Arithmetician

Overview

A once well respected professor at the University of Mathematics and Physics, the Arithmetician is a powerful warlock who has been sent on research missions by the University Headmaster, a powerful celestial entity known for its vast knowledge of mathematics, universal laws and geometries. Being blessed by the headmaster, the Arithmetician is able to use learned formulae to modify values of rolled hit points for spells, actions, and saving throws.

"Magic": the Gathering

In order for the Arithmetician to gather their web of formulae, they must copy down formulae from other sources into a personally owned magical artifact known as a "textbook," costing base value 20GP per formula. Formulae from the textbook may be used as a bonus action/reaction in response to an action from the Arithmetician, ally, or foe. Formulae may also be used in place of spell slots. Each formulae has its own classification (cantrip, 1st level, etc.) based on its power, and may be placed in the equivalent spell slot every short rest. The available formulae able to be added this way are limited.

 (optional features):

• Diverging Spells:

Starting at 17th Level, the Arithmetician has mastered Refraction, and can now increase the number of targets/projectiles a spell has, at a maximum of 5 additions, being reset the conditions for Passive Deduction, as well as a short or long rest. For each additional target/projectile, an additional die of whatever is relevant to the spell's hit die is added. For spells modified by formulae, the additional die is added after the formula is used.

• Heightened Mastery/Achieved Ignorance:

Once an Arithmetician has reached the 20th Level, they may apply formulae to any spell, regardless of the application or relevance. For each formula applied this way, the user takes 1d6 psychic damage.

(Replacement Feats)

• Forced Translucence:

Starting at the 6th Level, the Arithmetician has found a method to alter the transparency of armor, in doing so making it easier for their spells to connect. Whenever you attack with a spell, so long as that spell produces a projectile, you may reduce the target's AC by up to 4. This effect lasts until the turn ends, and causes connecting spells to deal 10% less damage for each decrease in the AC.

• True Researcher:

Starting at the 10th level, the Arithmetician has begun conducting research on prepared formulae that have already been recorded. Whenever you use a prepared formula from a spell slot, if that formula has already been learned, you may modify a non-damage value in that formula anywhere from a 50% reduction in the value up to a 200% increase in the value. Doing so causes the formula to be unusable until the combat ends or a short or long rest has been completed.

• Cold and Calculated:

Once the Arithmetician has reached the 20th Level, they have mastered the ability to calculate their own accuracy perfectly. Once per long rest, you may entirely ignore one dice roll, instead choosing the highest value on the dice (this does not cause a crit). Doing so gives you disadvantage on the next two proceeding actions that you would perform.

Convergence and Dispersion

Starting at 3rd Level,  the Arithmetician is able to modify the conical range of a spell as a bonus action. This can be done between the spells original range and up to 45 degrees of difference. A spell effected by this also has its hitpoint value modified, with each 15 degrees changing the spells effectiveness by 1 hitpoint per dice rolled (concentrated increases, diffused decreases). A maximum diffused spell gains advantage.

Gained Interest

Starting at 6th Level, the Arithmetician gains the ability to compound a spells effectiveness through a ritual. The ritual's length is plugged into the equation D=v(1±1/10)^t, where v is the rolled value, t is the ritual length in minutes, and D is the final outcome. The longer the ritual is held, the more powerful the spells becomes. The ritual must be done with no movement and the "textbook" in hand, opened to the dedicated page. When Gained interest is applied, no other formulae may be applied to the spell (voided by Compounding Formulae).

Compounding Formulae

Starting at 10th Level, the Arithmetician may use two formulae on one spell (the lower level formula's result is applied to the higher level formula). At Level 10, the two formulae must be Level 1 or lower, increasing by 1 Level with every 2 Levels the Arithmetician gains. Whenever Compounding Formulae is applied, the user gains disadvantage on the used spell, up until the 12th Level. This does not allow for any formula to be used on any spell, making the available compounds limited.

Passive Deduction

Starting at 14th Level, the Arithmetician gains the ability to passively increase their spells range at the cost of Spell Slots. For a Level 1 Slot, it increases the spells range by 10 ft, with each additional Level increasing it by 5 ft from the previous. Spell Slots consumed this way can be replenished when the character reaches full health (only applies if an increase in hp happens to reach max), on a critical role, or after two combats have passed. Spell slots renewed any other way than a short or long rest have a reduced Level until a short or long rest.