## Challenge Rating (CR) Calculation

## What is Challenge Rating?

A monster's challenge rating (CR) is an estimate of how difficult a monster will be to fight. CR is the average of two more specific metrics: *offensive* CR (the monster's expected damage output) and *defensive* CR (the monster's durability).

The *Dungeon Master's Guide* (DMG) details how to calculate CR in *Chapter 9: Dungeon Master's Workshop* under the heading *Creating a Monster*. This page will be easier to understand if you have access to the DMG.

Keep in mind that CR is not a perfect metric of monster difficulty. CR often ignores features that can have a big situational impact on encounter difficulty. And of course, CR does not take your specific party composition into account when estimating difficulty. All that to say, CR cannot be the only thing you consider when trying to estimate how difficult it will be for your players to fight a particular monster.

On the **Prismatic Dragon Generator** and on this page, we make the distinction between *nominal* CR and *calculated* CR. Nominal CR is the "target" CR of the creature; the nominal CR is listed in the stat block and determines XP and Proficiency Bonus. Calculated CR is the actual average of the offensive CR and defensive CR, calculated as described on this page. A monster's nominal CR and calculated CR should be close to each other (or equal), but that is often not the case.

As explained below, we analyzed the existing published dragon families and discovered that their calculated CRs were almost always higher than their nominal CRs, especially for adult dragons. Given that, we chose to balance the prismatic dragons similarly, so that each prismatic dragon is more comparable to existing dragons of the same nominal CR. Within the *Advanced Options* of the **Prismatic Dragon Generator**, I've included a table which summarizes the generated dragon's CRs: nominal, calculated, offensive, and defensive.

## Offensive CR Calculation

Between offensive and defensive CR, offensive CR is usually the more complicated one to calculate. At the core of offensive CR calculation is the question: how much damage per round will the monster do in expectation, and how difficult will it be to avoid that damage?

### Expected Damage per Round

For a dragon, her best source of damage is almost always her breath weapon. However, breath weapons aren't always going to be available for use due to the recharge mechanic. Thankfully, the DMG tells us how to account for this variability: assume the dragon will have her breath weapon available one turn in every three rounds. On turns the dragon doesn't have her breath weapon available, she will use her multiattack. Add up the expected damage from her breath weapon and two multiattacks, then divide by 3 to get the expected damage per round!

However, this doesn't take legendary actions into account. If a dragon has legendary actions, assume that she uses all of them to deal damage every round. Most dragons have a Tail Attack and a Wing Attack which cost 1 legendary action and 2 legendary actions respectively.

I assume that a dragon will do one Tail Attack and one Wing Attack each round. Without more specific guidance from the DMG, I assume one character will be caught within the Wing Attack and fail the save. Add the damage from Tail Attack and Wing Attack to the expected damage per round.

### Expected Attack Bonus and Save DC

Using the expected damage per round and the Monster Statistics by Challenge Rating table in the DMG, you can identify the dragon's offensive CR, along with the expected attack bonus and save DC for that CR. The DMG tells us to adjust the offensive CR up or down by 1 for every 2 points the dragon's attack bonus/save DC are above or below the expected attack bonus/save DC. However, I'm not satisfied with that calculation.

I want to have one adjustment to offensive CR which takes into account the relative contributions of each source of damage. For each source of damage, compare its attack bonus or save DC to the one expected for this CR. Each source will have its own suggested shift to CR: plus or minus 1 for every 2 points above or below expectation. To determine the overall shift to offensive CR, take a weighted average of the sources' shifts: multiply each source's shift by its damage contribution, add the products together, and divide the sum by the expected damage per round. Keep in mind that Tail Attack and Wing Attack are happening each round, while the dragon's breath weapon is 1 in 3 rounds, with multiattack being used on the other 2 of those 3 rounds.

### Example Calculation

As an example, let's calculate the offensive CR of a typical adult orange prismatic dragon.

Her damaging breath weapon is her Acid Breath, which deals 45 (13d6) acid damage on a failed DC 19 Dexterity saving throw. The DMG tells us to assume 2 characters will be caught in her breath weapon and fail the saving throw. Once every three rounds, the dragon's Acid Breath contributes an expected 90 damage with a save DC of 19.

The dragon's multiattack uses her Frightful Presence (accounted for in her defensive CR calculation), followed by one bite attack and two claw attacks. The bite attack deals 17 (2d10 + 6) piercing damage plus 3 (1d6) acid damage, and the claw attacks each deal 13 (2d6 + 6) slashing damage. In total, the dragon's multiattack deals a total of 46 damage, all with an attack bonus of +11. This multiattack gets used twice every three rounds.

Finally, the dragon's legendary actions are taken into account. The tail attack deals 10 (1d8 + 6) bludgeoning damage with an attack bonus of +11, while the wing attack deals 13 (2d6 + 6) bludgeoning damage with a save DC of 19. These legendary actions each get used once each round.

This adds up as follows:

(90 + 46 + 46) / 3 + 10 + 13 β 83.67

This corresponds to an offensive CR of 13, which has an expected attack bonus and save DC of +8 and 18 respectively.

The breath weapon and wing attack both have a save DC of 19, which is 1 point higher than expectation, so their shift is +0.5.

The bite, claw, and tail attacks all have an attack bonus of +11, which is 3 points higher than expectation, so their shift is +1.5.

Finally, the weighted average of their shifts gets calculated as follows:

(0.5 * (13 + 90/3) + 1.5 * (10 + 46/3 + 46/3)) / 83.67 β +0.986

This rounds to a shift of +1, so this dragon's offensive CR is ultimately 13 + 1 = 14.

## Defensive CR Calculation

Calculating defensive CR is usually simpler than calculating offensive CR. To determine how durable a monster is, we need to calculate the monster's effective Hit Points (HP) and Armor Class (AC).

### Effective HP

Effective HP starts by looking at the dragon's expected maximum HP, which will henceforth be referred to as the dragon's "base HP". Two main prismatic dragon features can contribute to effective HP: Frightful Presence and Legendary Resistance.

If a dragon has Frightful Presence and is expected to fight characters of 10th-level or lower, the DMG tells us to add 25% of the dragon's base HP to her effective HP. I chose to assume that a prismatic dragon can be expected to fight characters of 10th-level or lower if its nominal CR is 17 or lower. Thus, Frightful Presence affects the effective HP total for adult prismatic dragons of the following colors: red, orange, yellow, green, blue, and indigo.

Legendary Resistance requires less guesswork about who will be fighting the dragon. The DMG tells us that the prismatic dragons add 30 HP to their effective HP per daily use of Legendary Resistance. For adult and ancient prismatic dragons, their 3/day uses of Legendary Resistance increase effective HP by 90.

The DMG gives guidance on how to adjust effective HP for Damage Vulnerabilities, Resistances, and Immunities. In my experience however, those modifiers are usually irrelevant to the durability of the prismatic dragons. Here's why I think that.

*Damage Resistance and Immunity.*

Adult prismatic dragons have resistance to bludgeoning, piercing, and slashing from nonmagical attacks, while ancient dragons have immunity to that damage. In my experience, most characters that use weapons have a magical weapon by the time they're facing an adult or ancient dragon.

Prismatic dragons of all ages have immunity to one damage type: the same damage type dealt by their breath weapon. Most characters are able to effectively deal damage of a different type, however.*Damage Vulnerability.*

Each color of prismatic dragon is vulnerable to one damage type. This can occasionally be relevant, and I've found that one party member is usually able to effectively target a prismatic dragon's damage vulnerability. Most of the time however, I don't factor this vulnerability into calculating CR.

If the assumptions made about magic weapon availability and damage type access aren't true for your game, then you should absolutely take these damage modifiers into account when trying to estimate the challenge a prismatic dragon represents.

### Effective AC

Effective AC tries to estimate how hard it is to generally "hit" a monster, whether that's with an attack or another negative effect. There are two relevant traits of prismatic dragons for effective AC calculation: Magic Resistance and saving throw proficiencies.

The DMG tells us to add 2 to a monster's effective AC if it has Magic Resistance, a feature that gives advantage on saving throws against spells and other magical effects. All prismatic dragons have Magic Resistance, so add 2 to their effective ACs.

The number of saving throw proficiencies a monster has determines the bonus to the monster's effective AC. The DMG tells us to add 2 if a monster has 3 or 4 saving throw proficiencies or to add 4 if a monster has 5 or 6 saving throw proficiencies. All prismatic dragons add their proficiency bonus to Dexterity, Constitution, Wisdom, and Charisma saving throws, for a total of 4 saving throw proficiencies. Thus, increase their effective AC by 2.

Based on the dragon's effective HP, you can find the dragon's defensive CR, along with the expected AC for that CR. Compare the dragon's effective AC to that expected AC; for every 2 points above or below the expected AC, adjust the defensive CR up or down by 1.

### Example Calculation

As an example, let's calculate the defensive CR of a typical adult orange dragon.

An adult orange dragon is expected to have a max HP of 187. Since she has the Frightful Presence feature and is expected to face characters of 10th-level or lower (nominal CR of 14), her effective HP is increased by 25% of 187: 46.75. The dragon's 3/day uses of Legendary Resistance add 90 to her effective HP.

The dragon's effective HP is therefore

187 (base HP) + 46.75 (Frightful Presence) + 90 (Legendary Resistance) = 323.75

This corresponds to a defensive CR of 17, which has an expected AC of 19. The dragon's effective AC is

19 (base AC) + 2 (Magic Resistance) + 2 (saving throw proficiencies) = 23

This is 4 points higher than expected, so the initial defensive CR of 17 should be shifted up by 2 for a final defensive CR of 19.

When averaged with the offensive CR of 14 calculated in the previous example, we get a final calculated CR of 16.5

This is 2.5 points higher than the dragon's nominal CR of 14, which is an intentional discrepancy that is typical for adult dragons.

## Things that Don't Affect CR

There may be some missing things that you expected to see included in the above CR calculations. Here are some notable ones, in no particular order.

**Innate Spellcasting**If a dragon can cast a spell which deals more damage than her breath weapon or multiattack, or if she can cast a spell which increases her effective HP, AC, or attack bonus, then that spell should be accounted for in her CR calculation.

The spells available in Innate Spellcasting for prismatic dragons were deliberately selected to be irrelevant to CR calculation. This is true even for white dragons, who can typically cast

*cure wounds*and*guiding bolt*once per day. Casting one of those spells during combat is usually less effective than using breath weapon or multiattack.

**Magic Weapons**The DMG explicitly tells us that this feature doesn't affect CR. If a character has the Heavy Armor Master feat, they may disagree.

**Secondary Breath Weapons**The prismatic dragons have exciting secondary breath weapons with varied effects. However, for CR calculation, it is almost always more beneficial for a dragon to use her primary breath weapon which deals damage.

**Wall of Prismatic Color**A dragon can exert substantial battlefield control by tactically using her wall of prismatic color. However, the wall's damage is easily avoided and situational, so we don't consider it relevant for general CR calculation.

**Change Shape**The DMG explicitly tells us that this feature doesn't affect CR. In my experience, this feature is very useful for exploration and social situations, but it is not effective to use it in combat.

**Variable Radiance/Shadow**Dragons already have darkvision, so glowing with bright light isn't going to be helpful for them. Variable Shadow (a black prismatic dragon feature) can be situationally relevant, but it is easily countered by creating some light.

## Analyzing CR of Existing Dragons

Using the above method for calculating CR, we analyzed the chromatic and metallic dragons. We did this analysis in 2019, well before the gem dragons had been published in *Fizban's Treasury of Dragons*. At some point in the future, we may take a look at CR for gem dragons and add them to this page.

Rather than include a table with all the details, I'll summarize my findings here.

### Offensive vs Defensive CR

Comparing offensive CR and defensive CR for chromatic and metallic dragons reveals their bias between offense and defense. This varies by age, with wyrmlings having roughly equal offense and defense, and young dragons having offense 1 or 2 points better than defense. Adult and ancient dragons are heavily skewed in favor of defense, with a defensive CR that's 2 to 4 points higher than their offensive CR.

### Nominal vs Calculated CR

As I've mentioned earlier on this page, chromatic and metallic dragons generally have a higher calculated CR than their nominal CR. Here I'll break it down by age.

**Wyrmlings**Wyrmlings are different from the other ages in that, on average, their calculated CR is 0.43 points

*lower*than their nominal CR. The extremes are chromatic black (weaker than nominal by 1.0) and metallic silver (stronger than nominal by 0.5).

**Young Dragons**On average, young dragons are 0.5 points stronger than their nominal CR. The extremes are metallic copper (weaker than nominal by 0.5) and chromatic white (stronger than nominal by 2.0).

**Adult Dragons**On average, adult dragons are 3.3 points stronger than their nominal CR. The extremes are metallic copper (stronger than nominal by just 2.0) and chromatic white and red (both stronger than nominal by 4.0).

**Ancient Dragons**On average, ancient dragons are 1.0 points stronger than their nominal CR. The extremes are metallic brass (weaker than nominal by 0.5) and chromatic red (stronger than nominal by 2.0).

## CR of Prismatic Dragons

Finally, given all of that context, here are some key points about how the CR of prismatic dragons was balanced.

### Offensive vs Defensive CR

We want the prismatic dragons to feel legendarily durable while remaining a reasonable overall CR. That's why all prismatic dragons have a higher defensive CR than offensive CR.

### Nominal vs Calculated CR

We generally tried to balance the prismatic dragons such that their calculated CR would be similar to the calculated CR of the metallic and chromatic dragons of the same nominal CR. However, we tried to have less variation within each age group. To summarize.

**Wyrmlings**On average, wyrmlings are 0.35 points stronger than their nominal CR. They range from 0.0 to 0.5 points stronger than nominal.

**Young Dragons**On average, young dragons are 0.5 points stronger than their nominal CR. They range from 0.0 to 1.0 points stronger than nominal.

**Adult Dragons**On average, adult dragons are 2.45 points stronger than their nominal CR. They range from 2.0 to 3.0 points stronger than nominal.

**Ancient Dragons**On average, ancient dragons are 0.85 points stronger than their nominal CR. They range from 0.5 to 1.0 points stronger than nominal.

### Nominal CR Progression

The colors of prismatic dragon have a consistent hierarchy of power. In order of ascending nominal CR, they are: red, orange, yellow, green, blue, indigo, violet, magenta, and white. Black is a special case. They have a longer lifespan, so even though they start at the power level of blue and indigo as wyrmlings, they practically surpass white dragons in power by the time they're ancient.

Thank you for your interest in the prismatic dragons! We hope that this page was helpful and answered any questions you might have about how we balanced the prismatic dragons. If you have any lingering questions, or if you've tried them out and want to send us your thoughts, feel free to send an email to dragons@palladiumturtle.com!