Lights-End-First-Edition/ruleset/forGameMasters/balancingConsiderations/spellcasting.md

Spell points

Spellcasting using a mana system is a bitch

Cost

The cost of spells in LE1e is loosely based on the fibonacci sequence, when basing a spell on another in dnd or pathfinder the fibonacci number of the spell level (starting at 2 for level one spells) is used, then adjusted for more fine-tuned balance

Spell level	SP cost
1	2
2	3
3	5
4	8
5	13
6	21
7	34
8	55
9	89

Using this sequence lets us use a non-linear scaling pattern, "bigger" spells can feel big pretty quickly, small spells feel small pretty quickly.

Where this model falls apart is in trying to get casters to not use only super big spells every time they cast one. Give them too many points and there is no reason not to cast nuke every turn, too little and they can't do more than one encounter while being useful. only enough to cast a level 9 equivalent spell at the level you want them to start thinking about casting them and your small spells have to do quite a bit for DPS casters to be able to deal damage. Give them enough to cast that same spell a couple levels early? now they can cast level 7 spell equivalents every turn in combat every combat they are a part of.

There are a few ideas to fix this, but it is quite difficult to balance between them. The goal is to keep big spells feeling big, and small spells feeling small, while still giving a reason to cast the small ones

Spell scaling

A major thing with scaling spells is that when you do, either new more-costly spells are better (which is a good thing, I think) or the player gets an ol' reliable at level one, that outscales anything that costs more than it does before it ever reaches the same cost. You have to be careful about all of the spells to make one spell that scales not just objectively better than another. Non-scaling spells should have more cost-efficiency than scaling spells, but the damage potential of the scaling spells is only limited by the amount fo SP the player has readily available.

Resource efficiency

A player with 150 SP might be able to cast a big scaled spell that deals 40d6 damage at once for all 150 SP, or they can cast 15 spells for 10 SP that deal 3d8 each. That big spell will feel big, but at the same time the small spells are efficient enough that the player can know without having to do math that they may deal more damage, just not all at once

Give the players an ol' reliable spell. The idea is to get spells that deal damage more efficiently than bigger spells, but never quite hit the same level. This is, of course, easier said that done. If I make a level one spell that deals 1d6 damage, and make the cost scale by +2 every time, it needs to scale 44 times to hit the same cost as a level nine equivalent spell. If we just increase the number of damage die, our 9th level spell has to deal more than 45d6 damage to be more worth it than our level one.

Regaining SP on a short rest

The idea behind this one is pretty simple, it means you can limit the maximum number of spell points below what what they might need to nuke the monster every turn every combat, giving back a lower number of points when the party takes a rest and them completely resetting them on a long rest.

Doing something like this discourages the indiscriminate use of their big spells, they know they can cast the small ones all the time, they will probably get the points back before their next long rest. However if they dip into more than they get back on their short rest, they have to start thinking about the spells they cast. Is it really worth it? will they need those points later? We want them to ask these questions when they cast a spell, that way, hopefully, they cast smaller spells more often

How many "encounters" do we expect players to have in a day (long rest)

Now the word encounter here is very loosely defined, this could be anything that requires resources to be used. Some form of puzzle, trap, environmental hazard, or combat encounter. All the will assume players are short resting after each combat encounter which are interspersed with minor encounters like traps, puzzles, and social encounters.

That said, for this we can just pull some numbers straight from the deepest reaches of our asses and say 2 to a 'minor' combat encounter with a boss or mini-boss fight, or 3 combats without a boss fight, and about 2-3 non-combat encounters between each one

I did have this set at 6 encounters/long rest previously, but chose to go with 3 combats and group the non-combats up because if we are accounting for every roleplay encounter, 6 is too few

Now for the math

With all of this in mind, its time to pull some formulas from the deepest pits of hell.

Step one: How much SP do we expect a player to expend

expected 'spell tier' per level

each character isn't expected to cast spells higher than a certain tier based on their level, with a different tier we want their average spell to be (about 2 tiers lower than their higherst level)

note: levels 1-5 don't follow this because we cannot subtract 2 without hitting a negative number (or 0), which don't exist as tiers

level	high tier	regular cast
1-2	1	1
3-5	2	1
6-7	3	1
8-9	4	2
10-12	5	3
13-14	6	4
15-17	7	5
18-19	8	6
20	9	7

How many spells will a player cast

lasting on average 4 rounds, a player will have time to cast at most 12 spells per combat encounter, 4 can be cast as advanced actions, 4 as basic actions, and 4 as reactions. No spell should be made that does not cost one of these actions.

12 spells per encounter is a bit extreme, but lets budget for one spell per round per combat encounter, meaning on the extreme end of 6 combats that is 3*4=12 spells between each long rest just on combat encounters, adding two spells across the 12-18 minor encounters (remember, these could be as simple as talking to an NPC or solving a puzzle) brings us to 26 spells between each long rest (complete SP reset)

How many SP will those spells take

The exact amount will vary, but our goal should be for their 'small' spells average 3 'tiers' lower than their 'high tier' spells. Say of those 26 spells, 2 are their 'high tier' spells, this leaves a level 10 character casting 24 tier 2 and 2 tier 5 spells between rests, which means we need to do math depending on our level ranges from before

Our function looks a little like this, where H is the SP cost of a high-tier spell for the level and L is the cost of a low-tier spell, and f(x) is the characters level

f(x) = (2*H) + (12 * L)

This is the simple version, where H and L are precalculated, it can probably be expanded as a function which only needs a characters level, but we have no need for that equation right now. At least for now, if I decide I need it later I suppose I will be stuck doing some more math

Level	2*H	12*L	f(x)
1-2	4	24	28
3-5	6	24	30
6-7	10	24	34
8-9	16	36	52
10-12	26	60	86
13-14	42	96	138
15-17	68	156	224
18-19	110	252	362
20	178	408	586

How many SP will the player regain from short rests

Now we have figured out our ideal per long rest SP quotas, we can get a better estimate for the amount of SP to regenerate per short rest. Again, numbers from the our ass, trying to get close to the low tier spell budget at the higher end of the range so high tier spells cut into the players reserves, and low tier spells can be cast without feeling like your dipping into those reserves.

If we use 1*level then we get 8*6=48 SP from rests at level 1, and 80*6=480 SP from rests at level 20. These numbers give us some pretty decent starting points, the ideal max SP goes from 52 at level 1 to 16.

Tried so hard to scale by a multiple of character level but it just does not math, either your are over budget by 300 SP until level 15 or underbudget by 700 at higher levels

To do this we can make some more of those tables that we love so much! at lower levels we shoot a little low on the SP regeneration, saying players get 8 SP on a short rest means that our ideal max SP is 4, which allows 2 level one spells which means just about nothing. You will notice that as level goes up the ideal max will fluxuate up and down, this is intentional, we will get into exactly why after this, but just keep that in mind

rewritting this entirely to better convey how we are choosing numbers

To properly choose an SP/short rest figure we can't really use an equation (well, strictly speaking we can) because our ideal SP grows exponentially, and any equation on either side makes the players have to recalculate the entire thing every level. So at best we can use one linear equation (add x to this number every level up). During gameplay the entire benefit of equations is that you can level infinitely, so doing that has no point. In practice, I have to make a module for foundry and making all values of SP a function of character level is much easier to program than hard coding everything. It also allows anyone who does want to go over level 20 to start using that equation, and ideally the difficicult equation will be the one that only needs to be solved by one person (Knowing most tables this one will fall on the GM 90% of the time so sorry in advance to all the GMs), and we have an easy linear equation for the one each player needs to solve on their own.

So which equation only needs to be done once per levelup and which one needs to be done multiple times? The SP per level will be more subject to change between each class than the SP/short rest, so in most cases the SP/short rest will be the same for everyone, while max SP is different between each class.

Now onto making those equations, the first one we need is how much SP increases each level, we will need this as part of the other equation to adjust for the maxSP pool the player will start with on a long rest. To figure this out, first we ask how much max SP do we want players to have at level 1, and how much for level 20. Say 10sp for level 1 and 200 for 20, that is a difference of 190 across 19 additions, or 10sp for each level. I wasn't thinking about that when chosing that but it works perfectly.

This means a characters max SP can be expressed as 10 * level so we will subtract that from our answer when we get to SP regeneration

The annoying equation is as follows, and will be explained in sections after the full definition

$ \begin{aligned} \ &\text{let } x = \text{Character level} \ &\text{let H} = \begin{cases} 2 _1 & \text{if } 1 \leq x \leq 2 _1 \ 3 _2 & \text{if } 3 \leq x \leq 5 _2 \ 5 _3 & \text{if } 6 \leq x \leq 7 _3 \ 8 _4 & \text{if } 8 \leq x \leq 9 _4 \ 13 _5 & \text{if } 10 \leq x \leq 12 _5 \ 21 _6 & \text{if } 13 \leq x \leq 14 _6 \ 34 _7 & \text{if } 15 \leq x \leq 17 _7 \ 55 _8 & \text{if } 18 \leq x \leq 19 _8 \ 89 _9 & \text{if } 20 \leq x _9 \end{cases}\ &\text{let L} = \begin{cases} 2 _1 & \text{if } 1 \leq x \leq 7 _1 \ 3 _2 & \text{if } 8 \leq x \leq 9 _2 \ 5 _3 & \text{if } 10 \leq x \leq 12 _3 \ 8 _4 & \text{if } 13 \leq x \leq 14 _4 \ 13 _5 & \text{if } 15 \leq x \leq 17 _5 \ 21 _6 & \text{if } 18 \leq x \leq 19 _6 \ 34 _7 & \text{if } 20 \leq x _7 \end{cases}\ &S=\frac{(12L+2H-10x)}{3} \end{aligned} $