR critters, but that doesn't mean they don't have a slightly different version of something like it that they use.