How do spell slot recovery abilities work with the Variant: Spell Points system?

Question

I am considering using the Variant: Spell Points system from page 288-289 of the DMG. I asked a related question on the overall balance of this rule. This question is more focused on the mechanics of implementing it.

---

Some Druids and all Wizards have abilities that allow them to recover spell slots during a short rest, and there are a variety of other spell slot recovery abilities in the game. For example, the wizard's Arcane Recovery feature states:

[...] Once per day when you finish a short rest, you can choose expended spell slots to recover. The spell slots can have a combined level that is equal to or less than half your wizard level (rounded up), and none of the slots can be 6th level or higher.

For example, if you're a 4th-level wizard, you can recover up to two levels worth of spell slots. You can recover either a 2nd-level slot or two 1st-level slots.

How does this feature work when using the Variant: Spell Points system?

Initially I thought you would simply regain the equivalent number of spell points to the slots you could recover. However, the conversion is somewhat ambiguous due to the flexible nature of the recovery.

To use the example from the text, a 4th level wizard can recover 2 levels worth of spells. If they recover a 2nd level slot that is equivalent to 3 spell points. If instead they choose to recover 2 1st level spell slots that would be equivalent to 4 spell points. What is the correct way to handle this?

Answer 1

General Formula

The conversion from spell slots to spell points doesn't use nice numbers for on the fly calculation. That being said, there is a precise mathematical formula for calculating the number of spell points you regain if the game would have you regain a certain number of "spell levels".

$$ \text{Spell Points regained} = \lceil \frac{11}{8} \times \sum_{}^{\text{Spell Slots} \\ \text{ regained}} \text{(Spell Slot Level)} \rceil $$

Applying this to regaining an individual spell slot the formula tells us that each spell slot level is worth 1.375 spell points, rounded up to the nearest integer.

Arcane Recovery and similar features

So in a situation like Arcane Recovery where you regain up to "half your class level worth of spell slots rounded up", the adjusted calculation is:

$$ \text{Spell Points regained} = \lceil \frac{11}{8} \times \lceil \frac{\text{(Class Level)}}{2} \rceil \rceil $$

Here you are just skipping the summation of the levels from the more general formula (since your calculation of \$ \lceil \frac{\text{(Class Level)}}{2} \rceil \$ already gives you that total).

But why does this not yield 4 spell points instead of 3 for a caster wishing to make 2 1st level slots instead of 1 2nd level slot?

With Arcane Recovery you are recovering the spell slots simultaneously, not separately.

You apply this formula to the whole operation of regaining spell slots. If each spell slot is worth 1.375 spell points, you convert each spell slot into it's precise value (in the case of two 1st level slots that is 1.375 + 1.375 = 2.75). Rounding is then performed as the last step of the operation. Which yields 3 spell points for 2 levels worth of spell slots.

If on the other hand you were a Sorcerer converting sorcery points into spell points, then each time you convert sorcery points into spell points you perform a distinct operation. However, this is balanced as Sorcery Points use the same conversion progression as Spell Points (for the portion of the Sorcery Points -> Spell Slot conversion table we have in the PHB).

For example, our prospective sorcerer would need to expend 4 Sorcery Points to gain 4 Spell Points, doing two 1st level slot conversions, or they could spend 3 Sorcery Points to gain 3 Spell Points doing a 2nd level slot conversion.

---

The notation \$ \lceil \text{a} \rceil \$ indicates you are taking the integer ceiling of the value contained within the symbols. That is, you are rounding the value up to the nearest integer.

---

If we break down the general formula for one spell slot of each level we get this table:

\begin{array} {|r|r|r|r|} \hline \text{Spell Slot} & \frac{11}{8} \times \text{(Spell Slot} & \lceil \frac{11}{8} \times \text{(Spell Slot} & \text{Spell Points} \\ \text{Level} & \text{Level)} & \text{Level)} \rceil &\text{ from the DMG} \\ \hline 1 & 1.375 & 2 & 2 \\ \hline 2 & 2.75 & 3 & 3 \\ \hline 3 & 4.125 & 5 & 5 \\ \hline 4 & 5.5 & 6 & 6 \\ \hline 5 & 6.875 & 7 & 7 \\ \hline 6 & 8.25 & 9 & 9 \\ \hline 7 & 9.625 & 10 & 10 \\ \hline 8 & 11 & 11 & 11 \\ \hline 9 & 12.375 & 13 & 13 \\ \hline \end{array}

so we can see our formula matches the progression precisely.