'Balance' covers more than just 'balance', if you see what I mean
It's a good thing to ask whether your creation balanced, as in whether it is more or less powerful than existing options.
But there's also the question of balance as in 'is a good addition?', 'is it out of place?' 'is it useful?', 'could it even have been published in 5e in the first place?' and wider questions. I'll address the latter first.
Why are you adding it?
If the answer is as simple as "because it's fun to try and make stuff", fair enough, by all means homebrew it, and if you're with a bunch of mates rolling around casually, then often no-one's going to mind. Homebrewing new content can be enormous fun for the brewer. I make new classes all the time.
However, for a more serious campaign where balance is being considered carefully, as it sounds you are, then a lot of fellow players [or your own players, if you're DM], might want more justification than that. And to do that, you need to answer 'yes' to the following questions:
- Does it let my play a character (as in mechanically) I otherwise couldn't?
- Does it let me play a character (as in person) I otherwise couldn't?
- DM: Does it add to the story of, or the story happening in, the world?
I've found most players and DMs are as concerned with 'why' than the nuances of power balance. The more detailed and difficult questions you need to think about for the latter are as follows:
(Please note I discuss these aspects of balance checking generally, using hypothetical examples and those from my own homebrew, before discussing the Alchemist specifically each time.)
"Does my class step on another class's (story) toes?"
This depends on how specialist you want classes to be. Are you aware of the 3.5 'Basic' variant where there were 3 classes? (Warrior, Expert, and Spell caster?). The 5E basic rules divide spellcaster into Arcane and Divine. The 5E full rules split arcane into two, divine in two, and warrior into three (fighter, barbarian and monk) before adding magic.
In my high-magic, high-tech, gods-at-war setting, I have added two new divine classes, a Favoured (Soul) and an Invoker (or 'Siphon', TBC). These are just making new specialisms of 'Divine Caster'. The Favoured is a servant of a deity, just as a Cleric is. Oh! I'm stepping on story toes. Or am I?
In my setting, Clerics are trained, organised servants of the pantheon, whereas Favoured characters are untrained, devoted to one master above all. So am I interfering with the Cleric's role? Certainly some PCs and NPCs who would have been Clerics might now be Favoureds. I'm stealing some of the Cleric's player base, perhaps. Is that a problem?
If your class is stealing a player-base (even just for story purposes), it is something to be aware of and that many could be uncomfortable with. But then, introducing Bard, Sorceror and Warlock into the basic rules is stealing the Wizard's players. The Nature Cleric and Ranger steal Druid players. Where do you draw the line?
I would draw the line here:
- The class does not replace an existing one, even if it takes some players (unless, for example, gods and Clerics don't exist in your world, so you make a Runepriest as an arcane gish/buffer/healer)
- The class does add a mechanical way of playing the alternative character type (this could be a mechanical combination, rather than a unique feature. See the example of my Adept class below.)
Does your Alchemist step on another class's (story) toes?
Are you stepping on any story toes with an Alchemist? I would say no. Casting a spell (examples: fireball, teleport) is not the same as alchemy (which goes wider than just potions - we could be talking self-augmentations, poisons, skin grafts, who knows?).
When people say "Just play a Wizard and call it alchemy"...
Opening asker, if you think, like me, that a character should be able to say "I'm a Dwarf Alchemist, behold my concoction!" instead of "I'm a Dwarf Wizard and this Fireball is actually me throwing a bomb really far", then your Alchemist isn't stepping on story toes.
"Does my class step on another class's (mechanical) toes?"
Ah, now we have to express our class's unique place in our story with a unique place in the mechanics. Probably: but on the condition you're not performing another class's mechanical role better, you may not have to be that unique to still have an acceptable class.
Let's take a setting which is relatively peaceful... why the heck should all clergy automatically have armour and weapons? Let's make a 'Priest' or 'Adept' class. Take the Cleric, strip out all armour and weapon abilities (including in the domains, maybe adding Divine Strike to cantrips), and give them Divine Recovery.
Yes, a lot of the time we're playing one of a Cleric's mechanical roles (buffer/healer), but then so do the Bard and Druid. Do we have a mechanical difference which reflects their story role?
Giving them Divine Recovery means their key mechanical difference is ingrained in the story difference. A Cleric is great at being in battle. Our Priest/Adept needs rest - needs peace and quiet. As the whole point is that we're making a peace-time, no-trained-for-battle sort of divine agent, the mechanic fits the story perfectly, even if it's not that unique.
Even when stepping on toes a bit, if your mechanic is at least a bit different, and mechanically expresses a story difference, then it's probably alright.
"Does your Alchemist step on another class's (mechanical) toes?"
Hmm. Are we stepping on the Wizard's mechanical toes? It depends on what mechanic you use.
As you're using spell slots, you need to ask yourself how that mechanic is actually reflecting a story difference between alchemy and wizardry. Personally my thought would be to only duplicate low level spells (2nd attacks, 3rd buffs, or something), but have it almost at will. Why, if I can make and carry one fireball-potion today, can't I make one a day for a week and then go nova with 7 when the fight comes? If I'm going adventuring, why can't I have a backpack full or kit?
Perhaps the alchemical components spoil, AND require the brewer's own blood, or something along those lines. I'm toying with an alchemist myself, and one possible idea is to make the proficiency or constitution bonus worth of potions etc. on a short rest, which last 8 hours before spoiling. (This is in addition to duplicating cantrips as long as they have a standard toolkit on them).
Is it too powerful? Is it too weak, or partially too weak?
Honestly that all depends on what you do with duplicating spells. If you're duplicating up to Fireball (which would be really nice), maybe you should only be able to get that at-will at level 18-20, because that's when a Wizard gets level 3 spells at-will. However, level 1 and 2 spells, the Warlock gets at earlier levels.
Your cantrip system up to 4d6 is less damage than other classes. Even if he can whip out literally any elemental type, bear in mind other get 4-6 cantrips so could have most elemental types available whenever they want. Just make it elegant. (going from 1d4 to multiple d6s is a bit odd: keep the 4 or 6 consistent)
It is hard to give you feedback without seeing more - but then it's probably hard for you to make more without getting feedback, I know.
Note, I've compared mostly to the Wizard, but if you brew stuff on a short rest or something, you will need to compare to the Warlock or Cleric Domains too.
As an exercise to try out balance, put your class in a hypothetical story situation and compare her to how a Wizard/Warlock/Trickery Cleric or whoever would do.
- Level 5: A mob of bandits descend on your caravan. Defend yourself! (Compare: Wizard's Fireball, Cleric's Haste on the caravan guards). How do your Alchemist's class features compare in a straight up mob fight?
- Level 10: The enemy are executing a flank attack. A company of hobgoblins will be crossing the long, fragile stone bridge leading to the village in one hour's time. (Compare: Illusionist making the bridge look out, Druid summomning creatures to re-flank their column) Maybe your Alchemist can cast Fireball but as a ritual, and take out the bridge or something. How does your class handle a large choke-point defence with some time to prepare?
- Level 15: The cult of the stonelord have taken up position in an old dwarf fortress. We can either assault the battlements or try and infiltrate an abandoned mineshaft under the water supply. (Compare: Wizard puts greater invisibility on a strike team, Bard makes a mass suggestion for one sub-faction to fight another, Sorceror sends Careful Spelled cloudkill, incendiary cloud, chain lightning, etc., as mob clearance) Can your class take on one of these roles and do it as well? Could they do several of these but not as efficiently each? Can they add something new? (Poison the water supply? Transform the overhanging cliff into a tsunami of acid?)
Maybe you can't come up with a specific plan, but thinking over those scenarios should help you decide what your class should and shouldn't be able to do, so you can think "Actually, if I give her delayed blast fireball, that just makes me a Wizard with Con instead of Wis, so maybe I'll make all her spectacular effects require preparation and slow application"
I hope that gives you some ideas to think about for balancing homebrew classes generally and some specific feedback on your Alchemist ideas.