D&D General Why is the multi-classing spell slot math so weird?

Wasn't it a bit more complicated than that - yes, a spell scaled with caster level -but the DC was based on spell level and caster ability modifier, so a 3rd level Fireball was easier to resist than a 5th Level Cone of Cold. Both deal the same amount of damage dice (at least until 10th level, Fireball ranged from 5d6 to 10d6, Cone of Could from 7d6 to 15d6, IIRC).
Requiring a whole feat to Heighten a Spell just for the DC however was rarely seen as worth it.
It depends on the spell too. Some spells (great ones even)
had a fixed dc for some of what they did. Sleet storm and web are the only two that come to mind but I'm sure that there were others
 

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I thought the RAW were to divide by 3, add the fractions, and then round down. If that’s true, then an AT5/EK5 would get a CL of 3, not 2. If we divide, then round down, then add up, it yields a CL of 2 (as you said). Which is it (by RAW)?
It is not 100% clear in the rules. The text in the 5e2024 PH says, "One third of your Fighter or Rogue levels (round down) if you have the Eldritch Knight or Arcane Trickster subclass." The phrasing doesn't anticipate someone taking both of those subclasses in one character, so I suppose it would be up to the DM to interpret whether you combine the numbers then divide, or do them separately.

Interestingly, the previous bullet says, "Half your levels (round up) in the Paladin and Ranger classes." Interesting that they used the "and" and "classes" there and the "or"/"subclass" (singular) in the next bullet. I would read that as calculating each subclass individually (as Tessarael did in their post), but if you rule otherwise in the case of the fighter/rogue, I think you need to do the same for a paladin/ranger for consistency (which hurts the latter option slightly, as a P1/R1 gets +2 caster levels if you calculate them separately, and +1 if you combine them and then divide).
 

It is not 100% clear in the rules. The text in the 5e2024 PH says, "One third of your Fighter or Rogue levels (round down) if you have the Eldritch Knight or Arcane Trickster subclass." The phrasing doesn't anticipate someone taking both of those subclasses in one character, so I suppose it would be up to the DM to interpret whether you combine the numbers then divide, or do them separately.

Interestingly, the previous bullet says, "Half your levels (round up) in the Paladin and Ranger classes." Interesting that they used the "and" and "classes" there and the "or"/"subclass" (singular) in the next bullet. I would read that as calculating each subclass individually (as Tessarael did in their post), but if you rule otherwise in the case of the fighter/rogue, I think you need to do the same for a paladin/ranger for consistency (which hurts the latter option slightly, as a P1/R1 gets +2 caster levels if you calculate them separately, and +1 if you combine them and then divide).
Right... I'm amazed at how often 5e wording is unclear... I think I've said this before, but back in the days of the 2e and 3.5e, we could resolve any rules lawyering dispute by simply reading the books more attentively. Now, we can't get anywhere without a Sage Advice ruling, which seems so weird to me (and also makes me feel like the boomer I am).

If we consider a Paladin 5 / Ranger 5, with individual rounding then adding, they get a CL 6, while with adding then rounding, they get a CL 5.

If we then consider an AT 5 / EK 5, with individual rounding then adding, they get a CL 2, while with adding then rounding, they get a CL 3

So one method yields 6 vs 2, while the other method yields 5 vs 3. In terms of "error margin" (compared to 1/2 and 1/3, respectively), the first method has an error of +20% and -40%, while the second method has an error of 0% and +22%...
 
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Right... I'm amazed at how often 5e wording is unclear... I think I've said this before, but back in the days of the 2e and 3.5e, we could resolve any rules lawyering dispute by simply reading the books more attentively. Now, we can't get anywhere without a Sage Advice ruling, which seems so weird to me (and also makes me feel like the boomer I am).
That’s because 5e tries to sound like it’s written in natural language, but actually uses its language very technically. It’s really hard to tell when a word or phrase is being used in its literal English meaning vs. when it’s being used as a jargon term with a specific game mechanical meaning. 3e was consistently natural, and 4e was consistently technical. 5e tries to split the difference and ends up being the worst of both worlds.
 

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