Like a poster there, I rigged up some evidence of diseased thinking; while I’m reasonably happy with the results they don’t actually indicate much. Still, I thought I’d share them.
Assumption 1: The frequency on the treasure tables factors into cost
There’s no reason this would be true, but I went with it. The DMG has some assumptions about how often over the lifetime of an adventurer they’ll find each broad challenge-band of hoard, and of course has tables for treasure table conditional on hoard and item conditional on treasure table. With that, I could figure out the notional average number of each item an adventurer would receive over their career or, even more valuably, the notional average number of each item a society of a mix of adventurers would receive over their careers.
Some items show up on more than one treasure table, of course (second level scrolls, I’m looking at you) and I further made some 3e-style the-rules-are-the-simulation-of-the-world assumptions, modeling the relative ratios in society of adventurers at each tier (so that I could have many, many more adventurers at the lowest levels than the highest levels). This makes sense, because without that, the wealth generated in the mid tiers produces a weird bulge where low level items are, in fact, rarer than mid level items because an adventurer is given more mid-level items over their career.
You can see the assumptions in the spreadsheet, but basically I assumed 500 tier 1 adventurers, 50 tier 2, 5 tier 3, and 1 tier 4.
Assumption 2: Pleasing curves about the log of the frequency of the items
Our society of adventurers gets an awful lot of healing potions over their career, and very few Apparatus of Kwalish drops. I normalized the items back into levels with fun curve fitting — this log base, that baseline, that curve. Even with that, potions of healing are STILL encountered in sufficient numbers to break the curve. But I assigned each item a “level” that tracks to their frequency in this assumption-laden global item ranking — rarer pulls are higher level.
This is not a good assumption. Level should, in D&D, mean power level, basically, challenge rating. The sovereign glue is just not that cool. And yet, based on only rarity and not better utility functions, my made-up-math shows it at level 20, along with the portable hole — because that’s the frequency you encounter them.
Assumption 3: The DMG pricing tiers are correct (with a proxy)
I gave up on data entry past a certain point, so I mapped the levels back to the hoard tiers, and called those rarity. That’s totally cheating, but basically I said that any item which, based on my magic order-preserving function from global frequency to “level”, was level 1-4 was uncommon, level 5-9 rare, level 10-16 very rare, 17-25 legendary, and 25+ artifact. And that each tier’s cost was 10* the previous cost. And that it was reasonable to price an item linearly between the low and high range for its tier.
I don’t feel too much shame over that, because my version of “common” is absolute; I might have classified some items on the wrong side of that divide, but any items which inverted (a designated-more-common item rarer than a designated-less-common item) are, on average and at the table, de facto more or less common than indicated*. So whatever, mine has made up stats behind it.
* Unless my “use the rules to simulate the world” thing comes back to bite me. When would that happen?!
I’m not sure I’ll use this thing as is; it still assumes permanent items are only twice the cost of consumables, and I have no idea how realistic its cost curves are. It’s possible the *right* thing to do is to map these item levels into challenge ratings and use a function of monster exp for cost, to reflect D&D’s love of exponential curves.
But even if my costs are crazy, surely an interesting fine-grained rarity-as-proxy-for-power system has some use? Wouldn’t you love to know which items are actually just-slightly-rarer than which other items? Now you can.