Analysis of Monster Sizes vs CR

[PhoenixPhyre]

I've heard a bunch of talk that monsters generally get bigger as you go up in CR. So now I'm interested in testing that hypothesis, using my data set of all 695 monsters in the MM, Volos, and MToF (the three big monster books I've got).

Size	Count	Range of CRs represented	Mean CR
Tiny	39	0 - 2, 4, 18 (one each of the last two, both "skull-type" undead)	0.9 (but strong outlier, removing the demilich from the average drops it to 0.45)
Small	54	0 - 7 (with only 1 of CR > 3)	0.75
Medium	335	0 - 21 (no major gaps)	4.4
Large	181	1/8 - 26 (no major gaps)	6.4
Huge	63	2 - 26 (no major gaps)	12 (11.9)
Gargantuan	22	5, 11-24, 30	20 (19.8)

One thing to note about the large+ ones (especially gargantuan) is the contribution of the various dragons--almost half (10/22) of the gargantuan monsters are the Ancient X Dragon stat blocks. Similarly with the huge dragons (10/63)

The averages here don't tell the full story. Because the mean CR of all monsters is only 5.6, with a standard deviation of ~6.1 (decidedly non-normal distribution). So Small and Tiny creatures are very skewed toward low CR, medium and large are spread fairly evenly throughout, huge are shifted moderately toward high CR (after adjusting for the repeated dragons, all of the huge ones being CR 10+), and gargantuan monsters are skewed very heavily toward high CR.

By creature type (most common size by type, number of that type at that size in parentheses):

Aberrations: tied 14/14 (of 37) between M and L.
Beasts: L (34/100)
Celestial: L (4/8)
Construct: M (16/29)
Dragon: L (12/47) (these are almost exactly split, but the wyvern, dragon turtle, and a couple others played the deciding role.
Elemental: L (11/33)
Fey: M (7/17) (2 L, 5 S, 3 T)
Fiend: M (40/84)
Giant: H (15/27)
Humanoid: M (136/154) (almost all the rest are small)
Monstrosity: L (38/80)
Ooze: tied 3/3 (of 8) between M and L (the other two are the Tiny Oblex Spawn and the Huge Elder Oblex)
Plants: M (8/19)
Swarm: M (8/8) (lol, although really those are Medium Swarms of Tiny Beasts)
Undead: M (30/43)

Is there a point? No. Just some numbers.

[Chronos]

I think that, rather than average CR for each size, it'd be more meaningful to see the average size for each CR.

And what's the gargantuan creature that's only CR 5?

[animorte]

Is there a point? No. Just some numbers.

There's always the benefit of thought-provoking content.

I think that, rather than average CR for each size, it'd be more meaningful to see the average size for each CR.

I also think this would be an interesting scale to see.

[PhoenixPhyre]

I think that, rather than average CR for each size, it'd be more meaningful to see the average size for each CR.

And what's the gargantuan creature that's only CR 5?

I can do that after work.

And the gargantuan CR 5 is the Brontosaurus.

Update: Sizes by CR band (because doing it per CR is just annoying to format in this table editor, see spoiler for full data)

CR Band	T	S	M	L	H	G
0 - 1/2	29	39	78	18	0	0
1 - 5	9	14	161	85	12	1
6 - 10	0	1	56	43	17	0
11 - 15	0	0	29	20	15	3
16 - 20	1 (demilich)	0	5	7	11	5
21+	0	0	1	6	6	13

Spoiler: Image with full results

Show

As expected, Medium monsters dominate all bands below CR 15. In fact, they dominate at every CR below 15 except CR 0 (where Tiny dominates), 11 (Large) and 14 (also Large). Usually by a crap-ton (a factor of 2 or more). They fall off hard after that. Large doesn't dominate, although it's just about always (past CR 1 or so) second-place until very high. Tiny and Small fall off real hard, with exactly 2 tinies above CR 2 and 1 small above CR 3.

Note that that seeming dominance of Gargantuan creatures at CR 21+ is just that there are 18 ancient dragons in that category (2 in the CR 16-20 band at CR 20). Similarly, 10 of the 26 Huge monsters in CRs 13-20 bands are the Adult dragons. Which might skew things quite a bit for those categories in those ranges.

[No brains]

Is there a margin of error to account for the fact that NPC creatures have a chance of being small? A Gnome Archmage isn't a totally alien idea and that's technically a cr 12 small creature.

[PhoenixPhyre]

Is there a margin of error to account for the fact that NPC creatures have a chance of being small? A Gnome Archmage isn't a totally alien idea and that's technically a cr 12 small creature.

I'm going straight by the stat blocks as presented. Any such changes would count as homebrew, at which points no statistics can be done. Sure, it's very mild, expected homebrew. But out of scope here. And would be very expensive to do and raise counting questions (do we manufacture a small and medium virtual block for each npc? If we do, there's the small chance of it changing cr, since small creatures use different HD than medium ones do. Etc.)

[Tanarii]

Can you add the median CR to your table?

[Just to Browse]

Love this, PhoenixPhyre. Thanks for doing it. I think the most interesting insight from this is that it shows how D&D alters the game's scope as level increases.

One of the most common ways that RPGs change with level is by increasing the statistics of PCs / their opposition. Maybe you attack more times, attack at a higher bonus, deal more damage on-hit, get a higher saving throw, yadda yadda. Enemies get the same, usually with stats growing to match. These are changes of scale. Scale is a valuable design lever, because it allows for a sense of easily-identifiable growth: a CR 1/4 goblin with +4 to hit might be terrifying at level 1, but it's a lot less scary at level 5. This allows players to feel like they are scaling up, but if all the game does is scale up enemies in kind, it can also paradoxically lead to feelings of disempowerment. Imagine you start off at level 3, fighting Orc Raiders who deal d6 + 3 on a hit and can heal themselves for 10 HP. After a couple months, you finish some quests and hit level 8, so the Orc Raiders aren't so scary, but now you're fighting Orc Mercenaries that deal d8 + 5 on a hit and can heal themselves for 30 HP. There's technically a sense of progression there, but it makes players feel less like they're growing in power, and more like they're trudging along a treadmill.

The way to fix this is to introduce changes in scope. Whereas scale adjustments involve increasing numbers, scope requires more work: you have to change the actual context of the challenges that players face. In D&D, spells are usually what dictate the pace of changing scope. Compare the AoE sizes of burning hands, fireball, and meteor swarm, for example:

• Burning hands might catch 2 people but sometimes you'll find yourself using it on a single creature. The spell's range is so short that you can't cast it from safety.
• Fireball is practically guaranteed to hit multiple creatures regardless of the fight outcome, and can also be cast from a safe distance, at times even avoiding sightlines to avoid counterspelling.
• Meteor swarm covers 4 large, non-contiguous areas, and its range is anywhere you can see! Want to cosplay Chicxulub? Fly into the sky and throw down buckets of dice just from just below the clouds.

Monsters also tend to change in scope as they get their own spells. Take Slaads: Red and Blue Slaads are simple beaters suitable for low T2 / high T1, but Green Slaads dramatically change the scale of a fight by turning into stealth attackers if they get the drop on the party, thanks to invisibility. Gray and Death Slaads can simply live in shadows because their invisibility is at-will, and the latter also poses a huge problem because it can dispatch individual members with plane shift. These statblock differences allow the various levels to feel different, because the kinds of enemies you fight change. In a slaad-focused campaign, the low levels will involve kiting closet trolls, and the high levels will involve executing your plan while fending off guerilla fighters wielding magical, melee-range rocket launchers.

Without spells (or custom abilities that tend to mimic spells), I've found that there isn't much of a difference in scope between the CRs. 5e features lots of featureless blocks with natural attacks, where scale is essentially all you see. You can go 10 levels fighting stuff like Brown Bear => Cave Bear => Owlbear => Sea Lion => Grick Alpha => Grey Render. But this relationship between size & CR makes me think... what if the secret to making higher levels feel different from low ones is to care about the size of creatures? Perhaps D&D should dial this up to make the high levels feel different: make your big creatures really big, and then include rules for climbing creatures and stabbing them. I think a Grey Render would be a lot more interesting if it were 20 feet tall and could inflict fall damage by just picking you up & dropping you.

[Chronos]

Then, too, there's almost no difference between small and medium anyway, in the 5e rules. "Smallandmedium" might as well be a single size category.

[PhoenixPhyre]

@Tanarii I did actually, and realized they're basically identical (to the significant digits presented) to the means.

Perhaps D&D should dial this up to make the high levels feel different: make your big creatures really big, and then include rules for climbing creatures and stabbing them.

There are rules about climbing on larger creatures--they're in the DMG. I've used them to great effect. Especially when the player in question was a halfling, so he could climb on Large (not just Huge+) creatures and murdilate them with even more impunity (advantage on a paladin who already rolls well and can reroll 1s, plus frequently[1] disadvantage for the enemy to hit...).

One other thing to remember (ok, 2) is that
a) size category doesn't constrain vertical very much--the giants are Huge but most of them are well over 20 ft tall. And goliaths are medium at 7-9 ft.
b) Gargantuan only has a floor, not a fixed size. That is, Gargantuan creatures control a minimum of 20x20, not a maximum.

I ran a combat where part of it involved a giant war machina. It had legs that could be interacted with separately (attack the joints), climbed up, and stuff to do on top. That particular instance was basically invulnerable to normal damage, but it had weak spots on its top and the joints could be locked up by hitting them. It ended up being something like 50' long by 20' wide by 15' high (5' gap, then 10' of body). One of its guards was a frost giant, who kept picking people up that tried to climb on it and throwing them flying.

For a mini, I just drew it on the map and moved all the minis when it moved instead of trying to redraw it.

@Chronos--small vs medium matters for a couple things (mostly PC-wise)--
* Grappling/shoving (small can only grapple medium, not large)
* Mounts (including climbing on creatures) (basically the inverse of grappling--small can ride anything medium or bigger and can climb on Large, while medium can only ride Large+ and climb on Huge+).
* what weapons you can use.

[Just to Browse]

Aren't the rules for climbing on other creatures just some anemic optional rules? IIRC it's just "to climb on a big creature, make a grapple check" and a handwavey "if a creature is big enough, treat it like difficult terrain". I may be misremembering.

Semi-related note: I tried using Colossus Climb rules from a 3rd party book Chamomile's Guide to Everything, but I found them too fiddly to be worth using.

[PhoenixPhyre]

Aren't the rules for climbing on other creatures just some anemic optional rules? IIRC it's just "to climb on a big creature, make a grapple check" and a handwavey "if a creature is big enough, treat it like difficult terrain". I may be misremembering.

Semi-related note: I tried using Colossus Climb rules from a 3rd party book Chamomile's Guide to Everything, but I found them too fiddly to be worth using.

The rules are:

If one creature wants to jump onto another creature, it can do so by grappling. A Small or Medium creature has little chance of making a successful grapple against a Huge or Gargantuan creature, however, unless magic has granted the grappler supernatural might.

As an alternative, a suitably large opponent can be treated as terrain for the purpose of jumping onto its back or clinging to a limb. After making any ability checks necessary to get into position and onto the larger creature, the smaller creature uses its action to make a Strength (Athletics) or Dexterity (Acrobatics) check contested by the target’s Dexterity (Acrobatics) check. If it wins the contest, the smaller creature successfully moves into the target creature’s space and clings to its body. While in the target’s space, the smaller creature moves with the target and has advantage on attack rolls against it.

The smaller creature can move around within the larger creature’s space, treating the space as difficult terrain. The larger creature’s ability to attack the smaller creature depends on the smaller creature’s location, and is left to your discretion. The larger creature can dislodge the smaller creature as an action—knocking it off, scraping it against a wall, or grabbing and throwing it—by making a Strength (Athletics) check contested by the smaller creature’s Strength (Athletics) or Dexterity (Acrobatics) check. The smaller creature chooses which ability to use.

So not quite a grapple check (it's basically inverted, and relatively generous since big creatures often don't have good Dex (Acrobatics)), and it's always difficult terrain.

That's about all I'd want, until the monster is big enough to really be a set-piece (like the one I described) in which case each one's going to be different and you won't really be attacking the monster, you'll be treating it as a bunch of separate, smaller monsters--stabbing at the eye, which might shoot beams at you, trying to damage an arm which makes attacks separately, etc.

[Thunderous Mojo]

One aspect to note, is unlike a Shove Special Action, which can be substituted instead of an Attack/Extra Attack, grabbing a hold of a larger creature takes one’s entire Action.

My Psi Warrior has grabbed at least two dragons at the back facing base of their knecks, and started going snicker-snack.

It was surprisingly effective, and made me think of the Dragon’s Dogma RPG.

[Rukelnikov]

Consider that CR 5.6 ~ 6 being the median is a bit misleading, its the 9th tier of creatures, or 10th if you count CR 0.

I think using 1/8 as 1, 1/4 as 2, 1/2 as 3, and n+3 for CR n, may yield a more usual distribution.

[Dr.Samurai]

b) Gargantuan only has a floor, not a fixed size. That is, Gargantuan creatures control a minimum of 20x20, not a maximum.

First of all, great work as usual, thank you for providing this PhoenixPhyre.

I want to highlight this part because this is how people get away with Forcecaging Tiamat and stuff like that. There's no depiction of Tiamat that I've seen where she would fit neatly in a 20x20ft cube. But because she's "Gargantuan", the assumption is that Forcecage will capture her. Not likely...

Aren't the rules for climbing on other creatures just some anemic optional rules? IIRC it's just "to climb on a big creature, make a grapple check" and a handwavey "if a creature is big enough, treat it like difficult terrain". I may be misremembering.

Semi-related note: I tried using Colossus Climb rules from a 3rd party book Chamomile's Guide to Everything, but I found them too fiddly to be worth using.

I've played with this optional rule. And while I'm all in favor of PCs getting to do cool stuff, and I think it could use a bit more work.

Once I climbed on a dragon to it's back between its wings, it was difficult to attack me. Further, it costs the dragon an entire action to attempt to dislodge me, which is terrible action economy for a boss monster. It seemed to me that once I was there, it was just a matter of swinging with Advantage. Which is great. But I think it could be a bit better.

[follacchioso]

Interesting. How did you get these numbers? Did you go through the list of monsters manually, or did you use any APIs?

[Tanarii]

Consider that CR 5.6 ~ 6 being the median is a bit misleading, its the 9th tier of creatures, or 10th if you count CR 0.

I think using 1/8 as 1, 1/4 as 2, 1/2 as 3, and n+3 for CR n, may yield a more usual distribution.

I can see either way.

It's common to represent 1/8, 1/4 and 1/2 as .125, .25, and .5. But they're actually step 1, 2 and 3 creatures so to speak, when determining total CR from offensive and defensive CR. As in you don't average CR 2 offensive and CR 1/8 defensive to CR 1. It "averages" 2 steps down or up, to CR 1/2.

However, for encounter building purposes they DO represent fractional amounts. For example, discounting action economy multiplier, you get 8, 4, or 2 times as many creatures as you would CR 1s. So from that perspective the fraction CR value is correct.

Regardless, I think it'd be interesting to see what CR ends up being the mean using your idea of start with CR 1/8 as 1 (effectively add 3 to all CRs 1 or higher), determine a mean value from that, then subtract 3 and consider that the 'average CR'.

[PhoenixPhyre]

Consider that CR 5.6 ~ 6 being the median is a bit misleading, its the 9th tier of creatures, or 10th if you count CR 0.

I think using 1/8 as 1, 1/4 as 2, 1/2 as 3, and n+3 for CR n, may yield a more usual distribution.

I can see either way.

It's common to represent 1/8, 1/4 and 1/2 as .125, .25, and .5. But they're actually step 1, 2 and 3 creatures so to speak, when determining total CR from offensive and defensive CR. As in you don't average CR 2 offensive and CR 1/8 defensive to CR 1. It "averages" 2 steps down or up, to CR 1/2.

However, for encounter building purposes they DO represent fractional amounts. For example, discounting action economy multiplier, you get 8, 4, or 2 times as many creatures as you would CR 1s. So from that perspective the fraction CR value is correct.

Regardless, I think it'd be interesting to see what CR ends up being the mean using your idea of start with CR 1/8 as 1 (effectively add 3 to all CRs 1 or higher), determine a mean value from that, then subtract 3 and consider that the 'average CR'.

I'm not sure it would really change the distribution very much...if anything it would make it worse. The skew here is that there are just way more monsters at low CRs than at high CRs, however you define them. So inflating the relative value of those low CRs just shoves everything toward the left.

As for treating fractional CRs as steps rather than fractions...meh. I'd have to rework the data set. Because for calculations it's way easier to treat those as fractions If I get really bored I might test it out thought.

@follacchioso I actually went through all 693 monsters in the MM, Volos, and MToF by hand and entered in their various parameters into a massive spreadsheet and am using that data set. As it turns out, recent versions of excel have some nifty tools where if your data is nicely formatted, you can just ask "what's the most common 'size' by 'cr'" and it will do all the work. The spreadsheet is linked in my sig (if the link hasn't rotted). I can't claim all the DPR calculations are exact, since there's some subjectivity there. But it makes an nice playground for testing claims about published monsters. I don't own MotM or any of the adventure or campaign books, so I won't claim anything about those, and I just got lazy in including Fizban's.

[Rukelnikov]

I'm not sure it would really change the distribution very much...if anything it would make it worse. The skew here is that there are just way more monsters at low CRs than at high CRs, however you define them. So inflating the relative value of those low CRs just shoves everything toward the left.

Yeah, but maybe at least you get a standard deviation where 1 delta to the left is still above 0 :S, I imagine it'd be a cumbersome task to do again unless you have a convenient dataset like a csv or json

[PhoenixPhyre]

Yeah, but maybe at least you get a standard deviation where 1 delta to the left is still above 0 :S, I imagine it'd be a cumbersome task to do again unless you have a convenient dataset like a csv or json

I'd probably do another column in my (massive, up to column AJ I think) summary table, since it's already all in excel...

As for the standard deviation, that comes from applying the stupid (in the "use the standard formulas even though it doesn't fit the distribution") formula to something with decided inherent asymmetry. I'd actually bet that the distribution of monster values (which dominates the curve here as far as I can tell) is much closer to a poisson distribution (non-zero component at 0 parameter value, mean close to 0, then large right tail). That is, the right tail is fat (relative to the left tail). Using the poisson standard deviation (square root of the mean) gives strictly positive values for +-1 standard deviation.

Another issue is that CR = 0 is a valid data point but CR = -1 is not, so there's a hard cut on one side of the distribution. And there are a lot of CR = 0 monsters.