An expected wealth by level table for 4E

[Squirrelloid]

Also originally on Gleemax.  Of obvious utility for anyone who doesn't want to have to deal with the difference engine.

Elsewhere I have extolled the virtue of a character wealth system wherein the rules make clear what wealth a level N character should have, and the DM audits PC wealth and adjusts treasure flow to be near these targets.  This is my best guess of what such a table would look like for 4E - an explanation of how the table was arrived at follows.

Please note that the table is wealth at the end of that level (all parcels collected), not at the start of that level.  If you're starting level N characters, use the N-1 entry to arrive at starting wealth.  (Obviously level 1 starts with 100gp).

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My Proposed 4E Expected Wealth by Level Table
Level   Expected Wealth
1   752
2   1824
3   3344
4   5440
5   8240
6   11699
7   16630
8   23622
9   33801
10   47372
11   64060
12   87878
13   121718
14   172614
15   239632
16   323072
17   442160
18   611360
19   864720
20   1199808
21   1617008
22   2212448
23   3058448
24   4325248
25   6000688
26   8086688
27   10563888
28   13293888
29   16627888
30   20005088

Expected Wealth is per character.  Some deviation is expected.

Of more use will be the expected wealth for the party - multiply the values by the number of players, and compare to entire party wealth.  (Due to the nature of the parcel system, some players could end up, temporarily, with drastically more wealth than others, especially when a level +4 item crosses a break point in the pricing scheme.  But the party as a whole should adhere more closely to the party's expected value).

Obviously I haven't bothered to round off the numbers like the 3e table does.  Deal with it.

This table is based on the assumptions listed below.  If you don't like it, don't use it.

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There are obviously some assumptions behind the table.  To start with, it is possibly to compute the average total value of a character's possessions at level N assuming he never loses any wealth, something I did in my Brace of Wands post and my post about the Difference Engine (both in the My Threads link in my sig).  However, this doesn't actually tell us how much a character has at level N.

Assumption 1: Player behavior isn't expected to be perfectly optimal.
In my difference engine thread I examined two different algorithms for advancing items, and thus for controlling loss of wealth to the difference engine.  One is a relatively greedy algorithm, which makes sure to routinely update each of weapon/implement, armor, and neck item for each plus of goodness.  I'm taking this as a minimum value - being less optimal than this requires players who truly don't understand the wealth system, and involves excessively frequent replacements of the same item.

The second algorithm I examined was a global optimization algorithm that made sure to have one of each useable item (8 total slots) before upgrading any, and then upgraded them all before performing a second upgrade, and so forth.  I don't think the designers intended the players to behave as rigidly as this, so this is an upper bound.

More optimal algorithms are actually possible, but require particular class builds with various lower level items that the character has no intention of ever selling, and many items that are easily swappable into slots or never use slots (eg, Portable Holes require no slot to use).  However, getting more optimal requires an insane amount of comparison of progressions and isn't easy to do in a generalizeable way.  Given the designers actually wanted players to not focus on the wealth system but just get back to the story, I think any such algorithm is too optimal to consider as intended.

Worse algorithms are also easy to imagine, for example, selecting items at random.  This is also clearly not intended.

As a basis for the actual table, I'm going to use the average value for the two explicitly discussed algorithms as a happy medium that should approximate expected PC item upgrade behavior by the designers. 

Note that assumption 1 covers loss of wealth from selling items.

Assumption 2: Mundane Expenses
I'm going to assume that mundane expenses (outside of 1st level gear at starting) aren't intended to drain character wealth at all.  This stuff is purely roleplaying oriented, and so I will attribute no drain on party wealth due to it.  In fact, I didn't even include the 100gp starting cash in the table at all, so just don't count mundane gear towards party wealth for balance purposes (ie, treasure adjudication) unless it can actually be sold (eg, art objects aren't mundane gear, they are cash on a stick.)

Assumption 3: Rituals
Acquiring the ritual itself is like acquiring a magic item.  It is part of your wealth, and thus is already accounted for in the above item algorithm to a large degree.

The cost to use algorithms is not included, and a major problem in the difference engine, because differential use of rituals leads parties to very different places.  Many uses of rituals serve roleplaying purposes, and don't necessarily need to be balanced against.  Ultimately, I don't want to discourage players from using rituals - I'm going to assume that the cost to use a ritual is not a permanent cost at all, and should be recouped by the player, with the sole exception of rituals that lead to a (relatively) permanent benefit which applies to adventuring life.  Ie, enchanting items clearly is a permanent wealth expense, as is becoming a lich (that state should be considered to have value = cost to cast the ritual).  Ie, rituals which result in states that are basically magic items useable during adventuring are treated as magic items (and thus arleady incorporated into the above assumptions).  Any other ritual is not a permanent cost, and no modification is necessary.

Ritual use is still limited by cash on hand - just because you will recoup those expenses eventually doesn't mean you can use rituals infinitely in the hear and now.  However, there is no long-term disadvantage to using rituals under these assumptions (basically, you tie up your funds for the short term to receive the short term benefits of the ritual, which strikes me as a fair exchange).

The rituals a wizard receives for free as a class feature do not count towards his wealth.

Assumption 4: Potions
Like use of rituals, use of potions can be a major contributor to the difference engine, and also leads to death spiral scenarios where having burned some critical amount of wealth in the difference engine, you are sufficiently worse compared to a party/character who hasn't that you need to feed proportionally more wealth into the difference engine to survive, leading to forever decreasing levels of cash and ultimately inability to survive at all.  As such, potions should represent temporary uses of wealth, not permanent uses of wealth, just like the use of rituals.

For the purposes of assumptions 4+5, I'm going to basically assume that the designers didn't consider the costs of them significant enough to plan on noticeable wealth loss thereby, so there's no need to adjust the table for their expectation of wealth outflow here.

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Basically, there are two types of expenses, those that are permanent, and those that represent temporary uses of funds which should be recouped while adventuring.  Permanent uses of funds lead to permanent benefits that can apply during adventures (known rituals, magic items), whereas temporary uses of funds lead to transitory benefits.