November 1, 2019

School of Arithmetick

Arcane Tradition
Notes from the Nails: been a while since we've done a wizard, eh? No prizes for guessing the inspiration here!

School of Arithmetick

Arithmeticians are particularly learnèd wizards who use numerical techniques to analyze natural phenomena and execute pinpoint magical attacks. Their skill with numbers extends into the metaphysical realm, warping the laws of probability and enabling them to achieve incredible efficiency in everything they do.

Mathematical Savant
When you choose this school at 2nd level, your arithmetical studies have begun to pay dividends. You have advantage on any Intelligence check made to perform mathematical calculations or solve numerical puzzles.

Stable Effect
Also at 2nd level, whenever you roll a d20, you can replace the d20 with 3d6. If the roll would be subject to a critical success or critical failure, these events only occur if all three dice land on 6 or 1 respectively.

Factorize Spells
At 6th level, you can perform calculations to modify your spells. As an action on your turn, you can factorize a spell that are able to cast which normally targets one creature of your choice and does not have a range of self or touch.
     When you take this action, you must select one statistic from the following list: HP, Strength, Dexterity, Constitution, Intelligence, Wisdom, or Charisma. Also choose 3, 4, or Prime. Then, examine the final two digits of the statistic you chose for every valid target within the spell's range, including yourself and any friendly, neutral, or hostile creatures in range. The creature becomes a target of the spell if its statistic is a multiple of the number you picked; it becomes a target if its statistic is a prime number and you chose Prime. You do not have to see the target or have a line of effect to it when you factorize a spell.
     After you have factorized a spell, you must use your action on your next turn to cast the spell (if you are unable to cast the spell, such as by being incapacitated, the factorization is wasted). It then affects all of the targets that were selected on the previous turn (even if they have since moved out of range). However, a factorized spell's power is attenuated: if creatures can make a saving throw to resist the spell's effects, they have advantage on the save, and if a spell would restore hit points or grant temporary hit points, the number of hit points is halved.

By 10th level, you are able to use minor magical charms to accrue tiny amounts of power with every step you take. For every 10 minutes you spend walking, you regain 1 hit point, and earn 1 copper piece and 1 point of XP.

Advanced Numerology
At 14th level, you have complete mastery of all things arithmetical. If, when making an ability check or saving throw, you beat the target DC by 10 or more, you can conserve some of the success, adding a 1d4 bonus to the next ability check or saving throw you make. Whenever you reduce a creature to 0 hit points, any excess damage you did beyond what was necessary to reduce them to 0 is also conserved; you can add half of the excess to the next damage roll you make. If you reduce more than one creature to 0 hit points simultaneously, you can store the excess from only one of the creatures of your choice.
     Both of these bonuses can be stored for up to 1 minute, after which they disappear.

Sidebar: Prime Numbers
As a quick reference, the prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

11/3/19: Factorize Spells: CR/Level removed from statistics


  1. Nope, I became an English major for a reason.

    1. And I became a math major for a reason...

      This is beautiful

  2. Does a factorized spell automatically hit if the stat matches the number criteria we picked, or do you still make attack rolls like normal?

    1. Yes, you still need to roll to hit. By 'affect' I mean the spell proceeds as normal.

  3. This might not seem so, but it's grossly overpowered.

    The average of 3d6 is the same as that of d20, but the distribution is completely different. The result is a huge increase in chances to succeed on things you're good at (need 8,9, or 10), without any detriment (since you'll use 1d20 otherwise).

    If you need 9 or higher for something (for example, hitting an AC 18 opponent when you have +9), a d20 will give you 60% to do so. 3d6 would give you 160/216=74% (the rough equivalent of an extra +3 to the roll). If you need 8 or higher, instead of 65% you'll have 83%.
    The effect stays extreme if you need, say, 4 or more (over 99.5% instead of 85%), but those situations will be rare.

    If you need 11 or higher then using the ability will hurt you, but you can just choose not to do so (and also, these situations will be rather rare for attack rolls and skills you're proficient in).

    Sure, you'll need to know the DC in order to know when to use the ability, but that just makes things worse, since it means the class rewards metagaming (which is rarely a good idea).

    Factorize is hilarious and cool, but it rewards metagaming even more, and can be absurdly, obscenely overpowered as well (being able to cast Haste on your entire party at levels 5,6,7,8,9,11,12,13,15,16,17,18 and 19 is only one example).

    Accrual is horribly abusable and practically impossible to keep track of for money and XP.

    Advanced numerology isn't as terrible, but it does mean the wizard will first release a rat before using any area damage spell.

    Overall, it's a funny concept (I really did laugh hard at factorization) but completely unplayable and OP.

    1. Your bit on Factorize leads to potential for even more metagame, if during char creation the party picks a collective dump stat of 9(Id imagine Strength would be a likely contender for everyone but the Barbarian), then it would always work, its also possible a party would have 8, 12, or 16 in a stat, leading to the same result.

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    3. Point of order: given that this one was inspired by Final Fantasy Tactics and is meant to be fairly comedic, I don't mind if it encourages metagaming. I think a lot of the situations you bring up (shared dump stats, nighttime pacing, throwing a single rat alongside your fireball, etc.) would be hilarious in practice and the fun & RP opportunities are worth the imbalance.

      The FF class it's based on is also hilariously overpowered. In that game it's balanced by the fact that it's so slow that other classes get to take two or three turns for every turn the arithmetist gets, which is why factorisation costs an action. I reckon hasting everyone on the *second* turn of combat isn't nearly as impactful as it would be if you could use it on the first turn.

      And sure, 3d6 increases your success rate on easy-medium challenges, but I don't think it's gamebreaking. I've heard of DMs banning d20s completely and just using 3d6 for everything, because the swinginess of the d20 can get pretty annoying tbh.

    4. There is a world of difference between "everyone uses 3d6 at all times" and "this one guy can do it when he thinks it's to his advantage" though.

    5. I'm generally pretty cool with the d20 and 3d6 replacement. It requires some metagaming to be good, but it's also only profitable in a pretty narrow range of rolls, where the chance of failure is already pretty low.

      I think, for the sake of balance, CR and Level should be removed from Factorize. Those encourage a really special type of powergaming, which is extremly reliable on a level-by-level basis.

    6. The 3d6 replacement, as I think I've demonstrated, is practically giving you +3 on EVERY ROLL YOU'RE GOOD AT. I would NOT call that a "narrow range of rolls", considering you make way more rolls you're good at than other rolls, and needing 9+, 8+ or 10+ to hit is probably more common than any other number required.

      Also, Munchlord is correct about the balance issue at hand.

      Factorize can easily Hasten everyone for the entire combat if you know combat's coming and prepare accordingly. It also allows mass use of other spells, some of which (fly c0mes to mind) last for an hour and can therefore easily be cast before battle.

      Also, you should make sure it only works on spells that require 1 action, because it costs nothing for long-casting spells.

      Look, when it comes down to it, it's the DM's choice, and most of those abilities will be impossible to balance. However, I think this should at least be tagged as Silly to clarify that it doesn't necessarily meet the standards expected from a playable class (which you have held valiantly in the past, against seas of dumb, unbalanced homebrew that flood the internet).

    7. Ok, I take back FLy (it's touch). Other relevant spells which are easy to abuse (or use very weirdly) outside of combat include (again, not including most in-combat options, as the action-required factor at least partially helps):

      Life Transference
      Sending (to a large percentage of ALL people in the multiverse. Not exactly abuse, but I had to include it XD)
      Suggestion becomes (practically) mass suggestion outside combat
      Giant Insect for hundreds of giant scorpions
      Geas on every citizen in a crowded market
      Modify memory in an area
      Planar Binding
      Heal (11 cleric 2 wizard)
      Planar Ally to call every outsider called by a specific name (not truly abusable, but definitely a funny image I wanted to share)
      Telepathy with a % of ALL creatures with which you're familiar
      Gate to summon every Steve outside of the material plane, or every Bjorn in Ysgard
      True Polymorph

      I'll admit that the range+target restrictions limit the buff options to very few (albeit existing) abusable ones, plus the few that can kill or main entire villages.

    8. Sending not being abuse is definitely a matter of definition, because the ability to do multiverse-wide directly-to-mind spam is definitely an abuse of common decency.

  4. Accrual seems completely broken, especially when taking into account various abilities that let you preform light activity in lieu of sleeping. Like, perhaps, walking? For each time the party sleeps, this pacing wizard would magically get 8x60/10=48 Gp, Xp, and Hp.(Although the hp probs wont do much since theyre taking a long rest anyways.)

    1. CP*, not GP* my bad, but my point still stands on xp, god forbid that upon reaching level 10 that the DM decides to do a time skip, lets say a year, and the eccentric wizard decides to go on a long jaunt, gaining a potential 50k xp, and jumping 2 levels while the ranger decides to learn elvish.

    2. Personally, I'd be happy to remove the bit about XP, but I might need something to replace it with.

  5. Ok, I don't believe this subclass is "broken" in any way, but Accrual is...Well, it disrupts party balance due to the xp-gain. Mind you the xp way of lvling up is not the favourite amongst most tables and groups, because it will lead to fluctuation within the party, and this will only add to it. The money and health bit? Fine with it. Its not a big deal and wizards are some of the biggest money-spenders as far as classes go. An insomniac Wizard running in circles to have enough money for rent is hilarious to me. Heck a Brand Warlock and Arithmetick Wizard would make an interesting pair.