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5e monster manual on a business card

Tue, 07/31/2018 - 14:41

Lately I’ve been doing statistical analysis on D&D 5e monsters to see how they’re built, and I’ve learned some interesting things: the DMG monster-creation guidelines don’t work as expected, monster design formulae have stayed stable from book to book, and many of the complexities of the official monster-design process don’t significantly affect its outcome.

Today, let’s come up with simple instructions for creating monsters in line with the Monster Manual, replacing the faulty instructions in the DMG.

Along the way, I think we can streamline the process. The Dungeon Master’s Guide has 9 pages on monster creation. I think we can fit the key rules on one page. Or even a business card. That way, you can create new monsters on the fly, not as a laborious game prep chore.

Here’s the finished business card! The rest of this post will explain how we came up with it.

Card front:

Card back:

If you prefer everything calculated out, here’s a one-page version with more explanation and an example

First of all, to reiterate what I learned in previous posts:

1) real monsters have fewer hit points and do less damage than those created by the DMG chart, and are more accurate

2) there is no significant correlation between any major monster stat (HP, AC, attack bonus) and any other stat. For instance, you might expect that a monster whose AC is high for its Challenge Rating should have lower hit points, attack bonus, or damage output to compensate. That’s not the case. Therefore, we can examine each monster stat separately without having to consider the others at the same time.

attack bonus

Here’s a scatter plot of the attack bonuses of all the Monster Manual and Mordenkainen’s monsters. The black line is the best fit line. (For comparison, the red line is a plot of the Dungeon Master’s Guide suggested attack bonuses.)

As you can see, the scatter plot shows us a nice, straight, easily graphable best-fit line. It works out to almost exactly:

attack bonus: 4 + 1/2 CR

So tidy! It’s almost as if the designers designed it that way! Hint: I think they did. While the DMG graph is arbitrary and inaccurate, actual monster design shows signs of being very carefully put together.

A note about CRs below 1: These complicate things. For the purposes of drawing graphs, think of them as negative numbers instead of fractions: CR 1/2 is really 0, CR 1/4 is -1, CR 1/8 is -2, CR 0 is -3. That’s the way that the linear values on the attack graph work out, and the way I’ve graphed it.

How much leeway do we have to adjust the attack bonus up or down based on our concept? The DMG advice is to adjust as much as you want, you can always adjust the CR later. We don’t want to adjust anything later! We’ll just look at our Monster Manual data and see how much variation there tends to be from the average monster accuracy.

For our attack bonuses, the average variance (which is a statistical calculation for determining how closely grouped numbers are) is low: 1.22. In other words, monster attack bonuses tend to be a little more than one point away from the average. And, as we’ve proved in previous steps, there is no correlation between high/low attack bonus and any other monster stat. So we could say, without doing too much violence to the Monster Manual data, something like, “Based on your monster concept, you may add or subtract up to 2 points from the attack bonus without affecting its CR.”

DC

Difficulty Class is similarly neat. In fact, its graph is nearly identical to the attack bonus (nearly every monster’s DC is their attack +7). In the following scatter plot, blue X’es are DC, and green triangles are attack bonus.

The DC best-fit formula is

DC: 11 + 1/2 CR

Variance is also the same for DC as it is for attack bonus. So on our final rules, we’ll say, “+-2 DC based on monster concept.”

Armor Class

From the scatter plot, Armor Class also looks like a fairly neat linear graph.

Expressed as a formula, this is very tidy: AC = 13 + 1/3 CR

From looking at the scatter plot, you can see that there will be a higher variance in AC than there was in attack and DC. The average variance is 1.65: 50% more than in attack and DC. Therefore, if we say “+-3 AC based on monster concept” we’d be allowing all but a few outliers.

hit points and damage

I did attack bonus, DC, and AC first because they were the easy ones. The remaining values, average damage and hit points, are a bit hairy, because they’re not nice, neat linear graphs.

Here’s one interesting thing about hit points and damage: they have a very strong relationship, especially at low level. Take a look at this chart where I graph median hit points (blue) and median damage x 3 (red).

To me it kind of looks like the average monster’s hit points is intended to be 3x the average monster’s damage (or, to put it another way, each monster should survive exactly three rounds of hits against one of its peers). Given the fact that the D&D designers have frequently mentioned three rounds as their target combat length, this seems plausible.

I admit, something about the chart above gave me pause. At high CR, doesn’t it look like there is an inverse correlation between damage and hit points? At CR 19 and 21, for instance, where damage is high, hit points are low. Did I miss something in my earlier analysis that showed no such correlation?

After looking at this graph, I did a more thorough statistical analysis. A note about my methodology: I calculated p-value for each pair of stats (above-median damage AC vs below-median HP, etc) and also for each stat paired with the presence of major special defenses, major special attacks, and legendary status. No correlation was significant to a value of p = .05. However, some more confident statistician should re-check my values with the Monster Manual dataset, since I’m not really a stats guy, just a guy with access to free web stats tools.

In particular, the seeming correlation we see on this chart, high damage to low hit points, does exist but is statistically insignificant: in the monster population as a whole, of the 227 monsters who deal higher-than-median damage, 101 have under-median hit points and 96 have above-median HP: a difference of 5 monsters either way. But some of the similar monsters happen to be clumped together. For instance, it just so happens that three low-HP, high-damage monsters are grouped together at that big red spike at level 18. I think we just have to say that, at high levels, our data is sparse and unreliable and we are going to have to be careful not to over-model the ups and downs of the graph.

At low levels, though, where we have dozens of monsters per CR (and where D&D play actually happens), I do want to be as faithful to the data as I can.

Take another look at the graph above and then listen to my crazy plan. Hit points and damage x 3 look pretty damn correlated: The correlation may or may not be intentional, but it’s there. Maybe we can come up with one trend line that will describe both hit points and damage?

Here’s that graph again, with my proposed best-fit threading the needle between the hit points and damage line. The data isn’t linear at low CRs, but high CRs are linear enough.

Here are the formulae for average damage and hit points:

Average damage below CR 1: 1, 3, 5, 8
Average damage between CR 1 and 7: 5 + (CR x 5)
Average damage above CR 7: CR x 5

Average hit points: 3x average damage for that CR

Unlike for AC, DC and CR, variance increases quite a bit for hit points and damage as the numbers get bigger. Take a look at this damage scatter plot, which sort of explodes into confetti once we get to the airy heights of CR 10.

For both hit points and damage, we can say Increase or decrease by up to 50% based on monster concept and get all but a few outliers.

Shouldn’t such a big increase or decrease – for instance, bumping a monster from 100 to 50 or 150 HP, or from 30 damage to 15 or 45 damage – change its CR? Perhaps it should, but it doesn’t in the corpus. There are plenty of examples of monsters with wildly varying hit points and damage potential sitting next to each other in the same Challenge Rating – without any other attributes which obviously compensate for the differences. Consider Geryon and the ancient green dragon, both CR 22.

Geryon: AC 19, HP 300, attack +16, damage per round 97
Ancient green dragon: AC 23 (+4), HP 385 (28% higher), attack +15 (-1), damage per round 151 (55% higher)

It’s wacky, but it’s how CR currently works. And I’m trying to describe CR here, not improve on it.

We need to do one other thing before we leave the topic of damage: on our new, improved monster-creation rules, we have to explain our average damage calculations so that people can turn each monster’s raw damage total into arbitrarily complex sets of attacks, including spells, area attacks, and limited-use abilities. This will be hard to explain concisely and clearly, but let’s take a shot at it.

Here’s a first draft: “Damage: This is the average damage that a monster can do each round during the first three rounds of combat. Assume 1) it always uses its most damaging attack(s) or spell which hasn’t yet been exhausted; 2) all area attacks target 2 enemies; 3) auras and similar traits target one enemy per turn; 4) variable-length effects like Swallow last one turn; 5) all attacks hit; 6) all opponents fail saving throws. Based on the monster concept, the monster’s damage may be dealt in one attack, or be divided between multiple attacks and/or legendary actions.”

This encapsulates the rules as described in the DMG. There’s one problem with these rules though. They’re facing the wrong way. They’re the instructions to take a Monster Manual creature and turn it into a single damage number. We need the instructions to take a single damage number and turn it into a Monster Manual creature. How about this:

Damage: This is the damage budget for all the monster’s attacks. Limited-use (daily, recharge, or situational) attacks do 4x the damage budgeted. Multi-target attacks do ½ the damage budgeted. Limited-use multi-target attacks do 2x. All other damage sources are 1 for 1, including at-will and legendary single-target attacks, auras, reactions, and variable-length effects like Swallow. If a monster has several at-will options (such as melee and ranged), the lower-damage options are free.

Here’s an example of how you could spend a damage budget on several attacks. Let’s say you imagine a fire-using spellcaster. You give her a 1/day fireball for 28 damage (spending 14 points of the damage budget); an at-will Fire Blast against one target that does 11 damage (spending 11 damage); and, to round it out, a 3-damage dagger attack (free because it’s an at-will option that does less damage). That would cost us 25 damage: right on the nose for a CR 4 creature. But because of the variance in damage, she could be pegged as anything between a strong CR 2 (on par with a pentadrone) and a very weak CR 10 (on par with a CR13 rakshasa).

monster traits

Nearly every monster, except for beasts and some boring humanoids, have some “schtick:” some special trait that makes them unique. It’s hard to quantify these. The DMG tries: it offers two pages of traits, listing the modification that should be made for each to the effective HP or AC. Most of these minor modifications, by the DMG rules, are worth a fraction of a CR. Given the wild fluctuations in power of same-CR creatures, this is illusory precision (I talk more about that here).

We can test common and seemingly powerful traits like legendary resistance and magic resistance and in almost all cases, the presence or absence of these traits has no correlation to higher or lower monster statistics. Therefore, they are not visibly affecting a monster’s CR. The only verifiable exceptions, as I mentioned here, are regeneration (which has a negligible but real effect, reducing some monster HP a by a few percent) and possession (which has a large effect, halving hit points) and possibly damage transfer. I think we can turn these three cases into a general rule: you may reduce damage-avoiding monsters’ hit points by the amount of damage you expect them to avoid over 3 rounds of combat.

what about saving throws?

I think we can improve on the original DM’s Guide rules in another way. The DMG chart has values for proficiency bonus, AC, HP, attack, damage and save DC. Monsters also need to make saving throws. Really, what we want to know is, “what does a saving throw look like for a monster’s good stat?” and “what does a saving throw look like for a monster’s bad stat?”

The bad saving throw is easy. It can be anything based on the monster’s story! For instance, the tarraque’s Dex save is +0.

For the good saving throws: calculating this was an afterthought and I didn’t feel like manually entering the good saving throws for the entire Monster Manual. I decided to see if a sample would be enough. I manually entered the best saving throws of all of the monsters up to page 84 of the Monster Manual, right before the start of the Dragons entry. I also added the ancient red dragon, so I could get the good saving throw of the strongest non-thought-experiment monster in the game. Based on how the data looked, I’d see if I had enough information or if I needed more. Here’s what I got.

This data is clearly tightly-grouped and linear: I don’t need any more sample to see that. It’s a hair off of 1 point of saving throw bonus per 2 levels. This formula will always keep us within about half a point of the real value:

3 + 1/2 CR

And the eye test tells me that variance is very low. I’d estimate it at +- 2. That is to say: the saving throw bonus column is equal to the Attack Bonus column minus 1.

By the way, 3 + 1/2 CR also works for a monster’s good skills!

putting it all together

OK, now we have everything we need to make a complete chart replacing the one in the Dungeon Masters Guide! This will give us out-of-the-box numbers that closely match the Platonic ideal of a 5e monster of any CR. Just tweak according to taste, add a special ability or two, and you are good to go. This is something you can do live at the table, not as part of your game prep!

Here’s the finished chart:

And here’s a PDF that you can print out and put in your DMG.

And if you want something really compact, here’s the important rules on a business card:

(front)

(back)

Categories: Tabletop Gaming Blogs

jeremy crawford talks about monster design

Fri, 07/27/2018 - 14:59

I’m pretty close to finishing up my monster design guidelines based on reverse-engineering the Monster Manual. Before that, though, I want to comment on an interesting episode of DM’s Deep Dive in which Mike Shea (Sly Flourish) interviewed D&D lead rules designer Jeremy Crawford about monster design.

Mike asked Jeremy about the table in the DMG for homebrewing monsters. It’s public record that I have my doubts about that table. Jeremy provided this interesting fact: apparently, the canonical formula for determining monster CR is encoded in an internally-used Excel spreadsheet. (We’ve seen this spreadsheet in action in the Mike Mearls Happy Fun Hour.) The table in the DMG was made after the spreadsheet, and was an attempt to reverse-engineer and simplify the spreadsheet’s formulas for DM’s home use: it’s not used as part of the process for creating for-publication monsters.

My research indicates that while D&D monster stats are internally consistent and carefully designed, their power levels don’t line up well with the DMG chart. This leads me to believe that the spreadsheet does what it intends to do, while the DMG chart does not.

I invite you to ponder this further mystery from the Deep Dive podcast:

In the podcast, Jeremy Crawford talked about how the D&D team approaches what he calls “action denial” attacks: paralysis, charm, etc. This is something I’ve wondered about. My initial research suggested that these attacks didn’t have much of an effect on CR, which I though was strange: taking out a combatant for a few turns seems like it should be a powerful ability.

Jeremy used paralysis as an example to illustrate the team’s approach. First, find the lowest-level spell which inflicts a condition. For paralysis, that’s Hold Person. Next, you translate that into damage by finding the damage output of the simplest pure-damage spell of that level. Hold Person is level 2, and its comparable damage spell is Scorching Ray, which does 6d6 (21) damage. Thus, the ability to paralyze is worth 21 “virtual” damage for Challenge Rating calculation purposes.

I see the logic in that, but it doesn’t scale the way I’d expect it to. If you’re fighting four opponents, I’d expect the ability to keep one of them paralyzed to be worth, say, 33% extra virtual hit points (the hit points you won’t be losing to the paralyzed opponent) – or some similar scaling benefit. If the ability is expressed as flat damage, 21 hit points damage is dominant at low levels and negligible at high levels.

And indeed, when checked against monster data, it doesn’t seem as if monsters are balanced exactly as Jeremy describes. Check out the chart below. This includes all ten CR-5 or lower monsters with a paralysis attack: the carrion crawler, chuul, ghoul, ghast, grell, pentadrone, mummy, revenant, thri-kreen, and yeti. (Above CR 5, the 21 virtual hit points of paralysis would rarely be relevant to CR because monsters generally have a more damaging attack options.)

In this chart, the blue diamonds represent the average damage output of a monster of each CR from 1 to 5. The red X’s represent the base damage output of paralysis-inducing monsters – without the 21-point “Crawford bonus.” As you can see, the paralyzer damage is very close to average monster damage.

The green triangles represent the average damage of paralyzers, once you take the 21 points of “virtual damage” into account. As you can see, adding this would skew monster damage way too high – doubling their effective damage in most cases! If this damage were really being taken into account the way Jeremy describes, all these low-level monsters would have to have very low-damage attacks – a ghoul with a claw doing 1 damage, for instance – to make room for all that virtual damage.

This is one of those unaccountable situations, like many others that we’ve discovered while investigating how monsters are built, where the WOTC instructions for building a monster don’t match the monsters we see in the manual.

My best guess for why this is: playtesting. It’s possible that monster stats started off skewed and exception-ridden. How could they not? It’s an incredibly complicated system. But then through the public D&D Next playtest, the NDA playtest, the internal playtest, and the good intuitions of the designers themselves, the proud nails were hammered down. Monsters were adjusted until they felt right. The tyranny of the spreadsheet was overthrown by humans, or at least reformed into a constitutional monarchy. And so, while the designers of D&D may be still using an occasionally flawed formula to initially prototype their monsters, they’re compensating for the Excel spreadsheet’s failings in later steps of design.

It’s interesting to compare the designers’ intent (as evidenced by what we know of their monster-design process) to the final product (the monsters in the rule books.)

The intent is to account for everything in a monster’s CR. Hundreds of monster traits are weighed to the fraction of a CR. Changing one stat has a ripple effect on other stats. As Jeremy said in the podcast, they’re still using the same Excel spreadsheet that they’ve been using for five years. I’m a programmer and I know what that means. Complication is added to complication, all adding up to the illusion of precision. No one really knows how it works anymore: look how hard it is to reverse engineer (see that DMG table I’ve been complaining about). From this end of the process, monster design has a baroque, stately, creaking majesty.

The final product, when analyzed, is simple, flexible, and streamlined. Challenge Rating gives a broad bell curve of possible hit points and damage outputs. Tweaking one number doesn’t affect another. A monster’s traits and special abilities have no significant, measurable effect on its Challenge Rating: every monster gets its schtick and they all sort of balance out. From this end, monster design appears to have a flexible, easygoing, organic solidity.

This is a common pattern in tabletop game design. Things start complicated. The more they’re used at the table, the simpler they become. I think Jeremy and the rest of the D&D team are geniuses, but their real genius lies in knowing and respecting the value of playtesting.

Next: the final rules for making monsters

Categories: Tabletop Gaming Blogs

How do you make a legendary monster? and more monster-math lessons from Mordenkainen’s

Thu, 07/19/2018 - 16:47

In my last post, I demonstrated, via too many charts, that the monster-creation math in the 5e Dungeon Master’s Guide doesn’t match the monsters in the Monster Manual. As an example: the average CR 1/4 monster has 13 hit points. The DMG suggests that they should have 43 hit points. Imagine your level-1 party mobbed by skeletons with 43 HP each instead of 13!

In my next post, I’ll be offering a chart to replace the one in the DMG, which lets you create monsters on the fly: monsters which are about as dangerous as you’d expect based on their Monster Manual cohort.

In between my last post and my next post, though, we need to do a little more analysis. Do legendary monsters skew the math? And has the math changed in recent D&D monster books, such as Mordenkainen’s Guide?

legendary monsters

Legendary monsters are the conceptual descendant of Fourth Edition’s “solo monster”: a single monster designed to challenge the whole party. If I remember right, solo monsters had 4x the hit points of a standard monster of their level. Are 5e’s legendary monsters’ HP similarly inflated?

There’s not much overlap, but it’s pretty clear that legendary and standard monster HP both fits on the same trend line.

I won’t show all the charts here, but I will tell you this: legendary monsters have basically the same armor class, hit points, attack bonuses, and save DCs as their non-legendary counterparts. The only chart that looks interesting, at first blush, is damage:

Legendary damage looks higher, right? But actually I think something else is going on. Dragons. They’re an outlier, with high stats in general: both high hit points and damage for their CR, plus a host of beneficial traits such as Legendary Resistance. Let’s break the legendary creature damage into dragons and non-dragons.

There are not a lot of non-draconic legendary monsters in the Monster Manual, but their damage totals (the green triangles) are on the same trend line as the standard monsters. The dragons form their own trend line, hovering threateningly over the other monsters.

So, in general, legendary monsters have the same stats as any standard monster. How is a legendary monster different?

Legendary monsters are more interestingly built. They have off-turn legendary actions. They may have lair actions. Some, but not all, have Legendary Resistance, so they can’t be shut down with one spell. But, apart from the dragons, they have the same hit points, damage per round, and other game statistics as any other monster of the same Challenge Rating.

Mordenkainen’s Guide

Our charts look plausible so far, but we’re hampered, especially at high level, by low sample size. Enter Mordenkainen’s Guide. Mordenkainen’s is notable because it’s chock full of high-level and legendary monsters: it contains as many CR 8+ monsters as the Monster Manual does, doubling my sample size for high-level monsters. (There are, of course, more monsters in Volo’s Guide and other sources, but I haven’t charted them yet.)

But are monsters in the Monster Manual and Mordenkainen’s comparable? Has monster design changed drastically in the four years since the Monster Manual was released?

First of all, how do Mordenkainen’s Guide hit points look compared to Monster Manual hit points?

Pretty much the same. In this graph, I’ve broken out the hit points of legendary and nonlegendary monsters from Mordenkainen’s so we can check our work from above: legendary monsters don’t have more hit points than other monsters. In fact, if anything, they have slightly fewer. Furthermore, the general hit point trend is the same for Monster Manual and Mordenkainen’s monsters.

I’ll skip over some other uninteresting charts: the long and short of it is, Mordenkainen’s Guide monsters have roughly same ACs, attack bonuses and save DCs as Monster Manual monsters of equal CR.

I do want to take a closer look at monster damage from Mordenkainen’s, however.

Here I’m graphing average Monster Manual damage/CR against Mordenkainen damage/CR. I’ve broken the Mordenkainen data into legendary and nonlegendary just to confirm that there is no significant difference between them. Mordenkainen damage is on par with Monster Manual damage. (Except for that spike at CR 18: that’s the sibriex, possibly the highest-damage-per-round monster in D&D except the tarrasque.)

Nevertheless, there is one statistical difference between the Monster Manual and Mordenkainen’s Guide damage that this chart doesn’t show.

The *standard deviation* – distance from the average – is much higher in Mordenkainen’s.

For the 75 CR 8+ monsters in MM, and the 75 CR 8+ monsters in Mordenkainen’s, the average standard deviation in the MM is 16, even including dragons, and in Mordenkainen’s it’s 21.

That means that high-level Mordenkainen’s Guide monster damage is 30% farther away from the norm compared to the Monster Manual. There is a little less predictability in how powerful a monster is given its CR. This may be a function of the increased complexity of the newer monsters. It may also be a sign that the game’s designers don’t care as much as they used to about adhering very closely to monster-creation guidelines. There’s more art and less math in Mordenkainen’s Guide.

Art is good. That said, there’s something to be said for consistency. Therefore, as a public service, here’s some monsters in Mordenkainen’s to watch out for if you want to avoid a TPK that surprises everyone, including the DM.

The Sibriex: this monster can drop 200 HP a round at CR 18, just about double what you’d expect from a CR 18 monster.

The Duergar Despot, CR 12: the despot fires the equivalent of two full-scale Lightning Bolts per turn. He can do 72 HP of damage to each PC he hits, which, in enclosed tunnels, may very well be all of them.

The Star Spawn Mangler, CR 5: on round 1 it can do 90 damage, all to the same enemy. A level 5 fighter may have 45 HP. DM and player alike may be surprised to see that front-line fighter not only dropped, but killed, during a surprise round, against an equal-CR opponent. Compare the Mangler’s damage to Geryon, the CR 22 legendary duke of Hell, who can do 77 damage on round 1. (Note: On round 2, the Mangler is useless. That’s how it’s balanced.)

Well, that ends my deep dive into… wait, you know what? let’s look at just one more delicious chart. Maybe two tops.

Challenge Rating and monster traits

One of my findings that surprised me the most from my examination of the Monster Manual was that a monster’s resistances and immunities don’t affect its hit points and damage. The DMG claims they affect hit points, and you can certainly find some MM monsters, like the wraith, who have lots of resistances and who have lower than average hit points. But those are balanced by other high-resistance high-hit point monsters.

Let’s look at the hit points of monsters with a lot of resistances and immunities in Mordenkainen’s.

There is no significant difference between the hit points of the general population and those monsters with 8 or more resistances and immunities!

There must be some traits that affect monster stats. Let’s look at regenerating monsters. We’d expect them to have lower hit points.

Finally, a correlation! Monsters with regeneration have lower max hit points than the general population – as we’d expect them to, since regeneration 10 over 3 turns should be worth 30 hit points.

Here are the monster traits which seem to have any noticeable correlation to stats:
Regeneration: Hit points lowered by 30 or more
Possession: Hit points halved
Damage transfer: With no degree of confidence because there are so few examples in either book, this may lower hit points or damage.

And that’s all I’ve found so far that makes any difference. The abilities to stun, charm, paralyze, or petrify don’t seem to make a difference to HP or damage, nor does magic resistance, legendary resistance, superior invisibility, or any of the other traits listed in the DMG – at least not enough to move the needle. That will all be useful information when we get to designing monsters.

I hope you enjoyed my descent into statistical madness! I want to point out here what I hope is obvious: I think 5e is great and I’m not looking to ruin anyone’s fun by examining its math. I just like figuring out how good things work, and, if possible, making them better.

In a few days I’ll deliver that much-promised build-a-monster-on-the-fly chart.

Categories: Tabletop Gaming Blogs

the 5e monster creation guidelines are wrong

Sat, 07/14/2018 - 23:11

While messing around with monster creation, I started comparing 5e Monster Manual creatures with the 5e guidelines for creating monsters (DMG page 274). Based on my number crunching, it looks like the DMG’s central monster creation chart, “Monster Statistics by Challenge Rating”, isn’t in line with the Monster Manual, and if you try to follow it you will get monsters that don’t look much like Monster Manual monsters.

This may be widely known and only new to me, but I haven’t found anything definitive or official on it. A fairly cursory search only turns up a few argumentative message board discussions and some pretty good Howling Tower posts (such as https://koboldpress.com/howling-tower-monster-stats-part-2/ where Steve Winter graphs the discrepancies but backs off the conclusion that the DMG chart is incorrect.

In this post, I’ll try to show the data that suggests to me that the chart is wrong.

Note: the process of creating a monster stat block is long and convoluted: according to the DMG it’s a 20-step process (!) and one of the steps involves executing another 4-step process detailed elsewhere. So there’s lots of room for error, and I could have a lot of things wrong. But the basic process is: figure out the monster’s Defensive CR, which is primarily determined by HP but modified by AC, resistances, and some traits; figure out its Offensive CR, which is primarily determined by average damage over three rounds of combat, modified for burst damage, area of effects, and various traits and abilities, and also by attack bonus or spell save DC; and then average the offensive and defensive numbers to get the final CR.

Hit Points

The first clue that the DMG​ chart is wrong is in the hit points column of the chart. According to the chart, for instance, a CR 1/4 monster has 36-49 HP. However, let’s look at some CR 1/4 monster hit points. Boar, 11 HP. Goblin, 7 HP. Skeleton, 13 HP. Wolf, 11 HP. The CR 1/4 monster with the highest HP is the mud mephit, with 27 HP, still significantly less than the low end of the DMG-suggested hit point range.

Here’s a chart of the DMG-suggested Hit Points versus the average hit points per level from the Monster Manual: purple bar is the DMG’s Hit Point recommendations by CR, blue bar is the actual average HP from the Monster Manual.

That weird dip at CR 18 is because the demilich is the only CR 18 monster. And in fact, there are so few data points above level 10 that any analysis above level 10 should be taken with a grain of salt. Even ignoring the demilich and the dearth of high level data, you can see that the Monster Manual Hit Points skew way low.

The DMG monster creation rules have lots of adjustments to be made: monsters with lots of resistances and immunities are to have their “effective HP” adjusted upwards; and defensive abilities, such as damage transfer, regeneration, or magic resistance also adjust the effective HP. However, on examination, these adjustments don’t actually account for the extra HP in the DMG chart. In fact, they don’t do much at all. Examine the following chart:

In the chart above, “mm no defenses” means those monsters with few resistances and no significant defensive abilities. You’d expect these monster to have the highest hit points. “mm low resistance” are the monsters with few resistances, whether or not they have defensive abilities. “mm high resistance” means those monsters with more than 3 resistances or immunities: you’d expect these monsters to have the lowest hit points. (Many of these bars are broken because there are CRs at which there are no monsters which meet these qualifications.)

In fact, below level 12 – where we have enough data points to do reasonable analysis – there are no significant hit point differences between monsters with high special defenses/resistances/immunities and those without. At high levels, it is plausible that high-immunity monsters may have lower hit points, though we really need more data points to be sure. However, the overall trend lines are clear: none of these groups of monsters has anything like the hit point totals recommended in the DMG – even the no-defense brutes.

Conclusion: In the Monster Manual, hit points are much lower than the values presented in the DMG. Furthermore, special defenses, resistances and immunities don’t seem to be related to hit points.

Armor Class

Now let’s add armor class into the analysis. In the DMG, hit points and armor class are both used to determine “defensive CR” so perhaps it doesn’t make sense to analyze one without the other.

First of all, a simple analysis of real Monster Manual AC versus expected DMG AC.

Apart from high levels, Monster Manual and DMG ACs are close: usually within a point of AC.

Could Armor Class solve our Hit Point problems? Perhaps low-AC monsters have proper DMG Hit Point values?

Here is a chart of the average hit points of monsters grouped by AC.

“Low ac hp” is HP of the monsters with AC lower than the DMG AC value. You’d expect these guys to have high hit points. “High ac hp” have higher than average AC and theoretically should have lower than average hit points. “Target HP” are the monsters whose AC exactly matches the DMG AC expectations.

As you can see, below level 11, there is no significant difference in HP between those monsters with high and low HP. Above level 11, things are swingy as usual because of fewer data points, but there is no obvious through line that suggests that there is any relationship between AC and HP.

Conclusion: In the Monster Manual, AC values are on par with those presented in the DMG. Hit points and AC do not seem to be correlated in any meaningful way.

Damage

It takes quite a few steps to calculate a monster’s “average” damage according to the instructions in the Monster Manual. The process is: figure out the average damage for the first 3 rounds of combat. Assume that all monster attack hits and all hero saving throws fail. All area attacks hit two people, and all ongoing effects (like being swallowed) last for one turn. Effects like Charge or Pounce happen once.

After all these calculations, here are the Monster Manual average damages by CR, compared to the DMG expectations.

(The gap in the blue line is for the demilich, the only CR 18 monster, whose max damage is hard to calculate.)

The Monster Manual damage is fairly close to the DMG expectation, though generally 10% to 20% low. This is odd: Monster Manual hit points are too low according to the DMG rubric, and damage is low too? It seems as if Monster Manual monsters are just weaker than the DMG suggests. But let’s do some further analysis to damage.

Perhaps monsters have a higher “effective hit points” because of special attack modes. If this is the case, those monsters with special attack modes should have lower hit points than simple monsters. To test this, I’ll separate out those monsters with powerful attack modes that don’t do direct damage, like charm, stun, paralysis, and instakill abilities.

As usual, below level 11 where we have the most data, there is no damage difference between monsters with and without special attack modes. At high levels, there are variations, but there is no clear winner.

Maybe there is some relationship between damage and hit points? Perhaps monsters with lower hit points do higher damage, and vice versa?

To test this, I’ll graph the damage dealt by below-average-HP monsters and above-average-HP monsters separately.

Again, below level 11, there is no difference at all between the damage output of beefy and glass-jawed monsters, and at high levels the correlation isn’t clear. If anything, there may be a slight reverse correlation with beefier monsters doing more damage.

Conclusion: The damage output of Monster Manual monsters is slightly lower than the DMG expectations. It’s not correlated with special attack modes or with hit points.

Attack bonus

We have another important value to look at: attack bonus. How do the monster manual attack bonuses compare to the DMG values? And do they correlate to any other monster stats?

First of all, the attack bonus numbers:

Attack bonuses are WAY off. Monster Manual values are consistently too high compared to DMG values throughout – as much as 5 points too low at level 24 (+12 vs +17).

This is starting to make sense. I think the DMG values are an early draft of the monster formulae. I bet that at some point, the developers decided that they needed to raise the accuracy and lower the damage of monsters, aiming for the same total damage. The DMG chart never got updated.

While we’re here, let’s just check for a few more correlations. Do high-accuracy monsters have lower damage output, or have fewer hit points? My guess is no, since we’ve hardly found any correlations yet.

Not only does attack not balance anything out, there may be a reverse correlation: hi-accuracy monsters also tend to be slightly higher-damage and higher-hit point than normal. In other words, within a given CR, some monsters are better all-round than others.

Conclusion: Attack bonus in the Monster Manual is way lower than in the DMG chart, and doesn’t correlate with any other monster attributes.

Save DC

Since we’ve come this far, we might as well look at the last column in the DMG chart: save DC.

The save DCs in the Monster Manual are quite different from those in the DMG chart. The DMG DCs are much flatter, ranging from 13 to 23, while the actual DCs range from 10 to 24. I don’t think I need to do a lot of analysis on DCs.

Now what?

It seems clear to me that the Monster Statistics by Challenge Rating isn’t the up-to-date version of the monster creation formulae. I bet it was accurate as of some iteration of D&D Next and never got fully updated.

It’s also apparent that there is not a lot of correlation between any monster stat and any other stat. All the complicated DMG steps involving adjusting and averaging don’t actually hold up to examination when we look at the Monster Manual monsters. The actual process seems to be something like

1. Start with appropriate numbers based on CR
2. Adjust any stat or two up and down, and add any trait or feature, based on story. Don’t make any further adjustments.

Which is great for us! This two-step system is way easier than the 20-step DMG version. We can even do it on the fly! All we need is an accurate CR-to-statistics chart.

Give me a few days: I’ll try to come up with a new monster-creation chart that will match Monster Manual monster math, and that is small enough to fit, say, on a business card.

In the meantime, here is a copy of the monster-stat TSV file I used to generate these tables. Please feel free to validate the monster stats, validate or invalidate my calculations, correct my assumptions, prove me wrong, or whatever else you want to do with this stuff.

Categories: Tabletop Gaming Blogs

How many magic items should the party have at each level?

Thu, 07/12/2018 - 18:35

If you’re playing by-the-book 5e D&D, how much magical treasure is a party likely to find? Is it less than other editions? Is that wererat’s immunity to normal weapons a big deal?

The DMG and Xanathar’s Guide offer some guidance: “Over the course of a typical campaign, a party finds treasure hoards amounting to seven rolls on the Challenge 0-4 table, eighteen rolls on the Challenge 5-10 table, twelve rolls on the Challenge 11-16 table, and eight rolls on the Challenge 17+ table.” That’s 45 rolls, roughly two per character level: three per level at CR 5-10, because level advancement slows there because that’s the game’s “sweet spot”. (I’m assuming that most fights are intended to be against a CR equal to character level, which may be a big assumption, but which looks borne out by this treasure distribution.)

Xanathar’s Guide has a further table, Magic Items Awarded by Tier, which specifies the number of major and minor items the party should expect to collect. For instance, during character levels 1-4, it says the party is supposed to accumulated 9 “minor” items (mostly expendable items like potions and scrolls, plus a few low-power permanent items) and 2 “major” items (like magic swords and shields and ioun stones and the like). During character levels 5-10, the party should find 28 more minor items and 6 more major items.

Because I like to check math, I decided to, well, check the math, and I found that the Xanathar’s chart is close to, but not 100%, accurate. For example, let’s take the number of major items collected during levels 5-10. Xanathar’s says 6 items will be accumulated over 18 treasure rolls. Let’s compare this to the Dungeon Master’s Guide treasure tables.

In one treasure roll for levels 5-10,, you have a 14% chance of getting 1d4 items from Magic Item Table F (an expectation of .35 items), a 4% chance of getting 1d4 items from Magic Item Table G (an expectation of .1 items), and a 2% chance of an item from Magic Item H (.02 items). Over 18 rolls, that’s 8.46 major magic items. Not a big difference from 6 – 40% off, which is in the ballpark – but if the Xanathar’s table is at all useful to you, you may like to have a more accurate version of the table.
My more detailed (broken down by level) and accurate chart is below.

I’ve also added a column for Magic Weapons: this is how many of the party’s major items can be expected to be magic weapons, based on the percentage of magic weapons on each treasure table. This is useful if you want to know, for instance, how big of a deal it is that gargoyles are resistant to, and lycanthropes are immune to, nonmagic weapons.

Magic Items Accumulated By Level

Level Minor Major Magic Weapon 1 2.75 .75 .21 2 5.5 1.5 .42 3 8.25 2.25 .63 4 11 3 .84 5 14.4 4.85 1.29 6 17.8 6.7 1.74 7 21.2 8.55 2.19 8 24.6 10.4 2.64 9 28 12.25 3.09 10 31.4 14.1 3.54 11 35.5 15 3.76 12 39.6 16 3.98 13 43.7 17 4.2 14 47.8 18 4.42 15 51.9 19 4.64 16 56 20 4.86 17 60.85 21.6 5.38 18 65.7 23.2 5.9 19 70.55 24.8 6.42 20 75.4 26.4 6.94

The discrepancy in numbers between my chart and Xanathar’s may be nothing more than rounding error in the Xanathar chart: despite different estimates per level, we end up in the same place. Xanathar’s Guide says that over 20 levels, a party will find “roughly one hundred items.” According to my calculations, the party should find 101.8 items – pretty damn close to 100. Of these, 75 will be minor items, and only 7 will be magic weapons.

Conclusion 1: Use my chart instead of Xanathar’s if you are a fan of unnecessarily high precision.

Conclusion 2: Magical treasure is given out rather sparingly in 5e, apart from minor items, which are given out like candy. Let’s take a 6-person party, three of whom are weapon users. Each character won’t have his or her own major item until level 6, and all three weapon users won’t have magical weapons until around level 9. That means that that CR 2 Wererat (or CR 1/2 jackalwere), will probably be an annoyance for some time.

Caveat: This treasure distribution doesn’t match my game, and it probably doesn’t match yours either. In fact, it may not match any real-world game at all. Are there any DMs who provide purely random treasure, and at the by-the-book rate of distribution? I know that when I DM, the monsters drop minor magic items at a much lower rate, and major items at a much higher rate. Another DM may be much stingier than me. But if you are striving to play by-the-book, this may help you.

Categories: Tabletop Gaming Blogs

spellbook PDFs for all the Monster Manual monsters and npcs

Mon, 06/04/2018 - 14:10

I made a new utility for DMs: HTML and PDF spellbooks for every Monster Manual monster.

If you’ve ever tried to DM a monster who uses a lot of spells – a lich, say, or an archmage – you’ll know that it is no picnic. Trying to pick out the lich’s next turn involves flipping through several spells in the PHB or in D&D Beyond. It sure would be nice if all the monster’s spells were presented together so you could just scan the page!

That’s what this tool is. Every spellcasting MM monster from angel (deva) to yugoloth (ultroloth) has its complete spellbook, in either HTML or PDF format, available here.

Also, I added a feature where you can login and design your own monster or NPC spellbooks. Just type in the name of a spell and the full text of the spell appears in the spellbook. You can also write up custom spells.

This utility was a real lifesaver the other night, when I was DMing a game. Midway through the battle, one of the players cast a Silence spell on my custom NPC necromancer. Normally this is a HUGE pain. You have to look up every single spell to check which ones don’t have a verbal component. Instead, I was just able to scan the PDF and quickly see how many spells the necromancer could still cast: none. All of his spells had verbal components. He was completely hosed.

Here’s that link again: The 5e Spellbook: Printable spellbooks for all the Monster Manual monsters

Categories: Tabletop Gaming Blogs

combined challenge-rating index for Monster Manual, Volo’s, and Tome of Foes

Mon, 05/21/2018 - 15:25

Back when 5e first came out, I made a one-page index of all the Monster Manual monsters, sorted by CR, with page numbers for each monster. Oddly enough, the Monster Manual didn’t have such an index!

Since I made it, I’ve found it insanely useful. I keep the PDF on my phone, and I have a copy taped to the inside back cover of my Monster Manual. I’ve used it before and during every D&D session I’ve run for the past 4 years.

Over the last four years, WOTC has released two major monster books: Volo’s Guide to Monsters and, as of a few days ago, Mordenkainen’s Tome of Foes. I’ve updated my PDF to include the hundreds of new monsters from these books. The PDF has ballooned up from 1 page… to 2 pages. Not a lot of edition bloat so far. In fact, there was some room left on the second page, so I included encounter-building guidelines distilled from Xanathar’s Guide to Everything. (My D&D group runs a bit hot so I have to throw more monsters at them than Xanathar suggests, but it’s a starting place.)

I hope you find this useful. Since it’s only 2 pages, you can still tape it to the left and right back cover pages of your Monster Manual.

Here’s all the D&D Monsters by CR!

Categories: Tabletop Gaming Blogs