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

If you have 2 levels as a Rogue or Fighter, the rule doesn't apply, since you add "One third of your Fighter or Rogue levels (round down) if you have the Eldritch Knight or Arcane Trickster subclass" (emphasis mine). You don't have the subclass at level 2, so rounding up from level 2 never comes into play.

If you pivot to Wizard after becoming a 4th- or 5th-level Eldritch Knight or Arcane Trickster, look at the outcome as described in the opening post. Under the existing rule, no slots are gained from the new Wizard level, which seems a little bizaare (to me, at least). Why shouldn't you go from the equivalent of a 2nd-level full caster to 3rd when you gain a level as a full caster?

The spell slots for Eldritch Knights and Arcane Tricksters are already based on 1/3 level rounded up; it would be more mathematically consistent, and I would argue thematically appropriate, to do the same when multiclassing.
You shouldn't because your spells known EK with 5 spells known &2 cantrip ps known just went from only being able to cast abjuration and evocation spells to spells from all school gained ritual casting three cantrips and six first level spells they are able to scribe spells into a spellbook they can prepare spells from in addition to ritual casting and arcane recovery all applicable to their EK slot progression.

If you must find a problem, that problem is the fact that the resulting multiclass is not preparing spells as a level 7 EK plus a level 1 wizard with the two pools of spells/slots kept entirely separate
 

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Regarding the invention of new feats and classes, I personally feel like that's a bit dicey. Not to say that everything in the splatbooks is perfectly well-balanced. In fact, there is clearly a commercial incentive for any additional player option to be gradually more overpowered the longer after the start of a given edition the splatbook comes out. But... even if the splatbook rules aren't perfectly balanced, they are nonetheless often not too bad, and it's pretty difficult to balance homebrew stuff correctly. But it certainly is feasible and if the DM/table likes it this way, then it's totally fine, of course.
It's a bit of a risk, but not much since I can always say, "Whoops! Yeah that's not working out right is it?" ask for thoughts from the players and rework mechanics or abandon ideas if need be.

Feats aren't hard for me to balance, especially given how much imbalance there already is in just PHB feats (I'm using 2014). Had to fix some of those. Doing better isn't hard!

Classes and subclasses are harder and can take a lot of time. For Warrior-Mage, since it fundamentally isn't doing anything that isn't already things in the game we have experience with, balance is almost entirely about comparison to existing classes. I made 1-20 level by level comparisons with Eldritch Knight, Bladesinger, Valor Bard, and Swords Bard, as the most relevant comparisons. That way I could compare the major combat values directly, as well as do a more subjective assessment of the exploration/social based abilities. For subclasses that isn't as useful and it's more feels based. I made a Universalist mage, as well as a Spirit Domain cleric (mostly OA 1e shukenja / 3e shaman without the martial arts), a Unity Domain cleric (more Buddhist-inspired priest with the martial arts), five Elementalist Wizard subclasses designed to work for Wu-jen, as well as (if you ignore Wood) Al-Qadim and more general Elementalist. Our warlock patron "The Shadowed" took a lot of work because the player was heavily involved, and the end effect is it is more complex than PHB subclasses but feels very rich and interesting. I think I posted it on a thread here a couple months ago.

Subclass balance is all about any unique special abilities they get, since lists of domain spells or generic abilities all subclasses get (like a cleric's potent cantrip or divine strike) are already mostly a balance neutral choice (though certain spells interactions need at least casual thought). For the Shadowed, as complex as it is, there wasn't a lot of difficulty with power balance and the work was mostly about conceptually covering the ground of multiple connected ideas (shadows, death, misfortune/curses) in a satisfying way so that if a patron really only covered one of those, this subclass would still feel appropriate. For Universalist wizard, after some effort comparing previous editions, looking at UA articles for abandoned 5e concepts, and considering existing 5e mechanics that work with the themes we identified, it came down to not having a lot of reference points that provided good balance comparisons, so it's a crap shoot. We'll have to see how it works when someone plays it. It won't be overpowered, but it might feel weak. The wu-jen elementalists all have unique meta-magicish special abilities to mess with their spellcasting a limited number of times, which is really hard to work with. Those ones are likely to have unforseen issues that might pop up and need to be addressed.

Really, with enough experience, the balance issues aren't so much with what can be seen (can't not see some obvious imbalances in published materials), or how it directly relates to other existing options (usually I remember those), but in all the little rare interactions that might not be seen. Take this feat with it, or use that ability with this spell, etc.

The biggest downside is just that much of this stuff will likely never get used just because there won't be enough campaigns for that many characters to be chosen, so a lot of it was only creating material to fill theoretical holes. At least that has basically all been done by now and it's as-needed work going forward.
 

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