I wanted to create a subclass for Wizard that uses an expendable die resource to augment its magic and benefit its allies, similar to how the Battle Master Fighter expends superiority dice to fuel maneuvers which augments its attacks and benefit its allies.
The following were some significant steps and motivations in my design process.
The following is the result of my design effort.
Arcane Expertise
At 2nd level, you gain proficiency in the Arcana skill if you aren’t already proficient in it, and your proficiency bonus is doubled for any ability check you make that uses Arcana.
Magical Savant
When you choose this school at 2nd level, you learn magical theorems that are fueled by special dice called savant dice.
Theorems. You learn three theorems of your choice, which are detailed under “Theorems” below. Many theorems enhance a spell or other magical effect in some way. You can use only one theorem per effect.
You learn two additional theorems of your choice at 6th, 10th, and 14th level. Each time you learn new theorems, you can also replace one theorem you know with a different one.
Savant Dice. You have four savant dice, which are d8s. A savant die is expended when you use it. You regain all of your expended savant dice when you finish a short or long rest.
You gain another savant die at 6th level and one more at 14th level.
Theorems
The theorems are presented in alphabetical order.
Applied Studies
When you make an Intelligence (Arcana, History, Nature, or Religion) check, you can expend one savant die to add it to the check. Alternatively, when you or a friendly creature who can see or hear you makes an Intelligence (Investigation) check, you can use your reaction and expend one savant die to add it to the check before or after making the check, but before any effects of the check are applied.
Beguiling Spell
When you cast a spell that forces a creature to make a Wisdom saving throw against being charmed or frightened, you can expend one savant die to make the spell especially beguiling and hard to ignore. Subtract the savant die from that creature’s first saving throw against the condition.
Damping Defense
When a creature damages you with a weapon attack, you can use your reaction and expend one savant die to reduce the damage by the number you roll on your savant die + your Constitution modifier.
Distracting Spell
When you hit a creature with a spell attack, you can expend one savant die to distract that creature, giving your allies an opening. You add the savant die to the attack’s damage roll. The next attack roll against the target by an attacker other than you has advantage if the attack is made before the start of your next turn.
Dual Strike
When you cast a spell with a duration of Instantaneous and it deals damage to a creature on your turn, you can use a bonus action to direct one of your companions to strike in tandem. When you do so, choose a friendly creature who can see or hear you and expend one savant die. That creature can immediately use its reaction to make one weapon attack against the same target, adding the savant die to its attack roll.
Elemental Flux
When you cast a spell that deals acid, cold, fire, lightning, or thunder damage, you can expend one savant die and choose one of the spell’s damage types from that list to substitute for another type from that list for the spell’s duration. The first time you roll damage for the spell using the substituted type, add the savant die to the damage roll.
Focusing Oration
When a friendly creature that can see or hear you misses with an attack, you can use your reaction and expend one savant die to refocus that creature’s efforts. Add the savant die to the attack roll, possibly changing the outcome.
Galvanizing Oration
When a friendly creature that can see or hear you makes a saving throw to end an ongoing effect on itself or to maintain concentration, you can use your reaction and expend one savant die to add it to the saving throw.
Maneuvering Spell
When you cast a spell with an area of effect, you can expend one savant die to direct one of your comrades to exit the area. Choose a friendly creature who can see or hear you in the area. Before the spell takes effect, that creature can use its reaction to move up to its speed, adding the savant die to its AC until it stops moving.
Mental Agility
When you roll initiative at the start of combat, you can expend one savant die to add it to the roll. When you use this theorem and aren’t incapacitated, you can’t be surprised on your first turn in combat.
Merciful Spell
When you reduce a creature to 0 hit points with a spell and the target isn’t killed outright, you can expend one savant die to hold back some of the spell’s energy and merely knock the target out. The target falls unconscious and is stable. You gain temporary hit points equal to the savant die roll + your Wisdom modifier.
Precision Spell
When you make a spell attack against a creature, you can expend one savant die to add it to the attack roll. You can use this theorem before or after making the attack roll, but before any effects of the attack are applied.
Reactive Cantrip
When a creature misses you with a melee attack, you can use your reaction and expend one savant die to cast a damaging cantrip that targets only that creature and has a duration of Instantaneous. Add the savant die to the cantrip’s damage roll.
Stirring Oration
When you cast a spell with verbal components on your turn, you can use a bonus action and expend one savant die to encourage one of your companions with an insightful speech woven into your spellcasting. Choose a friendly creature who can see or hear you. That creature gains temporary hit points equal to the savant die roll + your Charisma modifier.
Swift Spell
When you cast a spell that forces a creature to make a Dexterity saving throw, you can expend one savant die to make the spell especially swift and hard to avoid. Subtract the savant die from that creature’s first saving throw against the spell.
Tough Spell
When you cast a spell that forces a creature to make a Constitution saving throw, you can expend one savant die to make the spell especially tough and hard to withstand. Subtract the savant die from that creature’s first saving throw against the spell. This theorem can’t hinder a Constitution saving throw made to maintain concentration.
Expeditious Research
Starting at 6th level, you can use the Search action as a bonus action.
Improved Magical Savant
At 10th level, your savant dice turn into d10s.
Timely Epiphany
Starting at 14th level, when you roll initiative and have no savant dice remaining, you regain one savant die.
I am not at all concerned with whether the Pedagogy Wizard seems thematically or mechanically similar to the Sorcerer, so any similarity between the concept of theorems and of metamagic isn’t considered to be infringing on the use case of Sorcerers for purposes of my question, unless a theorem directly replicates a particular Sorcerer metamagic option.
(To the best of my ability, I’ve followed the recommendations on Meta for how to present a homebrew balancing question. I’m happy to accommodate actionable suggestions for improvement of the question. However, if I need to iterate the subclass design again after reviewing the answers, that will be done in a separate question. Finally, sorry for the wall of text. I hope it’s easy to follow.)
