Saturday, January 20, 2018

Spell-balancing math

MATH MATH MATH this post is full of math! Basically showing my thought process of how to balance spell power vs warrior damage.

So how should a spell like Magic Missile be balanced? The 1st-level spell slot is used by both level 1 and level 2 wizards, so we need to balance the 1st-level spell slot against both the level 1 and level 2 fighter.

Hold on, D&D's terminology is confusing. Let's revise the terminology.

Level refers to character level. In D&D, someone may be playing a level 3 Fighter.
Level Circle now refers to the advanced spells. So someone may cast a 1st-Circle spell like CBurning Hands or Magic Missile, using a 1st-Circle spell slot.

Levels refers to the advancement of the player character. Circle refers to more advanced spells or spell slots.  Okay?

So let me repeat my previous statement. The 1st-Circle spell slot is used by both level 1 and level 2 wizards, so we need to balance the 1st-Circle spell slot against both the level 1 and level 2 fighter.

Fighter damage = (weapon+MODIFIER)*Level
A level 1 fighter with a longsword will do (d8+3)*1=7.5 average damage (4 to 11)
A level 2 fighter with a longsword will do (d8+3)*2=15 average damage (8 to 22)

A 1st-Circle spell slot is used for both level 1 and level 2 wizard.
To balance against both a level 1 and 2 fighter, we take the average level of the fighter: level 1.5 Fighter
Damage of a level 1.5 Fighter = (7.5+15)/2 = 11.25 average damage is the number we compare against

So how much damage should a 1st-Circle compared to a level 1.5 fighter with a longsword? About double should be about right since spells are a limited resource. But here is the kicker: the wizard isn't allowed to do double the longsword damage all in one hit. Reason being, PCs sometimes have the same spells levelled at them. One-shotting someone with a spell is much less funny when you're on the receiving end. So the damage potential of spells has to be spread out, either in an AoE or through some common D&D tricks.

The D&D trick I'm thinking of is Magic Missile. Unlike every other damage spell, Magic Missile always hits. By virtue of always hitting, Magic Missile has about doubled its average damage (longsword hit-chance is about 60%). So we can have magic missile do 11.25 average damage, or about 2d10.

What about AoE spells like Burning Hands? Burning Hands has about the same chance as hitting as a long-sword attack, but it's considered more potent by virtue of hitting more targets. We can consider the AoE attacks to hit at least 2 targets. So again, we can just use 11 average damage or 2d10.

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Magic Missile
1st-Circle Evocation
Casting Time: 1 action
Target: Varies
Range: 4
Components: V, S
Duration: Instantaneous
Effect: 2d10 Force damage missile, +1 missile per Circle
Creates a magical force missile for each Circle used, each of which does 2d10 force damage. Each missile can be assigned to the same or different targets, before the damage rolls are made.

Burning Hands
1st-Circle Evocation
Casting Time: 1 action
Target: Small cone
Range: -
Components: V, S
Duration: Instantaneous
Effect: 2d10 Fire damage per Circle; Finesse save halves
Objects in the zones that aren’t being worn or carried will also be damaged.
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You know what? Rather than making players remember all the different spell damages, why don't we just keep it to 2d10 damage for every spell?

Well, every spell except Cure Wounds, which is a very different kettle of fish.

Incidentally, there's a certain classic D&D spell of the 9th-Circle spell called Power Word Kill;

Power Word Kill
You utter a word of power that can compel one creature you can see within range to die instantly. If the creature you chose has 100 hit points or fewer, it dies. Otherwise, the spell has no effect.
Since we know that spell gain power linearly (2d10 per Circle) in our system, we can balance Power Word Kill in the same way. Spells gain about 2d10 damage per Circle, so a 9th-Circle spell should do about 9*2*5.5= 99 damage. Just 1 short of 100! So Power Word Kill stays the same.

Is it a coincidence, I wonder? Probably not. 2d10, our benchmark for Magic Missile damage, actually does the same average damage as the 5E version of Magic Missile; 3(d4+1).
2*5.5= 11
3*(2.5+1) = 10.5

10.5*9 =94.5, just a little under 100. So although Magic Missile in 5E does scale linearly with spell slots, the average power of the spell slots is sort of designed to do so.

Sort of. Meteor Shower is a big exception. 2*(20d6) = 40x3.5=140 average damage. Yikes.

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But waaaaaaaait. Didn't I decide that Strength, Finesse and Cognizance only increases the damage, not the actual hit chance? Shouldn't it be the same for spells as well?

Whoops. Ok. So It looks like I should be introducing modifier damage into the spell damage equations. This goes against D&D traditions once again, mind you, but somehow I don't think D&D purists will really mind.

And so, aim is about 11.25 damage per circle. We're expecting a modifier value of +3. Erm... 2d6+3=10? A little low. 2d8+3=12? Now a little high. 1d12+3=9.5 is far too low.

Can only apply modifier once, otherwise modifier contribution becomes too important.... OR DOES IT?

Warriors apply their modifier once for every level in my game. If spells apply modifier only once per circle, then spells will apply modifier only once every 2 levels since PCs gain a new circle once every 2 levels.

Thematically, it makes more sense that spells are more dependent on modifier than weapon attacks. A weapon is still very dangerous in the hands of someone who is weak. A spell in the hands of someone without the right aptitude for it... much less so. So fine, let's apply ability score modifier twice for spells.

In that case, there's a clear case for 2[d4+Mod] = 11 average damage assuming a modifier of 3.

What about Power Word Kill? Hrm. At level 17, Players would have a modifier of +6. 18*(2.5+6)= 153. So about 150 Power Word Kill threshold is about right? Maybe.

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Since the spell-casting ability score doesn't affect hit chance, status affect spells need some other way to depend on the spell-casting ability score. Probably the duration of the status affect.

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