It was a slippery little sucker to nail but
Part 10: Construction: Evaluating CR is now up!
Wonder how it will compare to the DMG? Oh well all I can do now is wait for my DMG to arrive!
Nice work!
As a DM it's really a boon to have this sort of dissection of the monster math, and particularly the CR.
I've decided to use your work to analyze a custom beastie I've put together for my campaign: Smiling Jack (which I eyeballed to be CR 13). I will present my calculations for his Defensive Index, Offensive Index, and Challenge Index below. Once I have my DMG in hand the coming week, I will go back and analyze Smiling Jack's CR using the official guidelines, and see how your method and the DMG method compare.
Here's the homebrew monster (Smiling Jack) that I'm analyzing.
[SBLOCK=Smiling Jack (CR 13?)]
Smiling Jack
Medium aberration (shapechanger), chaotic evil
AC 17 (natural armor)
HP 143 (22d8+44)
Speed 30 ft, swim 40 ft
Str 14 (+2) Dex 16 (+3) Con 14 (+2) Int 16 (+3) Wis 14 (+2) Cha 22 (+6)
Saving Throws Wisdom +7, Charisma +11
Skills arcana +8, deception +11, insight +7, intimidation +11, nature +8, perception +7, performance +11, persuasion +11, stealth +13
Tools (+5) dice, painter's supplies, playing cards, puzzle-boxes
Damage Resistances acid, poison, necrotic, psychic
Damage Immunities cold
Condition Immunities charmed
Feats actor, skilled
Senses darkvision 120-ft (see fine in magical darkness), passive perception 17
Languages speak all languages, telepathy 90-ft
Challenge 13 (XP 10,000); Morkoth Warlock (Great Old One) 15
ROLEPLAYING
Bond. Dagon's Puzzle-Box. Among the many treasures that sunk with La Gloriosa was a puzzle-box which has the power to open gateways to forgotten Abyssal realms; Smiling Jack hopes to recover this puzzle-box in order to free his fellow imprisoned morkoth.
Ideal. Destruction. Like his master, Smiling Jack longs for the primordial days of old, when the land was bare of life and everything lived in the sea, subject to its will. (Evil)
Flaw. Smiling Jack delights in luring victims into a trap from which they cannot escape, whether physically, socially, or morally; even when he has the upper hand, he prefers a convoluted trap to an assured victory.
Personality Trait. Smiling Jack is extremely affable and can find humor in any situation. He also enjoys the latest fashions, no matter how garish, and has a fondness for fine scarves and offbeat art.
ELDRITCH INVOCATIONS
Abyssal Blast*, Agonizing Blast, Devil's Sight, Master of Myriad Forms, Master of the Tides*, Minions of Chaos, Voice of the Chain Master
TRAITS
Actor. Smiling Jack has advantage on Deception and Performance checks to pass himself off as another person, and he can mimic the speech of another person after listening to them for 1 minute.
Amphibious. Smiling Jack can breath both air and water.
Familiar. Smiling Jack has a crab familiar, which he can communicate telepathically with, perceive thru its senses, and speak thru as if it was one of his thrills.
Magic Resistance. Smiling Jack has advantage on his saving throws against spells.
Master of Myriad Forms. Smiling Jack can change his appearance as an action, as per alter self. Maintaining his new appearance does not require concentration. Whatever form he assumes it will always have an obscene creepy smile. His true form is a morkoth, which he reverts to if killed or subjected to moonbeam.
Innate Spellcasting. Smiling Jack casts the following spells (save DC 18, spell attack +11) without material components.
At-will: hypnotic pattern (see below), magic mouth
Once per day: blackwater tide*, glibness, mass suggestion
Rod of the Depths. The rod has 6 charges which it regains at the start of a new day. Smiling Jack can use it to cast control water (6 charges), to induce drowning in a creature (3 charges), to cause ocean water within 300 feet to become to exceptionally clear or murky (2 charges), or cast alter self (aquatic adaptation only) on others by touch (1 charge).
Spellcasting. Smiling Jack casts spells as a 15th level warlock (save DC 18, spell attack +11). He has 3 spell slots of 5th level, and regains his spell slots after a short rest.
Cantrips: eldritch blast, friends, minor illusion, prestidigitation
Level 1 Spells Known: arms of hadar (6d6), dissonant whispers (7d6), find familiar (ritual), tasha's hideous laughter
Level 2 Spells Known: detect thoughts, hold person (4 targets), phantasmal force, suggestion
Level 3 Spells Known: fear, hunger of hadar (2d6/2d6), sending
Level 4 Spells Known: control water (once per long rest), hallucinatory terrain, evard's black tentacles (3d6)
Level 5 Spells Known: conjure elemental (caller from the deeps, once per long rest), dominate person
Thought Shield. Smiling Jack's thoughts cannot be read by telepathy or other means unless he allows it. Additionally, whenever a creature deals psychic damage to him, they take the same amount of damage that Smiling Jack does.
ACTIONS
Multiattack (morkoth form only). Smiling Jack makes a bite attack and 2 claw attacks.
Bite (morkoth form only). Melee weapon attack. Attack: +7 hit, range 5-ft, one target. Hit: 13 (2d10+2) piercing damage, and Smiling Jack may initiate a grapple with a Dexterity (Acrobatics) check. When the creature ends its turn grappled by Smiling Jack it takes this damage again automatically.
Claw (morkoth form only). Melee weapon attack. Attack: +8 hit, range 5-ft, one target. Hit: 6 (1d6+3) piercing damage.
Eldritch Blast. Ranged spell attack. Make three attacks. Attack: +11 hit, range 120-ft, one target. Hit: 10 (1d10+6) damage, and Jack chooses which type: cold, force, necrotic, or psychic. If he deals cold damage, the target's speed is reduced by 10 feet until the start of his next turn. If he deals force damage, the target suffers disadvantage on their Concentration check. If he deals necrotic damage, the target reduces their maximum hit points by the same amount until taking a long rest. If he deals psychic damage, the target cannot take any reactions until the start of his next turn.
Rod of the Depths (costs 3 charges). Smiling Jack points the rod at a creature he can see within 60 feet, and the creature must make a DC 18 Constitution saving throw. On a failed save, water gushes from the creature's mouth and it begin suffocating as if it had just run out of breath; the creature can survive for a number of rounds equal to their Constitution modifier (minimum 1 round). After this time it drops to 0 hit points and is dying. Maintaining this effect requires Smiling Jack's concentration until the target is reduced to 0 hit points.
Create Thrall. Smiling Jack touches an incapacitated humanoid or aquatic beast, and that creature is charmed until remove curse is cast on them or the charmed condition is removed from them. He may have up to 5 charmed thralls. Smiling Jack can communicate telepathically with his thralls, perceive thru their senses, and speak thru them with his own voice so long as they are on the same plane.
BONUS ACTIONS
Aquatic Agility. When underwater in his true form, Smiling Jack can use his bonus action to Dash or Disengage.
Hypnotic Pattern. Smiling Jack can cast hypnotic pattern as an at-will innate spell, though on land the pattern must originate from Smiling Jack. Additionally, he doesn't need to concentrate to maintain it.
LEGENDARY ACTIONS
Smiling Jack can take 3 legendary actions each round, choosing from the options below. Only one legendary action option can be used per turn and only during or after another creature’s turn. Smiling Jack regains spent legendary actions at the start of his turn.
Deadly Lure. Smiling Jack causes any creatures charmed by his hypnotic pattern to move at half their speed (rounded down) toward the pattern, oblivious to hazards en route.
Eldritch Blast. Smiling Jack uses eldritch blast.
Entropic Ward. When a creature attacks Smiling Jack, he can impose disadvantage on the attack. If it misses then Smiling Jack has advantage on his next attack against that creature.
Spell Reflection. When Smiling Jack successfully saves against a spell of 5th level or lower, he can redirect the spell back at its caster (and possibly his or her companions if it was an area effect spell). Spells he reflects function as if cast with a 5th level spell slot (save DC 18, spell attack +11). If dispel magic is successfully cast upon him, he cannot use Spell Reflection against spells of an equal or lower level to the spell slot used to cast dispel magic for 10 minutes.
[/SBLOCK]
* * *
First, what's the target Challenge Index for a CR 13 monster? 207. Plus or minus 10, looks like.
Defensive Index + Offensive Index = Challenge Index
123.70 + 82.62 = 206.32
Wow! Pretty darn close to the target of 207! Assuming I haven't left anything out of my calculations (and that's a big IF).
* * *
Here are all my calculations...
[SBLOCK=Target Challenge Index]
Target Challenge Index = 15.3 x CR + 7.7
= 15.3 x 13 + 7.7
=207[/SBLOCK]
[SBLOCK=Defensive Index]
Defensive Index = (HP + HP_adj) x ((AC + AC_adj + Misc - CR_AC - CR_Misc) x .05 +1) x .5
HP = 143
HP_adj = 0
AC = 17
AC_adj = +2.75 (Magic Resistance) +1 (Entropic Ward) = 3.75
Misc = 16 (summation of saves, skills, damage resistances, and damage immunities)
CR_AC = 16.66 (calculated value)
CR_Misc = 5.4 (calculated value)
(143 + 0) x ((17 + 3.75 + 16 - 16.66 - 5.4) x .05 +1) x .5
= (143) x ((14.69) x .05 +1) x .5
= (143) x (1.73) x .5
= 123.70[/SBLOCK]
[SBLOCK=Offensive Index]
Offensive Index = (Dmg + Dmg_adj) x ((Attack + Attack_adj - CR_Attack) x .05 +1)
Dmg = 76.5 (I have a section below about how I got this damage number)
Dmg_adj = +0
Attack = +11
Attack_adj = +1 (Entropic Ward)
CR_attack = 10.38 (calculated value)
(76.5 + 0) x ((11 + 1 - 10.38) x .05 + 1)
= (76.5) x (1.08)
= 82.62[/SBLOCK]
[SBLOCK=Average Damage (Dmg)]
Rather than rely on a formula here, I ran thru 4 sample rounds of the monster's strategy, using what I felt would be an intelligent and reasonable mix of powers. I ignored attack values & critical hits, simply assuming every attack hits and deals average damage. This gave me a damage value for each round. I then summed up all the damage and divided it by 4 to arrive at an Average Damage (Dmg) value.
Round 1 - Dominate Person, Eldritch Blast (30), Eldritch Blast (30) = 60
Round 2 - Bite/Claw/Claw (25), Eldritch Blast (30), dominated PC's attacks (18) = 73
Round 3 - Hunger of Hadar (14 x 2 targets = 28), Automatic Bite (13), Eldritch Blast (30) = 71
Round 4 - Arms of Hadar (21 x 2 targets = 42), Eldritch Blast (30), Eldritch Blast (30) = 102
(60 + 73 + 71 + 102) / 4
= 306 / 4
= 76.5[/SBLOCK]
