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The most recent Sage Advice Compendium erratas the find familiar spell so that familiars are now stripped naked when dismissed to a pocket dimension. The Pact of the Chain warlock can summon a Sprite familiar; when initially summoned, it is wearing leather armor, which its statblock lists as the source of its armor class.

Is there a system in place for calculating what the AC is if the warlock dismisses the sprite to a pocket dimension, and then later causes the sprite to reappear as an action?

It looks like using the formula for player characters in leather armor (11 + Dex), would be consistent with the published Dexterity, but we know that the rest of the sprite's equipment (longsword, longbow) work differently because it's a monster, so I'd prefer DM-facing monster adjustment rules for this.

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An unarmoured sprite has an AC of 14

I'm taking your ruling that sprites reappear without armour as read. For that discussion see: Are Sprite familiars from the Find Familiar spell summoned with the equipment listed in their statblock?. For that matter this is equally applicable if the sprites doffs the armour or should the armour be destroyed.

The general rule for monster AC is given in the Monster Manual introduction (p. 7; emphasis added):

A monster that wears armor or carries a shield has an Armor Class (AC) that takes its armor, shield, and Dexterity into account. Otherwise, a monster's AC is based on its Dexterity modifier and natural armor, if any. If a monster has natural armor, wears armor, or carries a shield, this is noted in parentheses after its AC value.

and similarly in the Dungeon Master's Guide under Step 7. Armor Class of Creating a Monster Stat Block (p. 276):

A monster that doesn't wear armor might have natural armor, in which case it has an AC equal to 10 + its Dexterity modifier + its natural armor bonus.

Excepting the natural armour bonus, this identical to the PHB unarmoured AC (p. 14) of 10 + Dex modifier.

A sprite has no natural armour bonus (or has one of +0) thus has an AC of 10 + its Dex modifier of +4 = 14.

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    \$\begingroup\$ I think it's also worth noting that the SAC doesn't say "familiars are now stripped naked when de-summoned". Specifically, it says: "When you dismiss the familiar you conjure with the find familiar spell to its pocket dimension, can it take any objects it’s wearing or carrying with it? No, the intent of find familiar is that any objects are left behind when the familiar vanishes. This intent will be reflected in future printings of the Player’s Handbook." Up to you whether you want to speculate about intent, but I suspect this relates more to objects not listed in its statblock. \$\endgroup\$ – V2Blast Oct 7 '20 at 3:15
  • \$\begingroup\$ Following on from my previous comment, the question title currently just asks what a sprite familiar's AC is without any elaboration, but the body of the post asks "what the AC is if the warlock desummons and then later resummons the sprite" (i.e. dismisses it to a pocket dimension, and causes it to reappear). As a result, the latter seems like the primary question - and I've edited the question title accordingly - so the answer should explicitly indicate whether the querent's assumption about the sprite reappearing without armor is correct. \$\endgroup\$ – V2Blast Oct 11 '20 at 7:34
  • \$\begingroup\$ @V2Blast Added a note about taking that ruling as read (ie. as a DM's ruling for their table) and linked to the question which covers the SAC ruling on it. \$\endgroup\$ – Someone_Evil Oct 11 '20 at 11:11

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