The subject of 'Wealth by Level' came up in one of the recent 5e threads and it got me thinking..
5e doesn't exactly have any kind of guidelines for wealth by level. There are three things that it does have, though.
1) Random Treasure Tables (DMG p136-149)
2) Guidelines for at what sort of level you should find different rarities of magic item (DMG p135)
3) A starting wealth table for characters joining a campaign at higher than first level (DMG p38)
So, between the three of these, can we get an idea of what characters of a certain level might have accumulated during their adventures?
The first thing we need to do is throw away the starting wealth table. That table seriously under-estimates things. Even on its 'High Magic Campaign' column, a tenth level character is expected to have only a single uncommon item - and in any campaign other than that they're not expected to have any magic items at all until eleventh level. While I'm sure there are some campaigns out there that have so little magic, I'm sure that's not representative at all - it's clearly at odds with the other two sources of information.
The second source of information - the guidelines for level versus magic item rarity - are interesting. They don't give any indication of how much wealth or how many items characters are expected to have, but they do place soft guidelines for when you're supposed to start finding magic items of a particular rarity. Reversing the table, we get:
1st-4th level = Common & Uncommon items
5th-10th level = Common, Uncommon & Rare items
11th-16th level = Common, Uncommon, Rare and Very Rare items
17th -20th level = Common, Uncommon, Rare, Very Rare, and Legendary items
As you can see, this doesn't tally up at all with the starting wealth guidelines. Characters are expected to start finding rare items at 5th level, but apparently even in a 'high magic' campaign they're not expected to have more than a single uncommon magic item until they hit 11th level (by which point on this table they should be starting to find very rare items).
From the point of view of a campaign, of course, both these are only vague guidelines.
Something that's much bigger is the set of random treasure tables. All the guidelines in the world about when characters should expect to find treasure (and how much) are irrelevant if the DM is rolling random treasure on these tables. If the guidelines say that characters should be finding rare items at 5th level but the treasure tables don't give them out at 5th level, then they won't find them at that level despite what the guidelines say. Similarly, if the treasure tables give out legendary items at first level, it doesn't matter when the guidelines say the party should expect to find them. Unless the DM fudges their rolls, there's a chance they'll find them earlier than the guidelines say.
So the big question is: can we construct some kind of average wealth-by-level expectation from the random treasure tables? Assuming a DM is giving out random treasure as per the tables for the encounters that the players have, how much will they accumulate as they increase in level?
The way the treasure tables work is that there are basically four categories (kind of like the 'Treasure Types' in AD&D). These are based solely on the challenge of the encounter. They are:
Challenge 0-4
Challenge 5-10
Challenge 11-16
Challenge 17+
Notice that they follow the same 'tiers' as the other guidelines.
Each table works by giving you a random amount of money, plus a d100 roll which then gives you a random amount of valuable items and magic items. The magic items are in a bunch of tables (A-I), so for example if you roll a 64 on the table for Challenge 0-4 you get 2d6 gems worth 10gp each and 1d4 magic items from table B. This is on top of the 6d6x100 copper, 3d6x100 silver, and 2d6x10 gold you always get in a Challenge 0-4 hoard.
I've spent a good chunk of this weekend sticking all these treasure tables through Excel.
Firstly, I went through each of the magic item tables A-I and checked out the rarity of the items on each one. For example a roll on table F will always give you an uncommon item, but a roll on table H has a 2% chance of giving you an uncommon item, a 6% chance of giving you a rare item, and a 91% chance of giving you a very rare item (the percentages don't always add up to exactly 100% because I counted consumable items as half an item of the same rarity and I ignored the half a dozen or so cursed items).
Secondly, I went through the treasure tables for each challenge rating in a similar manner to see what the average treasure was, using my summarised magic item tables. For example if a roll on magic item table C gives you 0.54 chance of getting a rare item, and a roll on the Challenge 5-10 table gives you a 0.11 chance of getting 1d4 rolls on table C, then a roll on the Challenge 5-10 table therefore gives you an average of 0.11*2.5*0.54 = 0.1485 rare items from table C. Of course the actual chance of getting a rare item from a roll on the Challenge 5-10 table is more than that because you can get them from tables other than table C, so we have to sum all the chances.
Long story short (too late!) here is the average loot from each of the four treasure tables..
Challenge 0-4
196gp in money
180gp in valuable objects
0.38 common magic items
0.59 uncommon magic items
0.16 rare magic items
0.07 very rare magic items
Challenge 5-10
3,857gp in money
688gp in valuable objects
0.25 common magic items
0.68 uncommon magic items
0.25 rare magic items
0.13 very rare magic items
Challenge 11-16
31,500gp in money
4,700gp in valuable objects
0.16 common magic items
0.43 uncommon magic items
0.61 rare magic items
0.68 very rare magic items
0.09 legendary magic items
Challenge 17+
322,000gp in money
14,026gp in valuable objects
0.03 uncommon magic items
0.45 rare magic items
1.16 very rare magic items
0.62 legendary magic items
This gives us some idea of what characters will be finding. For example, on average one in four treasure hoards from a Challenge 5-10 encounter will contain a rare magic item, but only one in six and a quarter treasure hoards from a Challenge 0-4 encounter will contain one.
So if we can estimate how many encounters (and of what level) it takes a party to advance from each level to the next, we can estimate how many hoards of each category they'll have picked up (on average) as a result of those encounters and therefore how much money and how many items of which rarity (again, on average) the party will have found too.
This should give us an average 'wealth by level' estimate for campaigns in which the DM uses the random treasure tables, which can then be used as a baseline to which other campaigns can be compared.
So how do we estimate the encounters needed for each level?