What spell slot count formula can I use to base my homebrew mechanic on?

Question

I've noticed that for full table magic users (spells going up to 9th level), a new level spell slot opens up every two levels, it goes like this up until level 17 where it caps off at that point assumedly since there are no 10th level spell slots to be gained on levels 19 and 20.

It looks like there's some math going on behind the scenes here so I was wondering if anyone has had a crack at this and figured how similar tables could be constructed for homebrew content?

Context: I'm brewing together a system for a sorcerer which requires them to keep using spells to discharge their inner magic on a daily basis or risk their magic overflowing and potentially causing hilarious terrible things to happen to them and/or their party. I've got the capacity and mechanics down I just now need to figure out a way to keep the discharge effort consistent with the sorcerer gaining more and higher level spells as they level up.

To clear up some confusion I'll give an example situation.

Let's make it relatively simple and say I want a sorcerer to spend half of his magic every day or else he catches fire.

For 1st and 2nd level it's pretty straightforward:

• 1st level - player has two 1st level slots, has to use one to achieve 50%
• 2nd level - player has three 1st level slots, has to use two to achieve at least 50%
• 3rd level - this is where the problems start, player now has four 1st level slots and two 2nd level slots, using two 1st level spells and one 2nd level spell would be 50%, but what if they cast four 1st level spells, would that be the same? Is a 2nd level spell slot really twice as good as a 1st level spell slot? What about 3rd level spell slot?

I was looking for a mathematical formula which would detail the growth in slot amount and level to then perhaps somehow be able to extract an intrinsic value of a spell slot level, which would then allow me to assign a numerical figure to a casters spell budget, which I would be able to then apply percentage based goals upon.

Answer 1

You should read the section Variant: Spell Points, starting on page 288 of the DMG.

The easiest would be to just use the variant, as the half of all spell points is well defined. As the character is already a sorcerer (with Flexible Casting from level 2), changing completely to the variant will only simplify things.

If for some reason you wish to use spell slots, you could use the table on that same page that defines the "point cost" of a spell of a given level. You add up all his spell slots (maybe sorcery points too) and compare the value of used spell slots to that. You (or your player) will still need to keep track of the spell-point-equivalent of slots yet spent, though.

Answer 2

The multiclassing rules on page 164-165 of the Player's Handbook make it clear that all characters approximately use the same spell slot progression table, which is that of the wizard and cleric, but some "secondary" caster classes progress at one half or one third of that rate:

Spell slots. You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, half your levels (rounded down) in the paladin and ranger classes, and a third of your fighter or rogue levels (rounded down) if you have the Eldritch Knight or the Arcane Trickster feature.

You'll notice that this largely holds true for the paladin spell slot progression. They have no spells at all for the first level, because that would round down to zero, and their spell slots only change every two levels. It isn't exact, since the paladin gains his new slots at odd levels (5, 9, 13, 17), to match the other major casting classes. The ranger gains their spells at the same levels.

Primary spellcasting classes (bard, cleric, druid, sorcerer and wizard), as in those for whom spellcasting is their main ability, progress at the full rate. In other words, if you want to make a variant sorcerer, it should really use the standard sorcerer spell slot progression unless the class has other combat abilities like the paladin or eldritch knight fighter archetype does.

The secondary caster table is for paladin and ranger, who are in a sense hybrids of fighter-cleric and fighter-druid, respectively. Spells are their secondary abilities, so they have half progression. It's not precisely half, as it seems that the designers tweaked the table so, for example, you gain your new slots and odd levels and gain a third spell per day at level 3 to beef you up early on, and so you gain something when the primary casters do.

The tertiary casters are those who are magic-using archetypes of a class that isn't normally a magic-using class. This is for the fighter or rogue who dabbles in magic, and isn't recommended for a variant sorcerer.

Answer 3

Calculate the total amount of spell slot levels a sorcerer has at each level and say they have to spend half of that.

The idea came from the Ioun Stone, Reserve:

This vibrant purple prism stores Spells cast into it, holding them until you use them. The stone can store up to 3 levels worth of Spells at a time... The level of the slot used to cast the spell determines how much space it uses.

A 20th level sorcerer's spell slot table:

In this order: 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th 
                4  |  3  |  3  |  3  |  3  |  2  |  2  |  1  | 1

Calculating 4x1 for 1st level, 3x2 for 2nd and so on until 9th for 1x9 with a total of 89 levels worth spell slots.

Here is the table so you don't have to calculate each level.

As you can see at level 20 the sorcerer can cast a total of 22 spells. And has to spend total of 45 level slots (89/2).

That sounds like a lot of mandatory spellcasting to me. If you want you can modify this with sorcery points spent or proficiency or highest level spell slot available etc.

Some ideas:

1. Add each sorcery point spent as additional spell slot used. (Probably with the exception of converting sorcery points into spell slots or vice versa)

   Makes sorcery point a good way to discharge easily at lower levels, value drops as levels increase.

2. Spending at least 1 sorcery point while casting a spell adds your proficiency bonus to your slots spent count additional to the spell slot expanded for that spell.

   Makes metamagic the best way to discharge. Both for the lower levels and high.

Answer 4

As described, the sorcerer just has to burn some magic at the end of the day melting a rock or something.

This is a cost (not having spells ready during long rests), but you really, really don't want to burn too much bookkeeping effort to work out exactly how many spells you need to burn.

Keep it simple. Half (rounded up) of your highest level spell slots must be expended.

If you feel that is too liberal, require that both half of your highest level spell slots and half of your spell slots be expended.

Doing pointless spell point calculations or sorcery point calculations is going to be a waste of time on the part of both you and the player.

Answer 5

I seem to have noticed a general progression in DnD 5e (in terms of magic). It goes as follows:

1, 2, 3, 4, 5, 6, etc.

2, 3, 5, 8,12,17, etc.

where f(n) = f(n-1) + n-1 and f(1) = 2

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It is hard to explain where exactly this occurs, but it seems to be pretty recurring in psionics, sorcery points, etc.

You can use this to help calculate your magic overflow. For example, a 4th level spell slot would be worth 8 overflow points. Then, by the end of the day (or however long you want), the sorcerer must use at least half his overflow points worth of spell slots.

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Alternatively, each Xth level spell slot the sorcerer has can be worth X overflow points. I would try out both options and see what works for you.

Answer 6

What I came up with (in case anyone is interested):

In the end, I went and read through Variant: Spell Points to determine the intrinsic proportionate numerical values of each spell slot:

Combining this with the spell caster slot acquisition table:

I was able to gauge the relative magic power a spell caster possesses on each level. I then split up the levels by the Sorcerous Origin Feature acquisition milestones (Levels: 6->14->18), however, I did not like the large spread between levels 6 and 14, so I nudged the table split from 6th level to 8th. Then I twiddled around with how much of the sorcerer's power I'd want them to expunge on a daily basis to remain on the same charge level, then messed about with either rounding up or down the numbers that came out to what feels right and came up with the following table:

Assuming the capacity of said magic stays the same (say around 24 points per day) and the limit (LMT) I set in the previous table would nudge the sorcerer down by 24 points, I came up with a table which shows how many points (out of the capacity of 24) each spell will be worth each sorcerer level.

All of this, however, is a bookkeeping nightmare waiting to happen, so assuming that the magic bomb can be split up into 4 stages each of which can have a different effect (spread apart roughly say 6 hours each, or 4.5 hours if the magic does not accumulate during sleep) then the previous table can be mapped out to a more manageable state:

However, the math itself on this seems pretty wonky (there's a steep fall from level 1 to level 2, level 7 seems to offer too much leeway and at the end of the spectrum high-level sorcerers would have quite a bit of trouble keeping up with the magic accumulation when their lower rank spells are rendered quite ineffective.

However, this is all fine, since I only wanted a rough outline plotted, so now since I have it I can tweak this last table a bit, and in the end, I've settled on the following table: