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As anyone playing Dust to Dust or Fallen Earth knows, I think it's cool for characters to perform research to unlock new content, such as spells or crafting formulas. Games have a lot of ways for combat or social power to leave a mark on a setting; research is a way for a character's or player's intellectual ability to do the same. There's already a Researching downtime activity in the Player's Handbook, but it covers information-gathering rather than R&D. I'm proposing a system to cover the latter, working within the existing framework of Researching. I am pretty convinced that the majority of people who choose the Wizard class do so hoping that spell research will be possible in the course of play.
Researching
Let's start with what's already there in Researching.
This action applies equally to getting the word on the street in public-houses and uncovering ancient lore in musty tomes. Presumably story logic dictates what you can learn where.
The system is left highly arbitrary, which is good because locking DMs into a difficulty level to answer campaign mysteries would be a terrible mistake. A little more guidance wouldn't hurt, though.
You spend time. Time is money, and costs money: each day of research costs 1 gp above and beyond your living expenses.
A lot of downtime actions automatically cover your living expenses; Researching not only doesn't do that, it also costs extra money, and is mutually exclusive with other downtime activity.
It would probably be okay to let one character performing a high-paying downtime action, such as Practicing a Profession, support both herself and a Researching character by accepting a lower standard of living. It's... basically a scholarly patronage system within the party, which is neat enough to balance out the fact that it's a big advantage if it's an option.
"I need to go on the road and earn some gold so that you can unravel the mysteries of the cosmos." In this case, maybe not a euphemism for supporting a drug habit.
You might or might not make skill checks, at the DM's discretion. (This would be a really good place for some fail-forward design theory, giving the PC some new lead to chase but not a full answer.)
Several backgrounds also factor in here, but especially the Sage. Most backgrounds include the ability to reliably gather information from other people of the same background, while the Sage goes further to say that anything you don't know, you can figure out where to find - you are, in a sense, a walking card catalog of every known library. (This would be mind-bogglingly overpowered in Dust to Dust, but is basically fine in most D&D campaigns.)
What I've always liked about these abilities is that they give PCs social hooks without getting mechanically intensive or giving you a list of Contacts the DM might kill off to show how serious the threat is.
Dust to Dust has always had a very black-box style of research system - it's driven by numbers on the back-end, but the players don't see any of those numbers, and they only know the relative values of things based on descriptive text. We feel that this keeps their focus on the story and setting and looking for logically-applicable boosts to their research, rather than tinkering with numbers. On the other hand, this has been a source of frustration for some players, who don't feel that they can make decisions with enough basis. It's a balancing act, and one that we're always internally retuning.
Challenges
There are a few visible problems with enabling and encouraging spell research and other kinds of R&D research. Not all classes have expansible powers - any class with a fixed number of Spells Known doesn't have an obvious way to benefit from this, or any benefit has to be a side-grade rather than a pure expansion of options. The list of classes with expansible options is shorter than the list of classes without - clerics, druids, paladins, wizards, and Tome warlocks specifically adding rituals are about it.
The game does have a concept of alternate advancement that expands on your existing abilities outside the standard level progression, presented in the Training downtime action and a separate section in the DMG. If you attached a scaling cost for every additional item learned, PCs could pick up a few, and then stare into the bleak abyss of exponential cost growth.
We have, then, two kinds of learning, and the difference between these two kinds highlights the separation between classes. The first kind - non-scaling, listed above - has another consideration: clerics, druids, and paladins automatically have access to the full list found in the Player's Handbook. (Druids do not automatically gain all beast shapes, and these are a good area for research.) For them to gain anything new, they're drawing on other books (since it's up to the DM whether the spells of the Elemental Evil Player's Companion, third-party works, and homebrewed content are automatically available), or working with the DM to develop new homebrewed content. Wizards and ritual-researching Tome-pact warlocks are the only characters who perform R&D just to unlock content found in the Player's Handbook, but it's a lot of content that they can potentially unlock. (In the balance, wizards functionally complete two R&D projects of up to their highest current spell level every time they gain a level.)
A last type of research: crafting formulas. These are optional and limited to the context of magic item crafting, but if you've already embraced R&D as a concept, crafting formulas give PCs something else to want, to research, and to purchase, beg, borrow, or steal from NPCs. They're great for sandbox play, but just get in the way if you're playing through a mega-adventure. (Mega-adventures often have enough of a timeline that players can't really spare a lot of downtime for research, so this whole post may be of little use.)
The problem I've wrestled with up to this point is making the research process interesting in itself. As you know if you've ever played a video game with research elements, there's a whole lot of watching bars fill up. The dynamic comes to be about enduring the other challenges of the game while you wait for the bar to fill. This doesn't work quite right in tabletop play, where downtime passes swiftly and without a challenge, unless the DM interrupts it and stops the process entirely.
Therefore...
A research project intended to develop something new or reconstruct something old falls under the Researching action. It requires a number of Research Points (RP) based on its rank, rated from 1 to 10. (Still greater projects are hypothetically possible, but are the domain of 20th-level play and outside the general scope of this document. Most of the same rules should apply.) This is not intended to cover the in-character development of a new subclass, as absolutely nothing should grant a character a second subclass within a single class.
Rank obviously correlates to spell level. When researching something completely new to the setting, treat the research as one rank higher - prior work makes life a lot easier. For things that aren't spells, here are some suggestions:
A new Totem Spirit feature is rank 5, and should replace an existing feature.
A new Bard Song is rank 4, because this a big deal if it doesn't replace an existing feature.
A new beast shape for a Circle of the Moon Druid should equal the CR of the beast, minimum 1. With careful thought, the DM may see fit to expand this list to some monstrosities.
A new Battle Master Maneuver is rank 3.
A new Elemental Discipline is rank 3. A new way to spend ki for any other Monastic Order is rank 5, and should replace an existing feature.
A Hunter feature for rangers is rank 5, and should replace an existing feature.
A new warlock Invocation has a rank equal to half the minimum warlock level to take that Invocation. These should replace existing Invocations, but one extra researched Invocation won't cause the game to crack and shudder.
You should still ban Agonizing Blast and Repelling Blast, though. Yeah, I said it.
Crafting formulas:
Common: rank 1
Uncommon: 3
Rare: 5
Very Rare: 7
Legendary: 9
Feats are rank 3 or higher, and should still require Ability Score Improvement slots as usual - this research just expands your list of choices.
The number of Research Points that each project requires is (rank^2 * 50) + 50, so a range of 100 RP to 5050 RP. The 50-point bump is there to keep low-end projects from being completely trivial.
There are two methods of research: steady daily labor and experimentation. (For projects where experimentation does not make sense, it is not available as an option.) Through steady labor, working with musty tomes, exercise, daily prayer, or the like, the character makes progress each day equal to ability score bonus * proficiency bonus. The minimum ability score bonus is +1 (even for very low stats), so the results range from 2 to 30 RP per day. You can double your daily research rate by increasing your daily cash outlay by project rank * 3 gp (again, this is on top of your cost-of-living payment and your base 1 gp for the researching action).
Therefore: a master wizard can research a pre-existing 1st-level spell every two days... not that this is a good use of his time, in general, and he still has to spend time and money to inscribe this spell into his spellbook. The same master wizard can research a heretofore-unattested 9th-level spell in 169 days, or 85 days if he spends 2,635 gp instead of 169 gp. He should never not pay the extra money, but that's because we're talking about a wizard of 17th level or higher, who probably does not have basic solvency problems.
The second method is experimentation. During the course of an experiment, you accrue no research points, but you must keep paying the daily cost of the researching action, in addition to an up-front cost of 50 gp * project rank. At the end of project rank * 2 days, roll a skill check for the most relevant skill against DC 20. On a success, you gain RP equal to ability score bonus * proficiency bonus * days spent * 5. On a natural 20, you gain double this value. On a failure, you lose all progress. On a natural 1, your laboratory or other study area suffers catastrophic damage.
Experimentation is intended as an expensive and fast, but risky, approach to research. The risk tapers off considerably at higher levels. What destroys a cleric's or druid's sanctum sanctorum? Drawing the attention of a hostile power, of course - a risk you run when acting as the conduit for substantial amounts of divine power not contained in the formalities of a spell.
When collaborating with additional researchers, the character with the highest daily research rate counts as the primary researcher, and all other researchers add half of their daily research rate to the project. Under most circumstances, a project cannot take more than three researchers.
When gaining a Spell Known or class feature beyond what is normally allowed (for example, a Battle Master learning an extra Maneuver), add +1 Rank to the project for each spell, maneuver, or other feature you have already learned beyond the normal limits, across all of your classes.
For DMs, I recommend being up-front with players about research projects that you're not going to allow to succeed. A "naturalistic" approach would have scholars plumbing the unknown with a long string of failures as they refine their ideas - but in my view that's the point of the exorbitant amounts of RP needed for high-end projects. The character is failing, every day of the work, right up to the day she succeeds.
Research As Treasure
In addition to research performed in the laboratory, one can sometimes acquire someone else's research notes, or oddities that are useful in research but have no further properties of their own.
Research boosts may cover broad topics shallowly, or narrow topics deeply. In the table below, "each" means that there are eight separate narrow topics, one for each of the Schools of magic, and so on.
Broad Topics
Narrow Topics
Arcana
Each of the eight Schools, Planes, Magical Beasts, Astrology, Artifacts of Power, Curses
Acrobatics/Athletics
Each weapon type (use these to research Maneuvers and new feats)
History
Each present-day region, Each Historical Era, Each Organization, Dragons, Law
Mechanics
Security Devices, Architecture, Constructs
Medicine
Diseases, Poisons, Herb Lore
Nature
Beasts, Herb Lore, Weather
Religion
Each Faith, Undead, Celestials, Fiends, Relics, Spells, Curses
A Common Broad research boost provides 10 RP to an applicable project of up to rank 2. A Common Narrow research boost provides 50 RP to an applicable project of up to rank 2.
An Uncommon Broad research boost provides 25 RP to an applicable project of up to rank 4. An Uncommon Narrow research boost provides 125 RP to an applicable project of up to rank 4.
A Rare Broad research boost provides 100 RP to an applicable project of up to rank 6. A Rare Narrow research boost provides 500 RP to an applicable project of up to rank 6.
A Very Rare Broad research boost provides 250 RP to an applicable project of up to rank 8. A Rare Narrow research boost provides 1250 RP to an applicable project of up to rank 8.
A Legendary Broad research boost provides 500 RP to an applicable project of any rank. A Legendary Narrow research boost provides 2500 RP to an applicable project of any rank.
If you're using this system and randomly generating treasure, make the following change: Whenever rolling on the Art Objects treasure tables, roll a d12 instead of a d10.
25-gp table: 11 results in a Common Broad research boost, 12 results in an Common Narrow research boost
250-gp table: 11 results in an Uncommon Broad research boost, 12 results in an Uncommon Narrow research boost
750-gp table: 11 results in a Rare Broad research boost, 12 results in a Rare Narrow research boost
2500-gp table: 11 results in a Very Rare Broad research boost, 12 results in a Very Rare Narrow research boost
7500-gp table: 11 results in a Legendary Broad research boost, 12 results in a Legendary Narrow research boost
It's just about always cool to have an object or a piece of dungeon decor unexpectedly prove useful in research, so art objects, weapons, armor, and treasure chests can have carvings, runes, secret compartments with scraps of notes, and so forth. A single research boost is never applicable to more than one project, or more than once in the same project.
Design Notes
Obviously, this is in a first-draft state. Many of the numbers likely need some tweaking. It remains pretty mathy, but I am not sure there's a satisfying way to approach what the fiction says should be a challenging, long-term project without a hefty bit of math. I also wanted the game's tiers to matter, which is why proficiency bonus is multiplied for research rate, rather than a sum.
I'd like to refine this through a few iterations, until it's ready for release as a PDF. Who knows, maybe WotC will have released an OGL for 5e by then!
Also, this is my 300th post in Harbinger of Doom. Thanks for reading!