Base Class: Wizard
For Personal Use with the Theory of Magic
Margin of Error
Your study of the theory of magic has allowed you to estimate at the correct way to cast a spell at a higher level without expending the extra energy to do so. At 2nd level, whenever you cast a spell, you may attempt to upcast it without expending a spell slot of a higher level. The spell may not already be upcast. You may attempt an upcast an amount up to half your proficiency bonus, rounded down (max total level is 9), in this manner.
To do so, make an Arcana check with a DC equal to 13 + twice the amount you are upcasting. On a success, you cast the spell at the higher level while expending the normal spell slot. On a failure, you instead downcast the spell by the amount you are trying to upcast while expending the normal spell slot.
For example, if a 9th-level character is casting the 3rd- level spell fireball, they may attempt to cast it at up to 5th level. In doing so they must make a DC17 Arcana check, casting it at 5th level on a success and 1st level on a failure, both based on the Theoretical Spell table. In either case, a 3rd-level spell slot is expended
You may use this feature an amount of times equal to your Intelligence modifier, and regain all spent uses on a long rest.
Improved Docent
Your constant study of theoretical magic has improved your ability to comprehend the notes of others as well as streamlining your own spellbook. At 6th level, the time and money spend to copy any spell into your spellbook is halved. In addition, you may prepare an additional amount of spells per day equal to your proficiency bonus.
Counter Flow
By observing perturbations in the Gygax Field, you may partially counter this perturbation with your own. Starting at 10th level, when you would take damage from a spell, you may use your reaction to expend a spell slot, reducing the damage by an amount equal to the spell slot's level multiplied by your Intelligence modifier. Additionally, you gain advantage on saving throws made against the effects of spells.
Theoretical Limit
At 14th level, you learn to test the bounds of your theories. When casting a spell, you may either: increase the size of your spells' damage die by 2, roll max damage on all dice, add twice your proficiency bonus to the damage, change a single target attack spell to an 30ft sphere requiring a Dexterity saving throw against half damage, or change an area of effect spell with a radius of 40ft or less into a single- target attack.
You may use only one of these effects per spell and may only use each effect once per long rest.