Ah, necromancy. The forbidden magic. One of the eight schools of magic, necromancy is all about manipulating life-force. I think you could argue that healing spells like Cure Wounds ought to be necromancy, rather than evocation, but the image we usually get with this is specifically the raising of the dead.
Undead-raising spells are spooky, but can also be an interesting tactical choice for your morally-dubious spellcaster. (Though I did see a meme once that had that guy at the desk in the park with a sign that read "Necromancy is just recycling. Enchantment is slavery. Change my mind!" which, you know, there might be a fair point there - unless the souls of the undead minions are trapped in those bodies, of course.)
There are only a handful of spells that can raise the dead to fight for you. Some are damaging spells that raise a minion as a side-effect if you kill the target, like Finger of Death or Negative Energy Flood. For the purposes of this post, I want to look at the spells that specifically bring forth undead minions to serve you as the primary effect of the spell.
That gives us Animate Dead, Summon Undead, Danse Macabre, and Create Undead - actually a fairly short list.
The question I want to address is this: what spell gets you the most bang for your buck in terms of damage output from your undead minions.
Notably, a Necromancer Wizard gets an explicit boost to Animate Dead, which we can cover when we look at that specific spell.
These spells also come at different levels. Animate Dead and Summon Undead (the only "summon" spell out of Tasha's that isn't a conjuration spell) are 3rd level. Danse Macabre is a 5th level spell. Create Undead is 6th level.
They also have varying casting times, meaning that some might require you to plan well in advanced of using the minions, while others can be cast mid-combat.
Generally speaking, upcasting a spell is not usually as effective as casting a natively higher-level spell. A 7th level Fireball, for example, does 12d6 damage, while a Delayed Blast Fireball does that at minimum, with all the additional effects you can have with that spell. Or, for a lower-level example, upcasting Shatter to 3rd level does 4d8 (about 18) damage in a 10-ft radius sphere, while a Fireball does 8d6 (28) in a 20-ft radius sphere.
Still, I think that the best I can do to see how these spells actually compare with one another is to see how they do when cast at the same level. That means 6th.
We'll then take the minimum level a spellcaster would have to be to cast them (11th) as our baseline. So, we can probably assume a +5 Intelligence at this level as well as a +4 proficiency bonus.
Now, attack modifiers will vary here, so I think we're going to need to look at this not just on a "damage per hit" basis, but a "damage per attack" basis to see the general output.
There are a lot of other nuances, like the resilience of the minions - if the thing doesn't last a round, it's not going to be doing much damage. Still, I'm going to assume a sort of perfect scenario here - a level playing field where the minions can all attack while the monster is focused on some other target and not using AoE abilities.
I think, also, for the sake of the exercise, I'm going to have the available "material components" favor whatever allows for the higher damage output (admittedly, zombies and skeletons have very different strengths - a zombie can take a lot more punishment, but a skeleton has a higher chance to hit and can potentially fight from range).
So, let's look at each spell and see what our minions can do.
Animate Dead:
Oddly, this spell raises more minions by upcasting it for each level than the initial spell grants you - only 1 at 3rd level, but 2 additional minions for each level beyond 3rd. Thus, at 6th level, this can raise 7 minions. It takes 1 minute to cast, so this needs to be done outside of combat in most cases, and the minions remain raised indefinitely, but only under your control for 24 hours (though you can cast it again to get back that control.)
Notably, this spell does require you to use your bonus action to use it. Depending on your other class features, this might be a problem, but I think Wizards usually have this free.
We'll assume you have skeletons to raise for maximum damage output.
A skeleton has a +4 to hit and deals 1d6+2 on each shortsword or shortbow attack. A Necromancy Wizard adds their proficiency bonus to that damage, so it becomes 1d6+6.
At level 11, we're just into tier 3, so a "boss" level enemy might have an AC of 20, though it might not have quite progressed to that point. Let's give it a 19 AC to split the difference.
Thus, our skeletons have the following array:
Miss: 1-14, (70%) Hit 15-19 (25%), Crit 20 (5%)
Hit Damage: 1d6+2 (5.5)
Crit Damage: 2d6+2 (9)
Necromancy Hit Damage: 1d6+6 (9.5)
Necromancy Crit Damage: 2d6+6 (13)
Thus, each skeleton has the following damage on average per attack:
Normal: 1.375 + 0.45, or 1.825
Necromancy: 2.375 + 0.65, or 3.025
Now, with seven skeletons attacking for us, we get the following total damage per round:
Normal: 12.775
Necromancy: 21.175
So, there we go. That's Animate Dead at 6th level. Let's move on:
Summon Undead:
Summon Undead is one of the Tasha's spells, and is thus way simpler to implement. You don't actually need a corpse to raise with this one - you just need the 300 g material component. You have three options for minion type here. The Putrid version does have the chance to paralyze foes, which could make it way more powerful, but in terms of raw damage output, I think that the Skeletal minion's grave bolt does just slightly more damage (2d4 versus 1d8, so a difference of 0.5 damage on average) and also has the nice benefit of being ranged (actually, the Putrid minion only does 1d6 - it's the ghostly one that does 1d8. Either way, 2d4 wins.)
This spell uses the caster's spell attack modifier to determine the minion's chance to hit, which is probably going to help you out a lot. At 11, with our assumed stats, you have a +9 to hit. Using our AC 19 target dummy, that means you hit on a 10 or higher. Cast at 6th level, you get three attacks per turn, and the damage of each of those hits is also buffed by the upcasting.
Summon Undead only lasts for 1 hour, but can be cast as an action. It also does not require a bonus action to direct your minion, meaning that you can cast other (non-concentration) spells using your full action economy (though for a wizard, concentration might be a bigger thing than bonus actions. Animate Dead only requires you cast it again the next day so that your minions don't start killing indiscriminately.)
So, our array here is:
Miss 1-9 (45%) Hit 10-19 (50%) Crit 20 (5%)
Hit: 2d4 + 3 + 6 (spell's level), for an average of 14 damage
Crit: 4d4+3+6, for an average of 19 damage
Thus, per attack we have 7 + 0.95, which pretty obviously comes to 7.95
With three attacks, that means an average damage per round of 23.85
That's still a bit more than what the Necromancy Wizard gets with Animate Dead, and a whole lot more than any other spellcaster would get.
Danse Macabre:
This is a spell I really like, and as much as I love the Tasha's Summon spells (especially as a DM) this one has a lot going for it. At its base, 5th level, you animate 5 corpses as zombies or skeletons, and each subsequent level you get two more. That actually means that it keeps pace exactly with Animate Dead. This one does require your concentration, and only lasts an hour, but it can be cast with an action and the minions just go inanimate when it's over, rather than potentially turning on you.
This does also require your bonus action to control them.
However, in terms of combat, the big bonus this gets is that you add your spellcasting ability modifier to both their damage and their attack rolls.
So, other than requiring concentration, that makes this strictly better than Animate Dead. (While we'll eventually get a higher proficiency bonus, the buff to attacks is huge.) But let's do the math on it:
At 6th level, you've got 7 minions. Again, we're going to be favorable and say they're all skeletons.
However, by adding our spellcasting ability modifier to the attacks, a skeleton winds up getting a +9 to hit (4 from itself, 5, from our ability). Conveniently, this gives us the same hit/crit array as the Summon Undead example (though if we were to get something like a Wand of the War Mage or Rod of the Pact Keeper, we lose out slightly.)
Hit Damage: 1d6+7, or about 10.5
Crit Damage: 2d6+7, or about 14
Damage Per Attack: 5.25 + 0.7, or 5.95
We have 7 of these guys fighting for us, which gives us 41.65, running away with an enormous lead.
Create Undead:
Now for the weird one. This spell can only be cast at night - I don't know what that means for planes where "night" isn't really a thing. At its base level, you can animate three corpses to become Ghouls. Like Animate Dead, it requires no concentration, but does require you use a bonus action to command them. And also like Animate Dead, you need to re-cast this to retain control over the minions after 24 hours.
Upcasting this gets weird, allowing you to raise ghasts and wights and even mummies, but we're talking the 6th level version.
Now, a ghoul has different attacks. The Bite does more damage but with a lower chance to hit, while the Claws have a higher attack bonus and also a chance to paralyze foes. The DC for this effect is very low - it's just 10 - but paralyzing foes is hugely powerful, so it's worth consideration.
Let's assume, though, that our boss has a hefty Con save so we don't have to consider that.
The damage of the Bite is only 2 higher, with a corresponding difference of two when it comes to hit chance, so my instinct is that the Claws, despite their lower damage, are going to probably give you more damage over time (not to mention the possibility of their paralyzation effect.)
A ghoul's hit bonus with those claws is +4, and the damage is 2d4+2. Notably this will not gain the benefit of the Necromancy Wizard's subclass feature.
So, our array is actually the same as it was with our Skeletons in Animate Dead.
Miss 1-14 (70%) Hit 15-19 (25%) Crit 20 (5%)
Hit Damage: 2d4+2, or 7
Crit Damage: 4d4+2, or 12
Damage per Attack: 1.75 + 0.6, or 2.35
With three ghouls, that comes to 7.05 - which is by far the least impressive of these spells. Interestingly Animate Dead upcasts for much more damage. While the paralyzation effect is amazing if you can get it, with a DC of 10, it's just so rarely going to work even on relatively frail minions that, well, this doesn't really look like it's worth it.
My sense is that Create Undead is less for a player to use, and more for a big bad the party is going to face down the road to use while they're still in tier 1. 3 ghouls is a significant challenge for a party that's level 2 or 3, but I just cannot imagine this being worth the 6th level slot for a player character.
So, overall I think that Danse Macabre comes away as the clear winner of these four spells. Obviously, you can get Animate Dead and Summon Undead at an earlier level. I think that Summon Undead still has a place in your spellbook for a couple reasons - one is that you don't actually need any corpses to cast it. The other is that it's fairly versatile. Skeletons raised by Danse Macabre are still rather easy to kill and will be wiped out by AoE. An Undead Spirit minion, even in its frailest skeletal form, will have 50 HP when cast at 6th level, which means it should be able to survive a fireball (it's also got a 150-foot range in skeletal form, meaning that it can stay pretty far from the fight and shoot from afar).
Now, if you are a Necromancy Wizard, Animate Dead does have the advantage of a full day's duration, and the same subclass feature that buffs their damage also buffs their health by an amount equal to your Wizard level. That's not enormous, but it could mean survival of a big AoE attack, potentially.
Of course, as a Necromancy Wizard you get that spell automatically. It's more of a question of which spells to actually cast. I think that Danse Macabre and Summon Undead are the ones you want to pack.
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