How do I calculate DPR for spellcasters?

Question

The title says it all: it's fairly simple to get a melee/ranged attacker's DPR with the formula but what about Spellcasters?
I'm trying to gauge an NPC antagonist spellcaster's Offensive Challenge Rating but I have no idea how to go about getting the DPR. Specifically, I am concerned about the limits in casting spell slots and factoring in the different types of saving throws a target needs to make because unlike non-spellcasting creatures which compare their attack rolls with only the target's Armor Class, Saving Throws are compared with Constitution, Wisdom, mostly Dexterity.

Assuming only damage-dealing spells are cast, how do I calculate a spellcaster's DPR?

Answer 1

Spells are calculated much the same way that Melee/Ranged weapon attacks are. However there are three differences that you need to take into account.

1. Firstly, turn all Saving throws into Spell Attacks. The math is the same. So if a spell has a saving throw, flip it using the formula of d20 + caster_modifiers vs. 14 + monster_save. Then, it becomes the same as AC which can vary from monster to monster, and is thus normalised by DPR calculations.

2. The second step is to determine if the spell targets an area, or multiple enemies. Depending on the radius of the spell and the shape, the DMG gives an assumption of how many enemies might be hit, in the "Adjudicating Areas of Effect" section of the DMG on page 249. Based on the size and shape of the spell, you would repeat the formula that you use for melee/ranged weapons, for each assumed target. For reference the assumptions are: ( Cone - size/10, Cube - Size/5, cylinder - radius/5, line - length/30, sphere/circle - radius/5 )

3. Lastly, there are the different possible spell slots from which a spell can be cast and thus affect its damage. The best and easiest option here is to assume that a spell is cast from the highest possible slot, and give calculations for each spell at each spot level. Once you have those numbers you can see what the maximum possible value is for a particular spell caster with a particular set of spells, and use that maximum value for your DPR.