Balancing Damage Spells (Math based)

[Kryx]

Being a bit unsatisfied with the current balance of spells that do damage I decided to do some math to calculate the current situation. I then adjusted certain spells to be more powerful (and a few less powerful) in order to arrive at a better balanced system.

The Goal:
Make awful spells able to compete with other spells of equivalent levels. Examples of awful spells include Cordon of Arrows, Earth Tremor, Witch Bolt, Maximilian's Earthen Grasp, Melf's Acid Arrow, Blight, Immolation, Harm, etc.

The Method:

Add all damage spells to google spreadsheet.
Presume some chances to be hit and chances to save based on monster math.
Presume some math about how many creatures are hit on average based on certain AoE sizes.
Presume some math about how much more valuable bonus actions/reactions are.
Presume some math about how likely concentration breaks.
Presume some math about how much less valuable damage to multiple targets is than damage to a single target
Calculate the damage per target
Use the previously calculated number of targets to determine the total damage (reduce by a set amount because splitting damage is less valuable)
Add a modifier that has spells of higher level doing more damage per level.
Compare spells to average and then adjust until the weighted damage/level is at least competitive.

To find this resource valuable you'll have to agree that overarching assumptions have to be made even though things won't always play out as expected. If you have any suggestions on how to improve the assumptions please do let me know.

The Result:
Spell Balance (https://docs.google.com/spreadsheets/d/1N4QC6EmXE0avgk8jK1aubJcaFoZDYw8b_DuPHh8aBTc/edit#gid=0&vpid=C2)
Blue columns = auto calculated.
Golden text = changed from RAW
Green text = houserule spells
Fuchsia text = hard coded
Dmg/level weight column is colored based on how close to the average it is. The average is on the top right. Green = closer. Red = farther away (in either direction).

Please let me know if you have any feedback on the presumptions or the results.

[Tanarii]

Are you balancing, or just powering up spells below the avg (ie moving the avg up)?

For example, Lightning Bolt appears to be unchanged, instead of weakened.

[Kryx]

Currently I have buffed low damage spells to be competitive. Though that doesn't mean casters are better or any of those concerns. It just means casters have a choice to choose some of the options that were previously awful choices.
I'm not sure trying to balance everything is the best goal. Considering the amount of assumptions I have made if any of those change it would throw off the math. This is more of a general guideline approach for me. Especially for bonus action or reaction type values.

Though AoE damage spells are much easer and now that you mention it I think moving Fireball and Lightning Bolt down to 6d6 (from 8d6) is a good change.

The end question is: what is the baseline we're heading for. I think the baseline is around 9 of my value system as that is where most everything is (smite and most spells). So aiming for that is probably good, though becomes much harder with things like fire storm, meteor swarm, and prismatic wall.

[SharkForce]

I don't think of maximilian's earthen grasp as a damage spell. I think of it as CC. to me, the way to fix the spell is to let it scale in targets with spell level (and maybe to a lesser extent making the hands tougher).

I think a number of the spells in the list have other features that make it perfectly acceptable that they don't deal damage on the same scale; magic missile always hits when you need it to. sunbeam blinds people and can be used for multiple attacks. meteor swarm is a 9th level spell and quite frankly should be ridiculous if it is to be of any value next to other 9th level spells which are much more powerful in terms of changing the world and winning encounters.

some of the weaker spells can certainly use some help, but I do think it is important to take everything about a spell into consideration, not just the damage.

[Kryx]

I do think it is important to take everything about a spell into consideration, not just the damage.
Indeed. That's why some spells like Hunger of Hadar and Evard's sit around a value of 4. (Evard's got a slight damage boost).

The majority of the spells I touched don't have extra conditions.

Maximillian's Earthen Grasp can't really have multiple targets without turning it into a lesser Vitriolic Sphere. Restrained against 1 target is pretty good, but so is restrained against multiple (Evard's, Bones of the Earth). Though maybe 4d6 is too high. 3d6 is a 5.8 value.
Magic missile: Forgot it was auto hit somehow. Removed the buff as having no miss puts it above the average already.
Sunbeam: Untouched. It's completely RAW
Meteor Swarm: I don't subscribe to the belief that it's fine for the game to break down at high levels. I do not find the idea of world bending 9th level spells enjoyable. That said I don't see the 30d6 version being less useful in comparison to some others like Power Work Kill, Prismatic Wall, Storm of Vengeance, etc.

[SwordChuck]

Meteor Swarm: I don't subscribe to the belief that it's fine for the game to break down at high levels. I do not find the idea of world bending 9th level spells enjoyable. That said I don't see the 30d6 version being less useful in comparison to some others like Power Work Kill, Prismatic Wall, Storm of Vengeance, etc.

I've found that if you allow casters to have the same number of slots per level but cap spell known at 3 or 4 (but add in a few iconic higher level spells as rituals if the setting/game needs them) the game just works a hell of a lot better (for balance and in game consitency).

If you give spell casters a bit more flexibility when learning spells (cold fireball instead of fire fireball) things work pretty well. I wouldn't mind if the meta magic rules could be given as a feat or to more classes (druid would be awesome with metamagic).

[weaseldust]

(reduce by a set amount because splitting damage is less valuable)

Is that actually true? It's more that it's useful in different circumstances (vs multiple weaker enemies).

I don't think single-target damage spells and multiple-target damage spells are really in competition with each other. That is, when a spellcaster chooses between Chromatic Orb and Witch Bolt, they're comparing them based only on their effectiveness. When they choose between Chromatic Orb and Burning Hands, they're comparing the likelihood that the conditions they are designed for will come up.

My suggestion would be to balance the single-target spells against each other, and the multiple-target spells against each other, and leave it at that. (Versatile spells, like Scorching Ray and Magic Missile, would have to be balanced against both options, though.) You could try to balance the two kinds against each other later, but there will always be a fudge factor due to differences in encounter design and play style that isn't so important when comparing two single-target damage spells.


Another issue is that high-level damage spells aren't really intended to keep spellcasters on the damage curve so much as to provide 1/day gamechangers. I probably agree with you about the excesses of high level spells as they exist - I only ever use Wish to wish that Wish didn't exist - but I feel like the point of Disintegrate is to destroy something really scary rather than to deal X amount of damage. The particular amount of damage it does deal is just an estimate of how much is needed to destroy scary things. In other words, it's more like a precursor to Power Word Kill than a successor to Chromatic Orb.

[Kryx]

My suggestion would be to balance the single-target spells against each other, and the multiple-target spells against each other, and leave it at that.
I considered it, but in my experience nearly every encounter includes multiple enemies. It's very rare that there is only a single enemy. In most of those cases the current branch of AoE spells either match or outdamage the single target spells not only to the main target, but also that same damage on seconary targets (Fireball and Lightning Bolt being the biggest offender in the early levels.)
I think ignoring a level 3 fireball doing nearly the same damage or more damage as a level 4 blight and a level 5 immolation isn't a good route.

Damage to a secondary target being less valuable has been true for a long time. I was true in DPR discussions in 3.5, PF, and 4e. Not much has changed imo. In most cases a party will want to focus their damage in order to eliminate threats as dead threats = less damage received.

High level spells: I account for this factor. Damage/level is non-linear. Higher levels expect more damage per level. For example compare the AL column to the AN column to see that. AL is straight value/level whereas AN is weighted.

[SharkForce]

maximilian's is a strength-save targeted form of crowd control. if you scale it to multiple targets (casting as a 3rd level gives you 2 hands, 4th level gives you 3, etc), it will not be very similar to vitriolic sphere (dex save, no ability to select targets, no CC effects) at all, and will fill a hole in the sorcerer/wizard spell list that is currently not occupied by anything at all.

it will arguably be somewhat similar to entangle (but still different since entangle is an AoE that cannot selectively target and does not deal damage), but since the spells are on completely different class lists, there is little conflict there.

[Kryx]

I meant Watery Sphere.
Beyond that the spell is meant as a single target spell. The fluff of it doesn't work unless you start summoning multiple hands or treating it like Watery Sphere.

Though now that I noted that it can move/change targets it is within the normal value range and I've removed the buff.

[SharkForce]

every maximilian's <material> grasp spell from earlier editions gained more hands as the caster increased in levels, as far as I know. dunno why they didn't have it scale in 5th.

and no, it isn't like watery sphere. it's stuck on the ground, you can't move the targets around, and it deals damage. and it is targeted rather than being AoE.

[Kryx]

You are mis-reading what I'm writing. If you use 1 hand to grab multiple targets that would fulfill a similar role as watery sphere.

Either way the spell has been returned to RAW and is within the normal range. Let us stop discussing 1 specific spell, please.

[Zalabim]

I see Moonbeam and Call Lightning have the same "repeatable" modifier, but Moonbeam will repeat on a target that doesn't move without taking any action at all. Persistent/mobile effects need a separate modifier from just persistent or just mobile effects.

3rd level spells need to have a jump in power, since that's the level where martials get an extra attack and double their average damage. The XP/encounter table corresponds with this as well, doubling from level 4 to 5. With original values, a wizard has 10.5*4(burning hands) and 14*2(burning hands 2nd level) at level 3, for an average of 11.6~ per cast, 6 casts per day of AoE. At level 5, that's 10.5*4, 14*3, and 28*2(fireball) for an average of 15.5~ per cast, 9 casts per day of AoE. That's 1.33~* damage, 1.5* frequency, or twice as much AoE per day, with extra radius to compare to martials getting +1 damage per hit at 4 and double damage per round at 5.

You can't just lower Lightning Bolt and Fireball's damage.

Pretty sure Heat Metal is concentration. Flaming Sphere takes an Action to cast. In fact, Flaming Sphere and Moonbeam are very similar, having just different numbers and action type to move.

I'd give a flat value (but scaling with level) for a bonus action spell, rather than a multiplier on its damage value, since they still prevent casting other leveled spells. You can cast Spiritual Weapon and Attack, or Sacred Flame, which isn't the same as the whole spiritual weapon being better. There are very few actual Bonus Action damage spells, so I'm not sure this effects anything.

Shouldn't a wall of length 60 have at least the same number of creatures effected (on its initial cast) as a line spell of length 60? I'm away from my book, so seriously, is there some limitation I'm forgetting?

[Kryx]

Firstly, thanks for providing feedback! That's why I posted it here - to get comments and suggestions!


Persistent/mobile effects need a separate modifier from just persistent or just mobile effects.
I have scrapped the move field. It didn't make sense as all cases of movable were repeatable. Repeatable can handle it.


3rd level spells need to have a jump in power, since that's the level where martials get an extra attack and double their average damage. The XP/encounter table corresponds with this as well, doubling from level 4 to 5. With original values, a wizard has 10.5*4(burning hands) and 14*2(burning hands 2nd level) at level 3, for an average of 11.6~ per cast, 6 casts per day of AoE. At level 5, that's 10.5*4, 14*3, and 28*2(fireball) for an average of 15.5~ per cast, 9 casts per day of AoE. That's 1.33~* damage, 1.5* frequency, or twice as much AoE per day, with extra radius to compare to martials getting +1 damage per hit at 4 and double damage per round at 5.
Martials at level 5 do about 20-30 DPR at level 5 and very slowly increase after. See DPR of Classes (https://docs.google.com/spreadsheets/d/1d-9xDdath8kX_v7Rpts9JFIJwIG3X0-dDUtfax14NT0/edit#gid=655309186).
I've adjusted my AoE targets modifier to give us a more accurate avg. Fireball averages at 3.8 targets.
1 fireball at 8d6 does 28 damage, or 20.2 after save for half.
1 fireball at 6d6 does 21 damage, or 15.1 after save for half.
Each one hits about 3.8 targets. For RAW that's 76.76 damage. For 6d6 that's 57.38.
Assuming that secondary damage is less valuable than focused damage (usually true, not always) that gives us 2.7 targets or 54.54 damage for RAW fireball or 40.77 for 6d6 fireball.

So
a 8d6 fireball does about 2-2.5x the damage as a martial can do in a round.
a 6d6 fireball does about 1.5-2 the damage as a martial can do in a round.

This comes back to my earlier question of: "What is the baseline that we should aim for?". I'd love to do some more math around this.
The number of rounds per day is about 25 so full casters don't have to worry about slots after a bit.


You can't just lower Lightning Bolt and Fireball's damage.
It's entirely possible to do so, though as discussed above whether we should use that approach or boosting every other spell is up for debate. Either we boost every other spell to be competitive or we lower those 2. 5e designers have noted that fireball/lightning bolt are outliers as they are iconic as they want people to take them. I find outliers to be poor design as they force players to choose the best option or not be as good even if it goes against their flavor.
For reference in PF Fireball did 5d6 as a level 3 spell at level 5. Lightning Bolt was the same. In 5e it does 8d6. That doesn't necessarily mean they should be lower as 5e is different.


Pretty sure Heat Metal is concentration.
Fixed.


Flaming Sphere takes an Action to cast.
Fixed.


I'd give a flat value (but scaling with level) for a bonus action spell, rather than a multiplier on its damage value, since they still prevent casting other leveled spells. You can cast Spiritual Weapon and Attack, or Sacred Flame, which isn't the same as the whole spiritual weapon being better. There are very few actual Bonus Action damage spells, so I'm not sure this effects anything.
Bonus actions have different values. For Martials like Paladin they get a full attack + smite spells'. Other casters get cantrips. I'll need to handle this differently.
No ideas how to do this properly. Same with reactions.


Shouldn't a wall of length 60 have at least the same number of creatures effected (on its initial cast) as a line spell of length 60? I'm away from my book, so seriously, is there some limitation I'm forgetting?
I did assuming walls cannot all be cast on people, but that's only true for Prismatic Wall. I have fixed this. I now treat them as ranged lines.

I've added the following to my TODO:
Bonus action spells should potentially have a flat value added. Different for Paladin vs Caster
Same with Reactions
Determine proper balance between martial and caster Dmg

[Socratov]

how about cantrips? How could those be balanced out?

[Trasilor]

Being a bit unsatisfied with the current balance of spells that do damage I decided to do some math to calculate the current situation. I then adjusted certain spells to be more powerful (and a few less powerful) in order to arrive at a better balanced system.

The Goal:
Make awful spells able to compete with other spells of equivalent levels. Examples of awful spells include Cordon of Arrows, Earth Tremor, Witch Bolt, Maximilian's Earthen Grasp, Melf's Acid Arrow, Blight, Immolation, Harm, etc.

The Method:

Add all damage spells to google spreadsheet.
Presume some chances to be hit and chances to save based on monster math.
Presume some math about how many creatures are hit on average based on certain AoE sizes.
Presume some math about how much more valuable bonus actions/reactions are.
Presume some math about how likely concentration breaks.
Presume some math about how much less valuable damage to multiple targets is than damage to a single target
Calculate the damage per target
Use the previously calculated number of targets to determine the total damage (reduce by a set amount because splitting damage is less valuable)
Add a modifier that has spells of higher level doing more damage per level.
Compare spells to average and then adjust until the weighted damage/level is at least competitive.

To find this resource valuable you'll have to agree that overarching assumptions have to be made even though things won't always play out as expected. If you have any suggestions on how to improve the assumptions please do let me know.

The Result:
Spell Balance (https://docs.google.com/spreadsheets/d/1N4QC6EmXE0avgk8jK1aubJcaFoZDYw8b_DuPHh8aBTc/edit#gid=0&vpid=C2)
Blue columns = auto calculated.
Golden text = changed from RAW
Green text = houserule spells
Fuchsia text = hard coded
Dmg/level weight column is colored based on how close to the average it is. The average is on the top right. Green = closer. Red = farther away (in either direction).

Please let me know if you have any feedback on the presumptions or the results.

You really should do this for each spell list. Certain classes respond differently to their spell list. For example, a Ranger's damage spells are very different from a sorcerer's damage spells given that the sorcer uses spells as their primary form of attack while a ranger uses their ranged/martial as their primary attack. Also, I noticed that you include some ranger spells but not others - why?

You have too many assumptions. You currently have six assumptions (seven if you include the fact you treat all spell lists equally) - any one of which can change your results. Break these down into smaller datasets. I suggest that in addition to looking at each spell list individually you split spells between concentration/non-contration; standard/reaction/bonus action; and spells available levels 1-4, 5-10, 11-16 and 17+.

[Kryx]

how about cantrips? How could those be balanced out?
Those have to be handled separately, though I agree that they should be balanced.



You really should do this for each spell list. Certain classes respond differently to their spell list. For example, a Ranger's damage spells are very different from a sorcerer's damage spells given that the sorcer uses spells as their primary form of attack while a ranger uses their ranged/martial as their primary attack. Also, I noticed that you include some ranger spells but not others - why?

You have too many assumptions. You currently have six assumptions (seven if you include the fact you treat all spell lists equally) - any one of which can change your results. Break these down into smaller datasets. I suggest that in addition to looking at each spell list individually you split spells between concentration/non-contration; standard/reaction/bonus action; and spells available levels 1-4, 5-10, 11-16 and 17+.
You seem to have an idea that vastly differs from mine. If you want to make such a system I'd happily look at it, but what you're suggesting is quite different than what I have.
To address some points:

Spells are equivalent for all lists. This is a purposeful design choice of 5e. The developers have commented on this several times. A 4th level spell is a 4th level spell for all classes whereas in old editions it was not. Therefore the spells should be looked at collectively, not on an individual list basis.
I have only included damage spells. If it doesn't have damage it isn't included. The only ones that are not included are Flame Arrows and Hunter's Mark. Those aren't added because the way my JSON is formatted though looking at them now they can vary widely based on build. Though I could see adding them
Spell levels are what spells are balanced around, not blocks of character levels. They don't align with the martial boost points in the default spell system so I won't be going that route.
Too many assumptions - these exact same assumptions have been made by the team that designed the system. If you have a suggestion for how to handle it without assumptions then I'm all ears, but I don't see that happening.

[SwordChuck]

I think the issue with balancing spells, even with themselves, is how they get better when you use a higher slot.

If you instead had an outside source that made your spells better you could balance them easier. Having so many slots where any spells (most) automatically get better in some way is just too much variable.

Having the same number of slots but a lower number of "I'm making this better" points can be dealt with much easier and you could balance the spells and effects along with it.

You would also need to give better control abilities to non casters, this way when you balance control spells we actually have something to balance them with. Right now all grappling type spells have to compete with the grapple action... Which isn't hard to compete with (grappling is close range, size limitation, target number limitation, and HP dependant...).

××edit××

Alternatively if spells were taken away from the vancian x/day you could get rid of the outside power source and just have them work in such a way a wizard can say...

I cast fireball but I want it to grab the targets (arcana versus athletics or acrobatics for the grapple). Give it a bit of damage on following rounds (much like the battlerager barbarian spike things 5 + Int mid?).

[Demonic Spoon]

Spells are equivalent for all lists. This is a purposeful design choice of 5e. The developers have commented on this several times. A 4th level spell is a 4th level spell for all classes whereas in old editions it was not. Therefore the spells should be looked at collectively, not on an individual list basis.
Spell levels are what spells are balanced around, not blocks of character levels. They don't align with the martial boost points in the default spell system so I won't be going that route.

Just because each spell only has one spell level does not mean that all spells are intended to be equally powerful for any individual class.

To take a non-damaging example, the Druid summoning spells are way better than the wizard summoning spells, even for the same spell level. In addition to getting Conjure Animals earlier than wizards get Conjure Elementals, the druid summoning spells cost 1 action to cast compared to 10 minutes for wizard spells

As another example - if Hex were available to Eldritch Knights, would any EK not take it?


That said, I don't think that actually causes a problem for this analysis. The vast majority of direct damage spells that were changed on that list seem to be on the wizard/sorcerer/warlock spell list, which are the core blast-y classes. Most of the rest are the high-level Ranger damage spells - I assume that's intentional, since as I understand it Ranger DPR falls off in later levels.

[Kryx]

@SwordChuck: Your ideas fall into a homebrew system.


Just because each spell only has one spell level does not mean that all spells are intended to be equally powerful for any individual class.

To take a non-damaging example, the Druid summoning spells are way better than the wizard summoning spells, even for the same spell level. In addition to getting Conjure Animals earlier than wizards get Conjure Elementals, the druid summoning spells cost 1 action to cast compared to 10 minutes for wizard spells
The difference here is that elementals are considered more valuable than animals. You can see this in the Moon Druid who gets access to elementals much later in his career. You can see the exact same thing for Druid's Conjure Animals (3rd level) vs Conjure Woodland Beings (4th level). Fey are considered more valuable than animals. Beyond type Conjure Animals (Druid 3rd), Conjure Minor Elementals (Wizard 4th), Conjure Woodland Beings (Druid 4th) are word for word the exact same spell.
I think this is just a matter of the value of creature types.


As another example - if Hex were available to Eldritch Knights, would any EK not take it?
No moreso than any Paladin would do the most damage by choosing OoV which adds a lot of value out of Hunter's Mark as his bonus action isn't consumed already.
Hex, Hunter's Mark, and Flame Arrows are unique in that their value is heavily dependant on number of attacks. Those type of spells are limited on certain lists and I wouldn't suggest changing that.


That said, I don't think that actually causes a problem for this analysis. The vast majority of direct damage spells that were changed on that list seem to be on the wizard/sorcerer/warlock spell list, which are the core blast-y classes. Most of the rest are the high-level Ranger damage spells - I assume that's intentional, since as I understand it Ranger DPR falls off in later levels.
Indeed everything is Wizard/Sorc besides. I didn't touch any Ranger spells besides Cordon of Arrows.