D&D 5E Downtime Research Analyzed (and some thoughts on spell research)

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Running some numbers here for the downtime activity Research from XGE 132. I wanted to come up with some rules for researching spells, and this seemed like the best option of all the downtime activities.

General summary of the research rules:

• Time: 1 workweek
• Intelligence Check (will generally be +3 to +5 for a Wizard), learning 0 to 3 pieces of lore depending on the result.
• Advantage if access to well-stocked library or knowledgeable sage
• Bonus is +0 to +6 depending on gold spent (note I suspect a typo in the rules. The way the cost per bonus is worded implies that the baseline cost is 100 gp, but it's written as 50 gp, making me question if the typo is in the baseline cost or in the cost per bonus).

So how much does spending money to aid your research really help you? Turns out, not that much:

[TABLE="width: 1552"]
[TR]
[TD]Int Bonus[/TD]
[TD="colspan: 7, align: center"]3[HR][/HR][/TD]
[TD="colspan: 7, align: center"]4[HR][/HR][/TD]
[TD="colspan: 7, align: center"]5[HR][/HR][/TD]
[/TR]
[TR]
[TD]Gold spent[/TD]
[TD="align: right"]50[/TD]
[TD="align: right"]200[/TD]
[TD="align: right"]300[/TD]
[TD="align: right"]400[/TD]
[TD="align: right"]500[/TD]
[TD="align: right"]600[/TD]
[TD="align: right"]700[/TD]
[TD="align: right"]50[/TD]
[TD="align: right"]200[/TD]
[TD="align: right"]300[/TD]
[TD="align: right"]400[/TD]
[TD="align: right"]500[/TD]
[TD="align: right"]600[/TD]
[TD="align: right"]700[/TD]
[TD="align: right"]50[/TD]
[TD="align: right"]200[/TD]
[TD="align: right"]300[/TD]
[TD="align: right"]400[/TD]
[TD="align: right"]500[/TD]
[TD="align: right"]600[/TD]
[TD="align: right"]700[/TD]
[/TR]
[TR]
[TD]Gold Bonus[/TD]
[TD="align: right"]0[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]0[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]0[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[/TR]
[TR]
[TD]Total Bonus[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]10[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]10[/TD]
[TD="align: right"]11[/TD]
[/TR]
[TR]
[TD]Odds: No effect (C<=5)[/TD]
[TD="align: right"]10%[/TD]
[TD="align: right"]5%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]5%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[/TR]
[TR]
[TD]Odds: You learn one piece of lore (6<=C<=10)[/TD]
[TD="align: right"]25%[/TD]
[TD="align: right"]25%[/TD]
[TD="align: right"]25%[/TD]
[TD="align: right"]20%[/TD]
[TD="align: right"]15%[/TD]
[TD="align: right"]10%[/TD]
[TD="align: right"]5%[/TD]
[TD="align: right"]25%[/TD]
[TD="align: right"]25%[/TD]
[TD="align: right"]20%[/TD]
[TD="align: right"]15%[/TD]
[TD="align: right"]10%[/TD]
[TD="align: right"]5%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]25%[/TD]
[TD="align: right"]20%[/TD]
[TD="align: right"]15%[/TD]
[TD="align: right"]10%[/TD]
[TD="align: right"]5%[/TD]
[TD="align: right"]0%[/TD]
[TD="align: right"]0%[/TD]
[/TR]
[TR]
[TD]Odds: You learn two pieces of lore (11<=C<=20)[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]45%[/TD]
[/TR]
[TR]
[TD]Odds: You learn three pieces of lore (21 <= C)[/TD]
[TD="align: right"]15%[/TD]
[TD="align: right"]20%[/TD]
[TD="align: right"]25%[/TD]
[TD="align: right"]30%[/TD]
[TD="align: right"]35%[/TD]
[TD="align: right"]40%[/TD]
[TD="align: right"]45%[/TD]
[TD="align: right"]20%[/TD]
[TD="align: right"]25%[/TD]
[TD="align: right"]30%[/TD]
[TD="align: right"]35%[/TD]
[TD="align: right"]40%[/TD]
[TD="align: right"]45%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]25%[/TD]
[TD="align: right"]30%[/TD]
[TD="align: right"]35%[/TD]
[TD="align: right"]40%[/TD]
[TD="align: right"]45%[/TD]
[TD="align: right"]50%[/TD]
[TD="align: right"]55%[/TD]
[/TR]
[TR]
[TD]Sanity Check: total odds[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[/TR]
[TR]
[TD]Average Pieces Learned:[/TD]
[TD="align: right"]1.7[/TD]
[TD="align: right"]1.85[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]2.1[/TD]
[TD="align: right"]2.2[/TD]
[TD="align: right"]2.3[/TD]
[TD="align: right"]2.4[/TD]
[TD="align: right"]1.85[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]2.1[/TD]
[TD="align: right"]2.2[/TD]
[TD="align: right"]2.3[/TD]
[TD="align: right"]2.4[/TD]
[TD="align: right"]2.5[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]2.1[/TD]
[TD="align: right"]2.2[/TD]
[TD="align: right"]2.3[/TD]
[TD="align: right"]2.4[/TD]
[TD="align: right"]2.5[/TD]
[TD="align: right"]2.55[/TD]
[/TR]
[/TABLE]

How about advantage?

[TABLE="width: 1552"]
[TR]
[TD][/TD]
[TD="colspan: 21, align: center"]Advantage[/TD]
[/TR]
[TR]
[TD]Int Bonus[/TD]
[TD="colspan: 7, align: center"]3[HR][/HR]
[/TD]
[TD="colspan: 7, align: center"]4[HR][/HR]
[/TD]
[TD="colspan: 7, align: center"]5[HR][/HR]
[/TD]
[/TR]
[TR]
[TD]Gold spent[/TD]
[TD="align: right"]50[/TD]
[TD="align: right"]200[/TD]
[TD="align: right"]300[/TD]
[TD="align: right"]400[/TD]
[TD="align: right"]500[/TD]
[TD="align: right"]600[/TD]
[TD="align: right"]700[/TD]
[TD="align: right"]50[/TD]
[TD="align: right"]200[/TD]
[TD="align: right"]300[/TD]
[TD="align: right"]400[/TD]
[TD="align: right"]500[/TD]
[TD="align: right"]600[/TD]
[TD="align: right"]700[/TD]
[TD="align: right"]50[/TD]
[TD="align: right"]200[/TD]
[TD="align: right"]300[/TD]
[TD="align: right"]400[/TD]
[TD="align: right"]500[/TD]
[TD="align: right"]600[/TD]
[TD="align: right"]700[/TD]
[/TR]
[TR]
[TD]Gold Bonus[/TD]
[TD="align: right"]0[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]0[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]0[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]2[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[/TR]
[TR]
[TD]Total Bonus[/TD]
[TD="align: right"]3[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]10[/TD]
[TD="align: right"]5[/TD]
[TD="align: right"]6[/TD]
[TD="align: right"]7[/TD]
[TD="align: right"]8[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]10[/TD]
[TD="align: right"]11[/TD]
[/TR]
[TR]
[TD]Odds: No effect (C<=5)[/TD]
[TD="align: right"]1.00%[/TD]
[TD="align: right"]0.25%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.25%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[/TR]
[TR]
[TD]Odds: You learn one piece of lore (6<=C<=10)[/TD]
[TD="align: right"]11.25%[/TD]
[TD="align: right"]8.75%[/TD]
[TD="align: right"]6.25%[/TD]
[TD="align: right"]4.00%[/TD]
[TD="align: right"]2.25%[/TD]
[TD="align: right"]1.00%[/TD]
[TD="align: right"]0.25%[/TD]
[TD="align: right"]8.75%[/TD]
[TD="align: right"]6.25%[/TD]
[TD="align: right"]4.00%[/TD]
[TD="align: right"]2.25%[/TD]
[TD="align: right"]1.00%[/TD]
[TD="align: right"]0.25%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]6.25%[/TD]
[TD="align: right"]4.00%[/TD]
[TD="align: right"]2.25%[/TD]
[TD="align: right"]1.00%[/TD]
[TD="align: right"]0.25%[/TD]
[TD="align: right"]0.00%[/TD]
[TD="align: right"]0.00%[/TD]
[/TR]
[TR]
[TD]Odds: You learn two pieces of lore (11<=C<=20)[/TD]
[TD="align: right"]60.00%[/TD]
[TD="align: right"]55.00%[/TD]
[TD="align: right"]50.00%[/TD]
[TD="align: right"]45.00%[/TD]
[TD="align: right"]40.00%[/TD]
[TD="align: right"]35.00%[/TD]
[TD="align: right"]30.00%[/TD]
[TD="align: right"]55.00%[/TD]
[TD="align: right"]50.00%[/TD]
[TD="align: right"]45.00%[/TD]
[TD="align: right"]40.00%[/TD]
[TD="align: right"]35.00%[/TD]
[TD="align: right"]30.00%[/TD]
[TD="align: right"]25.00%[/TD]
[TD="align: right"]50.00%[/TD]
[TD="align: right"]45.00%[/TD]
[TD="align: right"]40.00%[/TD]
[TD="align: right"]35.00%[/TD]
[TD="align: right"]30.00%[/TD]
[TD="align: right"]25.00%[/TD]
[TD="align: right"]20.25%[/TD]
[/TR]
[TR]
[TD]Odds: You learn three pieces of lore (21 <= C)[/TD]
[TD="align: right"]27.75%[/TD]
[TD="align: right"]36.00%[/TD]
[TD="align: right"]43.75%[/TD]
[TD="align: right"]51.00%[/TD]
[TD="align: right"]57.75%[/TD]
[TD="align: right"]64.00%[/TD]
[TD="align: right"]69.75%[/TD]
[TD="align: right"]36.00%[/TD]
[TD="align: right"]43.75%[/TD]
[TD="align: right"]51.00%[/TD]
[TD="align: right"]57.75%[/TD]
[TD="align: right"]64.00%[/TD]
[TD="align: right"]69.75%[/TD]
[TD="align: right"]75.00%[/TD]
[TD="align: right"]43.75%[/TD]
[TD="align: right"]51.00%[/TD]
[TD="align: right"]57.75%[/TD]
[TD="align: right"]64.00%[/TD]
[TD="align: right"]69.75%[/TD]
[TD="align: right"]75.00%[/TD]
[TD="align: right"]79.75%[/TD]
[/TR]
[TR]
[TD]Sanity Check: total odds[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[TD="align: right"]100.00%[/TD]
[/TR]
[TR]
[TD]Average Pieces Learned:[/TD]
[TD="align: right"]2.145[/TD]
[TD="align: right"]2.2675[/TD]
[TD="align: right"]2.375[/TD]
[TD="align: right"]2.47[/TD]
[TD="align: right"]2.555[/TD]
[TD="align: right"]2.63[/TD]
[TD="align: right"]2.695[/TD]
[TD="align: right"]2.2675[/TD]
[TD="align: right"]2.375[/TD]
[TD="align: right"]2.47[/TD]
[TD="align: right"]2.555[/TD]
[TD="align: right"]2.63[/TD]
[TD="align: right"]2.695[/TD]
[TD="align: right"]2.75[/TD]
[TD="align: right"]2.375[/TD]
[TD="align: right"]2.47[/TD]
[TD="align: right"]2.555[/TD]
[TD="align: right"]2.63[/TD]
[TD="align: right"]2.695[/TD]
[TD="align: right"]2.75[/TD]
[TD="align: right"]2.7975[/TD]
[/TR]
[/TABLE]

Takeaways:

• Unless you're on a tight deadline with money to burn, it makes far more sense to spend an extra week researching than it does to throw gold at the problem.
• Go to the library.
• Your INT doesn't really matter all that much.
• I don't know why they didn't make this a skill check. All of the INT-based skills are appropriate to different avenues of research. A wizard should be better at researching arcane lore. A cleric should be better at researching divine lore.

As I mentioned before, I wanted to come up with some rules for researching spells, and this seemed like the best option. Given how little the gold actually makes a difference, I think it makes sense to allow a skill check rather than a raw ability check (any chance to reward a player for their choices while taking nothing away from anyone else ranks as a good decision in my book). Conveniently, proficiency goes to +6, just like the gold bonus, so I'm just switching them out. Using this system, spells will be broken up into "pieces of lore." I'm using (spell level + 1)**2, but it's just a matter of playing with the numbers until you get what you want. Using that formula, a young wizard could spend a month researching a new 1st level spell, and an archmage could spend the better part of a year researching a new 9th level spell. A researched cantrip would be to switch them out, since there's a hard limit on cantrips known.

According to this formula, a wizard researcher wanting to research 4 spells each from levels 1-8 would spend about nine years doing so, assuming they did nothing else.

[TABLE="width: 1808"]
[TR]
[TD]Spell Research[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD]Pieces of Lore required for spell:[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD](spell level + 1)**2[/TD]
[TD]Int Bonus:[/TD]
[TD="colspan: 4, align: center"]3[/TD]
[TD="colspan: 4, align: center"]3, Advantage[/TD]
[TD="colspan: 4, align: center"]4[/TD]
[TD="colspan: 4, align: center"]4, Advantage[/TD]
[TD="colspan: 4, align: center"]5[/TD]
[TD="colspan: 4, align: center"]5, Advantage[/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD="colspan: 2, align: center"]Min Gold Strategy[/TD]
[TD="colspan: 2, align: center"]Min Time Strategy[/TD]
[TD="colspan: 2, align: center"]Min Gold Strategy[/TD]
[TD="colspan: 2, align: center"]Min Time Strategy[/TD]
[TD="colspan: 2, align: center"]Min Gold Strategy[/TD]
[TD="colspan: 2, align: center"]Min Time Strategy[/TD]
[TD="colspan: 2, align: center"]Min Gold Strategy[/TD]
[TD="colspan: 2, align: center"]Min Time Strategy[/TD]
[TD="colspan: 2, align: center"]Min Gold Strategy[/TD]
[TD="colspan: 2, align: center"]Min Time Strategy[/TD]
[TD="colspan: 2, align: center"]Min Gold Strategy[/TD]
[TD="colspan: 2, align: center"]Min Time Strategy[/TD]
[/TR]
[TR]
[TD]Spell Level[/TD]
[TD="align: center"]Pieces of Lore[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[TD="align: center"]Avg Weeks[/TD]
[TD="align: center"]Avg Gold[/TD]
[/TR]
[TR]
[TD="align: right"]0[/TD]
[TD="align: right"]1[/TD]
[TD="align: right"]0.59[/TD]
[TD="align: right"]29[/TD]
[TD="align: right"]0.42[/TD]
[TD="align: right"]292[/TD]
[TD="align: right"]0.47[/TD]
[TD="align: right"]23[/TD]
[TD="align: right"]0.37[/TD]
[TD="align: right"]260[/TD]
[TD="align: right"]0.54[/TD]
[TD="align: right"]27[/TD]
[TD="align: right"]0.40[/TD]
[TD="align: right"]280[/TD]
[TD="align: right"]0.44[/TD]
[TD="align: right"]22[/TD]
[TD="align: right"]0.36[/TD]
[TD="align: right"]255[/TD]
[TD="align: right"]0.50[/TD]
[TD="align: right"]25[/TD]
[TD="align: right"]0.39[/TD]
[TD="align: right"]275[/TD]
[TD="align: right"]0.42[/TD]
[TD="align: right"]21[/TD]
[TD="align: right"]0.36[/TD]
[TD="align: right"]250[/TD]
[/TR]
[TR]
[TD="align: right"]1[/TD]
[TD="align: right"]4[/TD]
[TD="align: right"]2.35[/TD]
[TD="align: right"]118[/TD]
[TD="align: right"]1.67[/TD]
[TD="align: right"]1167[/TD]
[TD="align: right"]1.86[/TD]
[TD="align: right"]93[/TD]
[TD="align: right"]1.48[/TD]
[TD="align: right"]1039[/TD]
[TD="align: right"]2.16[/TD]
[TD="align: right"]108[/TD]
[TD="align: right"]1.60[/TD]
[TD="align: right"]1120[/TD]
[TD="align: right"]1.76[/TD]
[TD="align: right"]88[/TD]
[TD="align: right"]1.45[/TD]
[TD="align: right"]1018[/TD]
[TD="align: right"]2.00[/TD]
[TD="align: right"]100[/TD]
[TD="align: right"]1.57[/TD]
[TD="align: right"]1098[/TD]
[TD="align: right"]1.68[/TD]
[TD="align: right"]84[/TD]
[TD="align: right"]1.43[/TD]
[TD="align: right"]1001[/TD]
[/TR]
[TR]
[TD="align: right"]2[/TD]
[TD="align: right"]9[/TD]
[TD="align: right"]5.29[/TD]
[TD="align: right"]265[/TD]
[TD="align: right"]3.75[/TD]
[TD="align: right"]2625[/TD]
[TD="align: right"]4.20[/TD]
[TD="align: right"]210[/TD]
[TD="align: right"]3.34[/TD]
[TD="align: right"]2338[/TD]
[TD="align: right"]4.86[/TD]
[TD="align: right"]243[/TD]
[TD="align: right"]3.60[/TD]
[TD="align: right"]2520[/TD]
[TD="align: right"]3.97[/TD]
[TD="align: right"]198[/TD]
[TD="align: right"]3.27[/TD]
[TD="align: right"]2291[/TD]
[TD="align: right"]4.50[/TD]
[TD="align: right"]225[/TD]
[TD="align: right"]3.53[/TD]
[TD="align: right"]2471[/TD]
[TD="align: right"]3.79[/TD]
[TD="align: right"]189[/TD]
[TD="align: right"]3.22[/TD]
[TD="align: right"]2252[/TD]
[/TR]
[TR]
[TD="align: right"]3[/TD]
[TD="align: right"]16[/TD]
[TD="align: right"]9.41[/TD]
[TD="align: right"]471[/TD]
[TD="align: right"]6.67[/TD]
[TD="align: right"]4667[/TD]
[TD="align: right"]7.46[/TD]
[TD="align: right"]373[/TD]
[TD="align: right"]5.94[/TD]
[TD="align: right"]4156[/TD]
[TD="align: right"]8.65[/TD]
[TD="align: right"]432[/TD]
[TD="align: right"]6.40[/TD]
[TD="align: right"]4480[/TD]
[TD="align: right"]7.06[/TD]
[TD="align: right"]353[/TD]
[TD="align: right"]5.82[/TD]
[TD="align: right"]4073[/TD]
[TD="align: right"]8.00[/TD]
[TD="align: right"]400[/TD]
[TD="align: right"]6.27[/TD]
[TD="align: right"]4392[/TD]
[TD="align: right"]6.74[/TD]
[TD="align: right"]337[/TD]
[TD="align: right"]5.72[/TD]
[TD="align: right"]4004[/TD]
[/TR]
[TR]
[TD="align: right"]4[/TD]
[TD="align: right"]25[/TD]
[TD="align: right"]14.71[/TD]
[TD="align: right"]735[/TD]
[TD="align: right"]10.42[/TD]
[TD="align: right"]7292[/TD]
[TD="align: right"]11.66[/TD]
[TD="align: right"]583[/TD]
[TD="align: right"]9.28[/TD]
[TD="align: right"]6494[/TD]
[TD="align: right"]13.51[/TD]
[TD="align: right"]676[/TD]
[TD="align: right"]10.00[/TD]
[TD="align: right"]7000[/TD]
[TD="align: right"]11.03[/TD]
[TD="align: right"]551[/TD]
[TD="align: right"]9.09[/TD]
[TD="align: right"]6364[/TD]
[TD="align: right"]12.50[/TD]
[TD="align: right"]625[/TD]
[TD="align: right"]9.80[/TD]
[TD="align: right"]6863[/TD]
[TD="align: right"]10.53[/TD]
[TD="align: right"]526[/TD]
[TD="align: right"]8.94[/TD]
[TD="align: right"]6256[/TD]
[/TR]
[TR]
[TD="align: right"]5[/TD]
[TD="align: right"]36[/TD]
[TD="align: right"]21.18[/TD]
[TD="align: right"]1059[/TD]
[TD="align: right"]15.00[/TD]
[TD="align: right"]10500[/TD]
[TD="align: right"]16.78[/TD]
[TD="align: right"]839[/TD]
[TD="align: right"]13.36[/TD]
[TD="align: right"]9351[/TD]
[TD="align: right"]19.46[/TD]
[TD="align: right"]973[/TD]
[TD="align: right"]14.40[/TD]
[TD="align: right"]10080[/TD]
[TD="align: right"]15.88[/TD]
[TD="align: right"]794[/TD]
[TD="align: right"]13.09[/TD]
[TD="align: right"]9164[/TD]
[TD="align: right"]18.00[/TD]
[TD="align: right"]900[/TD]
[TD="align: right"]14.12[/TD]
[TD="align: right"]9882[/TD]
[TD="align: right"]15.16[/TD]
[TD="align: right"]758[/TD]
[TD="align: right"]12.87[/TD]
[TD="align: right"]9008[/TD]
[/TR]
[TR]
[TD="align: right"]6[/TD]
[TD="align: right"]49[/TD]
[TD="align: right"]28.82[/TD]
[TD="align: right"]1441[/TD]
[TD="align: right"]20.42[/TD]
[TD="align: right"]14292[/TD]
[TD="align: right"]22.84[/TD]
[TD="align: right"]1142[/TD]
[TD="align: right"]18.18[/TD]
[TD="align: right"]12727[/TD]
[TD="align: right"]26.49[/TD]
[TD="align: right"]1324[/TD]
[TD="align: right"]19.60[/TD]
[TD="align: right"]13720[/TD]
[TD="align: right"]21.61[/TD]
[TD="align: right"]1080[/TD]
[TD="align: right"]17.82[/TD]
[TD="align: right"]12473[/TD]
[TD="align: right"]24.50[/TD]
[TD="align: right"]1225[/TD]
[TD="align: right"]19.22[/TD]
[TD="align: right"]13451[/TD]
[TD="align: right"]20.63[/TD]
[TD="align: right"]1032[/TD]
[TD="align: right"]17.52[/TD]
[TD="align: right"]12261[/TD]
[/TR]
[TR]
[TD="align: right"]7[/TD]
[TD="align: right"]64[/TD]
[TD="align: right"]37.65[/TD]
[TD="align: right"]1882[/TD]
[TD="align: right"]26.67[/TD]
[TD="align: right"]18667[/TD]
[TD="align: right"]29.84[/TD]
[TD="align: right"]1492[/TD]
[TD="align: right"]23.75[/TD]
[TD="align: right"]16623[/TD]
[TD="align: right"]34.59[/TD]
[TD="align: right"]1730[/TD]
[TD="align: right"]25.60[/TD]
[TD="align: right"]17920[/TD]
[TD="align: right"]28.22[/TD]
[TD="align: right"]1411[/TD]
[TD="align: right"]23.27[/TD]
[TD="align: right"]16291[/TD]
[TD="align: right"]32.00[/TD]
[TD="align: right"]1600[/TD]
[TD="align: right"]25.10[/TD]
[TD="align: right"]17569[/TD]
[TD="align: right"]26.95[/TD]
[TD="align: right"]1347[/TD]
[TD="align: right"]22.88[/TD]
[TD="align: right"]16014[/TD]
[/TR]
[TR]
[TD="align: right"]8[/TD]
[TD="align: right"]81[/TD]
[TD="align: right"]47.65[/TD]
[TD="align: right"]2382[/TD]
[TD="align: right"]33.75[/TD]
[TD="align: right"]23625[/TD]
[TD="align: right"]37.76[/TD]
[TD="align: right"]1888[/TD]
[TD="align: right"]30.06[/TD]
[TD="align: right"]21039[/TD]
[TD="align: right"]43.78[/TD]
[TD="align: right"]2189[/TD]
[TD="align: right"]32.40[/TD]
[TD="align: right"]22680[/TD]
[TD="align: right"]35.72[/TD]
[TD="align: right"]1786[/TD]
[TD="align: right"]29.45[/TD]
[TD="align: right"]20618[/TD]
[TD="align: right"]40.50[/TD]
[TD="align: right"]2025[/TD]
[TD="align: right"]31.76[/TD]
[TD="align: right"]22235[/TD]
[TD="align: right"]34.11[/TD]
[TD="align: right"]1705[/TD]
[TD="align: right"]28.95[/TD]
[TD="align: right"]20268[/TD]
[/TR]
[TR]
[TD="align: right"]9[/TD]
[TD="align: right"]100[/TD]
[TD="align: right"]58.82[/TD]
[TD="align: right"]2941[/TD]
[TD="align: right"]41.67[/TD]
[TD="align: right"]29167[/TD]
[TD="align: right"]46.62[/TD]
[TD="align: right"]2331[/TD]
[TD="align: right"]37.11[/TD]
[TD="align: right"]25974[/TD]
[TD="align: right"]54.05[/TD]
[TD="align: right"]2703[/TD]
[TD="align: right"]40.00[/TD]
[TD="align: right"]28000[/TD]
[TD="align: right"]44.10[/TD]
[TD="align: right"]2205[/TD]
[TD="align: right"]36.36[/TD]
[TD="align: right"]25455[/TD]
[TD="align: right"]50.00[/TD]
[TD="align: right"]2500[/TD]
[TD="align: right"]39.22[/TD]
[TD="align: right"]27451[/TD]
[TD="align: right"]42.11[/TD]
[TD="align: right"]2105[/TD]
[TD="align: right"]35.75[/TD]
[TD="align: right"]25022[/TD]
[/TR]
[/TABLE]

This was primarily an informative post, but thoughts and opinions are welcome for both the analysis of official material and thoughts regarding spell research!

 

[MNblockhead]

Interesting. Thanks for sharing. This would work better in a prior campaign a ran where each session was rather stand-alone and each was a different level (i.e. 20 sessions, 20 levels) and the assumption being that the group got together aver perhaps years apart to address a thread, recover an artifact, etc.

It would be more difficult to apply the length of time in a typical campaign though. While I think that it fits the flavor of a wizard to have him spend years or even a life time to create certain spells.

I'm currently trying to determine how to address a player who wants to create his own spells. I'm just starting to think about it. I would use the "Creating a Spell" subsection of the "Dungeon Masters Workshop" in the DMG to help determine the level the spell should be. Then I would look at spells the wizard already knows that provide similar effects, which should help shave of time. I would encourage the player to come up with spells they want to create early on and have their character start research on them at lower levels. It could provide plot hooks and hopefully provide sufficient time that can be credited towards the research.

Still, given the times involved, I would make it possible to find ways for a character to truncate the time. For example, apprentices can continue working on it while the wizard travel. The wizard can work with colleague to gain advantage on rolls and divide up the work. A more advanced wizard can provide knowledge, advice, components, and other aid to decrease the time. These things all cost money. It give the DM a way to let the character have his spell sooner but at much greater expense.

You may also provide beings of great magic power who will help provide the character with what they need to succeed in the spells creation, in a much shorter period of time, but at a cost. An arch fey may place geas on the player to perform some service for it. A devil may want the character to give his soul or arrange for another to give up his soul. A far realm entity may require strange rituals that have unknown effects in the world. Etc.

I would also work in the Rival mechanic from XGE. I Rival could work to steal secrets, disrupt research, hire away apprentices, turn colleagues and mentors away from you, etc.

 

[BlivetWidget]

Yes, this does assume a fair bit of downtime, or a non-adventuring wizard (a wizard out on adventures is hopefully picking up spell loot along the way). The way time works in 5e is left pretty vague, and that's not a bad thing, but it means some tables are going to reach level 20 in the in-game equivalent of a month, while other tables are going to assume decades. The formula for pieces of lore per spell is easy to tweak to match any timetable, though. Just pick numbers that work for you. (spell level)**2 + 1 will shave off some time. Or get rid of the square and use a multiplier to really cut it down.

Multiple wizards working on the same project is certainly one way to cut down on the time, and multiple wizards cooperating can also greatly increase their spell count by agreeing to never take the same spells on leveling, then sharing their knowledge =). That's actually why I wanted to come up with some rules for solo research. Using only the available rules, a level 20 wizard can't discover any new spells, but he can take on an apprentice who can learn new magic and teach it to him... (seems rather silly to me!).

Best of luck in working out the custom spells. I looked into it, but decided to just stick with existing spells for a number of reasons. First and foremost, the game designers did not follow their own proposed guidelines in the DMG at all. For instance, Fireball, by their guidelines, ought to do 6d6 damage (it does 8d6). Cone of Cold, by their guidelines, should do 8d6 (it does 8d8). These are just two examples off the top of my head. The other issue is, if you're going to make a spell, why even bother if it doesn't give you some advantage you couldn't get otherwise? But if you can make spells more useful than what's in the book, do the other classes get to invent new attacks that are more powerful, too? Inventing new spells is one of those things that makes a lot of sense and would be a lot of fun but makes the non-wizard classes start to lose what appeal they had.