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For this question I am going to define these spells as, namely, Polymorph, True Polymorph & Shapechange. You must also, for the sake of this question, disregard any creature type limitations and implicit abilities (e.g. your answer should cover using "Polymorph", which only allows Beast forms, to turn into a creature with the Spellcasting trait)

Inspired from this question and the chosen answer I would like to take things a bit further and clarify the spellcasting abilities and options (class-oriented or otherwise) that a creature retains or gains after casting one of the aforementioned spells. Their text, in all 3 cases, includes slightly different variations of the passage

The target’s game statistics, (not) including mental ability scores, are replaced by the statistics of the new form.

along with others that further specify or add to a member of this line of spells.

Ideally the answers could present the relevant differences in a comparative X vs Y vs Z form regarding parameters such as:

  • retained/gained spell lists and slots
  • retained/gained ability to cast non-class spells (e.g. racial ability to cast Darkness)

along with the conditions under which they apply, and quotes that define or imply so, if any.

Even though the question relies on RAW, seeing as even the developers have claimed RAW is 'not really a thing' in 5e and the texts can be quite abstract, you are welcome to offer your own arguments for the intentional usage, especially if they are backed by posted answers/comments from said developers.

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  • 2
    \$\begingroup\$ With these 3 spells, answers will have to include at least 2 entirely separate answers. More generally, your question is less of a question and more of an "analyze these things for me". \$\endgroup\$ – Miniman May 26 '15 at 6:10
  • \$\begingroup\$ It's also unlimited in scope - if specific class features have the potential to interact differently with these spells, answers would have to go through every single one. \$\endgroup\$ – Miniman May 26 '15 at 6:18
  • \$\begingroup\$ I believe that all 3 provide different merits/limitations regarding spellcasting in particular, which are not immediately obvious and wanted to convey that in my question. Perhaps the optimization tag should be here too. Got any suggestions for formatting? \$\endgroup\$ – Eldebryn May 26 '15 at 17:20
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Comparison

Here is a quick and dirty summary of the main differences between these spells.

                Polymorph        True Polymorph  Shapechange
Level            4               9               9
Cost             Nil             Nil             1,500gp
Range            60 feet         30 feet         Self
Limits           Beasts only     None            Must have been seen
                                                 No constructs or undead
Statistics       Creature’s      Creature’s      Creature’s STR, DEX, CON
                                                 Your INT, CHA, WIS
Proficiencies    Not mentioned   Not mentioned   Yours but may use creature’s bonus if better
                 (creature’s?)   (creature’s?)
Class, Race      Creature’s      Creature’s      Yours 
Abilities                                        (Subject to capability)
Equipment        Merged          Merged          Falls off OR
                                                 Merged OR
                                                 Worn
Change form      No              No              1 Action

Source Information

Of specific relevance to the question are these words that each spell uses:

Polymorph

The new form can be any beast whose challenge rating is equal to or less than the target’s (or the target’s level, if it doesn't have a challenge rating). The target’s game statistics, including mental ability scores, are replaced by the statistics of the chosen beast. It retains its alignment and personality.

...

The creature is limited in the actions it can perform by the nature of its new form, and it can’t speak, cast spells, or take any other action that requires hands or speech.

Shapechange

You transform into an average example of that creature, one without any class levels or the Spellcasting trait.

Your game statistics are replaced by the statistics of the chosen creature, though you retain your alignment and Intelligence, Wisdom, and Charisma scores. You also retain all of your skill and saving throw proficiencies, in addition to gaining those of the creature. If the creature has the same proficiency as you and the bonus listed in its statistics is higher than yours, use the creature’s bonus in place of yours. You can’t use any legendary actions or lair actions of the new form.

...

You retain the benefit of any features from your class, race, or other source and can use them, provided that your new form is physically capable of doing so. You can’t use any special senses you have (for example, darkvision) unless your new form also has that sense. You can only speak if the creature can normally speak.

True Polymorph

The target’s game statistics, including mental ability scores, are replaced by the statistics of the new form. It retains its alignment and personality.

...

The creature is limited in the actions it can perform by the nature of its new form, and it can’t speak, cast spells, or take any other action that requires hands or speech unless its new form is capable of such actions.

Also relevant is this quote from the Monster Manual (p.6)

A monster's statistics, sometimes referred to as its stat block, provide the essential information that you need to run the monster.

And (p.11)

INNATE SPELLCASTING

A monster with the innate ability to cast spells has the Innate Spellcasting special trait. Unless noted otherwise, an innate spell of 1st level or higher is always cast at its lowest possible level and can't be cast at a higher level. If a monster has a cantrip where its level matters and no level is given, use the monster's challenge rating.

An innate spell can have special rules or restrictions. For example, a drow mage can innately cast the levitate spell, but the spell has a "self only" restriction, which means that the spell affects only the drow mage. A monster's innate spells can't be swapped out with other spells. If a monster's innate spells don't require attack rolls, no attack bonus is given for them.

SPELLCASTING

A monster with the Spellcasting class feature has a spellcaster level and spell slots, which it uses to cast its spells of 1st level and higher (as explained in the Player's Handbook). The spellcaster level is also used for any cantrips included in the feature.

The monster has a list of spells known or prepared from a particular class. The list might also include spells from a feature in that class, such as the Divine Domain feature of the cleric or the Druid Circle feature of the druid.

A monster can cast a spell from its list at a higher level if it has the spell slot to do so. For example, a drow mage with the 3rd-level lightning bolt spell can cast it as a 5th-level spell by using one of its 5th-level spell slots. You can change the spells that a monster knows or has prepared, replacing any spell on a monster's spell list with a different spell of the same level and from the same class list. If you do so, you might cause the monster to be a greater or lesser threat than suggested by its challenge rating.

The "Vibe"

It retains its alignment and personality.

which all the spells use suggest that the original being is inside the new creature in some way. Its who they were just in a different shape.

Shapechange has the vibe that not only your personality but your knowledge and skill is still intact; you are simply wearing the new creature - this feels similar to the druid's shapechange ability.

Polymorph and True Polymorph on the other hand have the vibe that they have become the creature, not just physically but mentally as well. There is a suggestion that they remember who they were in True Polymorph but this is by extrapolating from the fact that if you turn them into an object, "the creature has no memory of time spent in this form".

Spellcasting

Shapechange is the easiest, that's you in there; provided the shape you have chosen can do so, you can cast the spells you have memorised. You have the slots used and unused that you had before and if you use them while Shapechanged they are gone when you revert.

The others use:

The creature is limited in the actions it can perform by the nature of its new form, and it can’t speak, cast spells, or take any other action that requires hands or speech unless its new form is capable of such actions.

While somewhat ambiguous the only sensible way of parsing the sentence is that if it has hands or speech then it can cast spells that require S/M & V components respectively.

So whose spells are they that it can theoretically cast?

Well it has "the creature's statistics", unless polymorphed into itself (which is a huge waste of a spell) they are not the spells of the original creature; they must be the spells of the new creature.

It is up to the DM to decide if you can choose to polymorph into a "Drow Mage" or if you are limited to just "Drow" for example. If this is allowed then you get access to the "Innate Spellcasting" and "Spellcasting" traits that are an integral part of the "Drow Mage".

It is also up to your DM if you can polymorph into a specific person - "my friend Sally, the 18th level Cleric" or if you are limited to what is in the Monster Manual - "Priest".

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