D&D (2024) 5e 2024 − The Monster Math

Then your formulas are wrong?
I am unsure what you are critiquing.

Yes, the highest Attack Bonus in the new Monster Manual is +19, belonging to the Tarrasque whose CR is 30.

But a DM can create other epic monsters, one that has a higher CR, such as CR 30 whose expected Attack Bonus is about +20, for example.

It is also possible that some monsters with CR 30 have a higher than expected Attack Bonus, such as +21 or whatever makes sense for the concept.
 

log in or register to remove this ad

I am unsure what you are critiquing.

Yes, the highest Attack Bonus in the new Monster Manual is +19, belonging to the Tarrasque whose CR is 30.

But a DM can create other epic monsters, one that has a higher CR, such as CR 30 whose expected Attack Bonus is about +20, for example.
Not by the guideline of stat mod + prof. Bonus
 


Not by the guideline of stat mod + prof. Bonus

Pirates Of The Caribbean Code GIF by Brian Benns
 

Remind where these absolute limits for Ability and Proficiency are in the 2024 core rules?

Plus, depending on concept, the Attack Bonus might add a magic item or magic boon bonus.
It depends how n what your goal here is. I may have misunderstood, but I thought you were trying to analyze the 2024 monsters and figure out how monster creation works. If so, then you have an error, if that was not your goal then you can ignore my comment. I was trying to helpful, not get into an argument
 

It depends how n what your goal here is. I may have misunderstood, but I thought you were trying to analyze the 2024 monsters and figure out how monster creation works. If so, then you have an error, if that was not your goal then you can ignore my comment.
Yes, the goal is to "analyze" the new Monster Manual, understand its methods for creating monsters. It is deeper than reprinting a particular monster statblock from the Monster Manual. It looks to understand how it was put together. What the process is, what the constraints are. The math. This same math can create new monsters for future products, that arent in the current Monster Manual.


I was trying to helpful, not get into an argument
I appreciate it.
 
Last edited:

The expected AC for each CR, on average, is highly consistent. Individual monsters can vary, depending on concept, but dont seem to stray too far.

On average, the AC in the 2024 Monster Manual improves by 0.42 of a point for each CR. In other words, for every 5 CRs higher, the AC is 2 points higher. This formulaic pattern seems to match closest the actual average for each CR in the following way. The averages from the Monster Manual are in parentheses on right. The red are slightly under the expected value, the blue slightly over. Everything is within 10% of expectation.

2024 Monster Manual AC (Yaarel).png
 

Now for the hard part. DPR. The numbers come from Teos at Alphastream, calculating DPR for each monster statblock in the new Monster Manual, and determining the average for each CR. They are for "Damage Per Round" against a single target. (Not area effects against multiple targets.) For purposes of calculations the attacks are assumed to always hit, and any saves against them always fail.

There are many ways to deal damage, and monsters can vary significantly by concept. For example, one monster might deal less damage but be more accurate, tough, and relentless. Even so, higher CR monsters tend to deal more damage than lower ones. Overall a pattern emerges, that represents the feel of D&D as a combat game.

The monsters at each CR average an overall amount of damage-dealing. Because the damage averages can diverge considerably from the expectation, there are actually two ways to interpret what the expected progression actually is. One interpretation is, the expected damage is improving linearly and steadily at each higher CR. The other interpretation is, the expected damage is gently accelerating, dealing more and more damage, according to a geometric curve across each higher CR. The acceleration might be taking into account the higher CRs having more attacks to multiply the damage, effects that add ongoing damage, and so on. The curve is probably more accurate to describe the actual numbers in the Monster Manual. But the line is simpler, easier to implement, and might be the intended guideline that the monster designers use as the guideline, for which, a particular monster modifies according to concept. Whether the line or the curve is "better", ultimately depends on which approach seems to make the monsters that are the most fun for the most players.


The simplest formula is linear: DPR = 9CR. At CR 1, the monster is expected to deal somewhere around 9 hit points of damage per round. At CR 10, the monster is expected to deal somewhere around 90 hit points of damage. And so on for any CR. The formula is surprisingly simple for an aspect of the math that is so complex with so many variables.

When comparing the 9CR formula to the averages in the Monster Manual, many CRs deviate significantly from it. Yet the straight line has points of contact with it, at the some of the lowest CRs, higher CRs, and across some of the central CRs. It may well be the intended guideline.

Yet when looking at the actual averages in the Monster Manual, all of the deviations from the line at lower CRs are lower than the linear expectation, while all of the deviations at higher CRs are higher than the linear expectation. The expectation itself may be a curve, that starts low but curves higher and higher at the higher CRs.

As a kluge, I offer a geometric formula that seems to describe the curve well enough. Where the averages deviate from the curve, the formula suggests obvious corrections, such as for when the average of the next higher CR has almost no improvement. This "curve formula" is a convenient description of the averages. It doesnt derive directly from any specific gaming mechanic. Here the exponent, "to the power of" ^1.4, describes a gentle curve upward. The curve tightly follows the averages, so trying to tweak the formula to match more closely the average at one CR tends to skew it away from it at an other CR.

DPR = 10 + 3(CR^1.4)

In comparison, the line formula produces DPR that is deadlier at lower CRs. The curve formula produces DPR that is deadlier at higher CRs. Which is better for the game?

In the DPR table below, the average DPR for each CR in the Monster Manual appears in parentheses in the central column. On the left, is the simple line formula, 9(CR). On the right, is the curve formula, 10 + 3(CR^1.4). A number in red means the formula generates a DPR that is lower than the average in the Monster Manual, being 90% of it or less. A number in blue means the formula generates a DPR that is higher than the average, being 110% or more. Note, for the curve formula at CR 30, the DPR is high, but right on the edge only slightly beyond the 10%, and is a reasonable guideline to produce monsters at this CR.


2024 Monster Manual DPR (Yaarel).png
 
Last edited:

Yes, the goal is to "analyze" the new Monster Manual, understand its methods for creating monsters. It is deeper than reprinting a particular monster statblock from the Monster Manual. It looks to understand how it was put together. What the process is, what the constraints are. The math. This same math can create new monsters for future products, that arent in the current Monster Manual
What evidence do you have that they used maths?
 

I got curious about 2014 vs 2024 encounters, so now that we have the new monster math and encounter guidelines I matched out 2 examples. Thought some people would enjoy it.

2014 Level 10 encounter 4 characters:
Medium Challenge is 4 CR 3 Monsters
Total HP: 240; Total Damage/Round: 80

2024 Level 10 encounter 4 characters:
Medium Challenge is 4 CR 6 Monsters
Total HP: 436; Total Damage/Round: 186
These comparisons are invalid. A tipoff is that the terms for encounter difficulty have changed from 2014 to 2024; 2024's "Moderate" is not 2014's "Medium" (there is no "Medium" in 2024), it's equivalent to 2014's "Hard". To make some valid comparisons:

2014 - 10th level, 4 characters, Medium difficulty => 4800 XP (the floor) - 7599 XP
4 CR 3 monsters (taking into account numerical adjustment) is 5600 effective XP
Total HP: 240; Total Damage/Round: 80

2024 - 10th level, 4 characters, Easy difficulty => up to 6400 XP (the ceiling)
4 CR 4 monsters is 4400 XP
Total HP: ?; Total Damage/Round: ? (not sure where you were getting these to update)

The difference between the two isn't as great as you might've thought.
 

Remove ads

Top