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It seems that if a couatl changes shape into a humanoid, it can get racial features. But if it decides to turn into a variant human and picks the Tough feat, is its level its CR (4) or its number of hit dice (13)? What if it changes into a mage that specifies it's an "x-level spellcaster"? (I know it wouldn't get spellcasting, but if this feat would normally be unavailable for creatures without levels, would doing this give it a usable level?)

This actually probably applies in exactly the same way to the less-complicated situation of "NPC humanoid, what's its level?" but maybe it's different?

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    \$\begingroup\$ Welcome to RPG.SE! Take the tour if you haven't already, and check out the help center for more guidance. \$\endgroup\$ – V2Blast Sep 25 '19 at 1:36
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The Change Shape feature does not work in this way

The Couatl's Change Shape feature states:

The couatl magically polymorphs into a humanoid or beast that has a challenge rating equal to or less than its own, or back into its true form [...]

The Couatl thus cannot turn into a variant human because that is a Player Character race option, and thus does not have a challenge rating.

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    \$\begingroup\$ So when the Monster Manual says you can add racial traits to NPCs(page 342), that doesn't apply to monsters? Is there somewhere that the difference between a monster and an NPC is specified? \$\endgroup\$ – 47948201 Sep 24 '19 at 23:37
  • \$\begingroup\$ @47948201 If that is your question then you should ask that separately. The Change Shape feature is completely separate from doing that. I'm not entirely sure how to phrase such a question though besides the general "What do I do when a feature calls for a Monster's level?" \$\endgroup\$ – Medix2 Sep 24 '19 at 23:52
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    \$\begingroup\$ @47948201 looks at the traits of the humanoids in the Monster Manual. They do not have the same features as the relevant PC race. \$\endgroup\$ – Caleth Sep 25 '19 at 12:27
  • \$\begingroup\$ @47948201 That section is very specific about what traits each race gets. The Feat trait of the Variant Human is not one of them. \$\endgroup\$ – David Coffron Sep 25 '19 at 13:55
  • \$\begingroup\$ @47948201 If you add racial traits, like a feat, to a monster, you should determine the effects of the feat then use that to change the monster's CR. If you add 8 HP or 26 HP, this could change the monster's defensive CR in different ways, which in turn changes the monster's CR. \$\endgroup\$ – Yakk Sep 25 '19 at 14:18
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Player Characters do not have Challenge Rating

As Medix2 mentions in his answer, the Couatl's Change Shape feature is concerned with CR. Player Characters, like those that involve the Variant Human traits, do not have CR, as can be inferred by the description of CR in the Introduction of the Monster Manual (emphasis mine):

A monster’s challenge rating tells you how great a threat the monster is

There are no rules for evaluating a CR for Player Characters. Now, monsters can have racial traits as described in the Dungeon Master's Workshop under NPC Stat Blocks, but Variant Human is not one of the races that can be applied to NPCs using these rules.

Some Guidance

While there is no official way to apply feats to monsters and NPCs, you can always apply them by customizing the monsters. When doing this, the CR may change, which you can recalculate using the rules in the Dungeon Master's Workshop for Creating a Monster.

If applying a feat that depends on level, you can use the rules on NPC Stat Blocks for adding races to NPCs for some inspiration. The Dragonborn for example grants the NPC the following trait:

Breath Weapon (use challenge rating instead of level to determine damage)...

This shows one way to determine what would be an appropriate level to use. In your specific case, a Couatl would count as level 4.

It doesn't really matter what level you use to apply the feat. Just choose whatever level would best work for the power increase you want to give to the monster or NPC.

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    \$\begingroup\$ For further guidance there is also the true polymorph spell which lets you use level if the target doesn't have CR. If you want to turn a creature with levels into a monster the maximum CR you turn them into is CR = level \$\endgroup\$ – Medix2 Sep 25 '19 at 15:06
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If I were looking at this, the closest spell equivalent would probably be True Polymorph -- where in CR is equal to level. So, as such, I would have the Couatl be able to become a generic 4th level humanoid e.g. a 4th level fighter might be a good fit. Though, in fitting with an answer to a previous shapechange question, the Couatl is limited to one humanoid shape (i.e. It can only become Joe the human fighter for exmple and not also Greybeard the dwarf or some other humanoid too...as far as monsters go, I would have a list of preferred shapes -- though I'd be flexible)

How specific and detailed the character sheet you'd create depends on what role you'll want the Couatl to be playing in the campaign -- a one off monster vs a recurring NPC and ally vs enemy. I would have no issue with a variant background on the sheet as long as it fits the character concept.

For a one off, maybe you'd go the generic character sheet -- where as a recurring NPC, maybe you'll want more detail -- depending on how much you'll need to know about them -- I mean are they going to be in combat vs non-combat situations.

Also, I'd take into account whose control the Couatl is under..is it a DM NPC or a PC NPC or a PC...for the first you might need less info, vs the other two you might need more.

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