School of Arithmancy

To most spellcasters, magic is an art of intuition, imagination, and will. A wizard studies the principles of the arcane, commits hundreds of spells to memory, and learns to shape supernatural forces through careful practice. To the wizards of the School of Arithmancy, however, this understanding is incomplete.

They believe magic is mathematics.

Every spell is an equation. Every creature is a collection of variables. Every physical law is a constant waiting to be measured. Distance, velocity, mass, vitality, probability, and even the circumstances of a creature's existence can be reduced to numbers. Where other wizards see a battlefield filled with dozens of independent creatures, an Arithmetician sees a complex mathematical system in which every participant occupies a precise position within an enormous equation.

Arithmancy is the study of these relationships and, more importantly, the art of manipulating them. An Arithmetician does not necessarily need to be stronger than an opponent, faster than them, or more powerful than them. They merely need to understand what the numbers say.

 

Arithmancy

Beginning when you choose this school at 3rd level, you can replace the standard targeting of a spell with a mathematical formula. As an action, you can use Arithmancy to alter a spell you have prepared. Instead of a normal casting, you choose one parameter and one calculation from the tables below. When you do, the spell instantly affects every creature that meets the criteria within the spell's range.

This effect cannot be used on a spell with a range of Self, a spell that requires concentration, or a spell with a casting time longer than one action. You can use this ability a number of times equal to your Intelligence modifier. You cannot use this feature again until you finish a long rest.

Parameters:
d6 Parameter
1 - Level: A creature's level.
2 - Strength: A creature's Strength score.
3 - Speed: A creature's base walking speed.
4 - Armor Class: A creature's current armor class.
5 - Position: A creature's distance in feet from you.
6 - Remaining HP: A creature's current Hit Points.

Calculations:
d6 Calculation
1 - Multiple of 3: The parameter result is an exact multiple of 3.
2 - Multiple of 4: The parameter result is an exact multiple of 4.
3 - Multiple of 5: The parameter result is an exact multiple of 5.
4 - Prime Number: The parameter result is a prime number (2, 3, 5, 7, 11, etc.).
5 - Odd Number: The parameter result is an odd number.
6 - Even Number: The parameter result is an even number.

Expanded Algorithms

You have mastered more advanced mathematical theories and can apply them to your spellcasting. Your Arithmancy parameters and calculations tables increases to a d10, granting access to these additional options:

Expanded Parameters
7 - Max HP: A creature's maximum Hit Points.
8 - Initiative: A creature's initiative bonus.
9 - Remaining Spell Slots: The number of remaining spell slots a spellcaster has.
10 - Hit Modifier: A creature's current attack / spell attack modifier.

Expanded Calculations
7- Greater Than: The parameter is greater than a number you choose. 
8 - Less Than: The parameter is less than a number you choose.
9 - Divisible By: The parameter is divisible by any single-digit number you choose.
10 - Equal to: The parameter is equal to a number you choose.

When using Greater Than, Less Than, Equal To, or Divisible By, you declare the number as part of casting the spell.

Numerical Certainty

Your calculations become more precise. When you use your Arithmancy feature, you can now choose to exclude allied creatures who would be harmed by your spell or enemies from being healed or benefitting from a spell.

You can regain one of your expended uses of Arithmancy after you complete a short rest.

Statistical Devastation

You push your calculations to their theoretical maximum. When you use Arithmancy, you can choose one of the following enhancements:

• Maximized Outcome. Any variable numerical effect of the spell (damage dice, healing dice, temporary hit points, etc.) is treated as rolling its maximum value.
• Forced Remainder. Creatures that meet your condition have disadvantage on their first saving throw against the spell.

You can use this feature a number of times equal to your Intelligence modifier (min 1) until you finish a Long Rest.