So, why haven't I been making anything despite the pandemic? · 7:01am Mar 31st, 2020

Well, you see...

I don't have a lot of satisfying reasons. One of my major time-consumers is still at play: I'm still working as I was before, and my weekends have D&D sessions still. Mainly, I've just had some more interesting project ideas come up.

I've been running two little data projects for two of my newer hobbies. One of them involves building a couple empirical survival models for some reloader's brass casings for a rifle I've been shooting, and the other is an investigation on the relative efficiency of spells in D&D.

Regarding the D&D project, it's actually kind of simple:
There's a spell called Magic Missile that (conventionally) always hits and does fairly consistent damage. As a level 1 (on a scale from 1 to 9 of beginner's spells to master's magic), it's not amazing, but it can be upcast (cast at a higher level with a bonus to potency).

There are other spells, though that also deal damage. In circumstances where spells other than Magic Missile might be expected to perform just as well (assuming you aren't trying to cast spells like Fireball on a Fire Elemental, where their potency would be halved or worse from the get-go), at what point should a rational player consider something other than Magic Missile?

You see, in D&D, damage-dealing spells other than Magic Missile generally can "miss" or be "saved against". I mean that, in normal circumstances, virtually every other damage-dealing spell can do zero damage if the roll to hit something with it (or the save the creature must make to avoid damage is too high) is too low, or, as with virtually all area-of effect spells, a roll with a chance for a targeted creature to resist some damage dealt (usually this amounts to halving the damage, although failing to succumb to an additional effect imposed upon victims of the spell is thrown in, as well as in some cases even less damage being dealt because there is a residual damage effect to be felt on the next turn on a failure to save).

Now, it is pretty easy to figure out average and standard deviation of damage any and all spells in D&D 5e do when you assume they don't miss or aren't saved against. However, this assumption is false and naive. For any spell other than Magic Missile in D&D, mean and SD should be calculated based on a chance to hit/hit with full effect on a given enemy.

Decision making for spells is also made generally with an idea that spells won't hit or won't hit with full force each time. As a fight goes on, depending on the DM and a person's tendency/permission to play the metagame, players may know or learn that a creature they're up against has a certain level of chance. So, there can be a decision threshold for when certain spells may be more potent in general than Magic Missile. In fact, one would hope that Magic Missile is not the default spell to cast at every level; otherwise, other damaging spells may be pointlessly situational.

Average damage is but one part of the picture. I aim to use the coefficient of variation in my analysis (how variable is the damage of these spells relative to the average damage they do). The idea is treating spell slots (a finite resource for spellcasters in D&D) like investments into damage, which is really apt, I feel. I could invest a spell slot in the guaranteed damage of Magic Missile, but why should I if I can cast a damaging cantrip I think will hit most of the time for more damage if I determine that it's about as consistent but doesn't cost a resource?

I'm very excited, and this, as well as my other data project, are already in the works. I can post updates, if you'd like. Currently, I have all the data I need for basically all spells I'd want to compare to Magic Missile, as well as all the levels for Magic Missile, thanks to the resource AnyDice. I've coded all the importation and data manipulation to set up for running the code. I'm now working on a for loop to cycle through every possible "hit probability" from 5% to 100% and calculate mean, standard deviation, and CV for whatever roll a spell takes. The tricky part is adding in halved damage for saving throw successes and halved AND reduced rolls associated with spells like Melf's Acid Arrow and Vitriolic Sphere.

I'm excited, though. I'm intending to store the numerical outputs, along with comparisons to Magic Missile, into a spreadsheet that would catalogue virtually all canon damage-dealing spells and compare them to Magic Missile cast at the same level the spell is cast at, including upcasting.

Can you tell I have statistical steam I'm not blowing off by not doing anything actuarial?