The Numbers Game

One of the aspects I really came to enjoy about D&D 3e, 3.5e, and Pathfinder 1e was the nice behind-the-scenes math that related to PC wealth by level and encounter design. I was a physics and math major in college, so I was naturally drawn to this aspect of the game. A sort of "doing your taxes" kind of sub-game for the DM to play between sessions (and I mean that in a good way!). 

As our time playing Pathfinder 1e wore on, I began to grow a bit tired of the constant +1, -2, this that and the other bonus that creeps into every roll. I wanted a more streamlined experience, where the treaure you acquire was not instrumental to the success of your character later on. I would argue that improperly equipped (or perhaps even improperly built) characters in those systems are not going to succeed at high level play. In a way that is a great thing: the challenge assumes the players as the are, fully equipped and min/maxed, ready for a tough fight. I always lamented the fact that some classes do much better than others in the combat power game, and some are destined to feel like support roles. I do not like that at all.

At any rate, when D&D 5e came along, I was very interested in a new system that appeared to drain the swamp of all those myriad bonuses and promised to promote faster play. So I bought the books. I have run a few sessions here and there, mostly for my children, but I am now working toward a short campaign to be played with my regular gaming group at some point. I still do not know whether this version of D&D can deliver on the promise of faster, more even play.

As part of my initial study of the new system, I was surprised to see the magic item system mostly neutered from earlier versions of the game. No specific prices for items listed, just a range of possible values. The max weapon bonus was a +3, full stop: a far cry from something like a +5 holy longsword of speed. With no real magical item economy and with squishy or undefined prices for the items that character most wish to acquire, this puts the whole notion of treasure (why get it, how to spend it) in a strange light. Add in the fact that characters have a natural limit of only 3 attuned item slots and this edition seems very different, indeed.

So: how much treasure is right for a campaign? Gone are the ever helpful "PC Wealth by Level" tables. We are left to our own devices, out in the economic wilderness, where the amount of money the PCs have doesn't even seem to matter that much. Let's try to put some numbers to the problem.

What we find is that this edition is inconsistent. The best places to get a glimpse at the what the designers intend for us is two spots in the DMG, which disagree by a fairly wide margin.

Spot 1
Chapter 7: Treasure, page 133.
"You can hand out as much or as little treasure as you want. (ed. That's an understatement. With the economy de-fanged and the max bonuses de-clawed, treasure probably matters less in this edition that ever before). Over the course of a typical campaign, a party finds treaure hoards amounting to seven rolls on the Challenge 0-4 table, eighteen rolls on the Challenge 5-10 table, twelve rolls on the Challenge 11-16 table, and eight rolls on the Challenge 17+ table."

Of course I had to go through and generate an expectation value for the accumulated treasure per PC, based on this specific data. So have a bunch of people all across the internet. We all came to roughly the same conclusion, in terms of PC wealth due to coins, gem, and artwork (assuming 4 players in a party): at 20th level each person has over 800,000 gp. 

This doesn't count magic items, which are rolled for separately as part of the treasure tables. When you work out those averages, you find that, by 20th level, each character should have gained the following magic items: 1 legendary item, 1 very rare item, 1 rare item, 2 uncommon items, and 5 each of the very rare "charged" items (think of something expendable, like a healing potion), rare charged items, uncommon charged items, and common charged items. 

Spot 2
Chapter 1: A World of Your Own, page 38.
Here we see something that is as close as 5e gets to having the old familiar Average PC Wealth by Level table (a personal favorite of mine). This is a table, at the bottom of the page, called Starting Equipment. We get a snapshot here, of at least what a starting character would have, at 1st level, 5th level, 11th level, and 17th level. From this data, we can generate an idea of the amount of money you might get if you wished to build a character from scratch at a level other than 1st.

Sadly, this data does not match the treasure accumulation discussed above. I have extrapolated some of the intervening data and show the difference below. Starting wealth is the flat graph, the broken hoard treasure system is the disjointed graph.



What to Make of This?
I am of two minds. First, I assume that we can take the designers of 5th edition at their word: You can hand out as much or as little treasure as you want. Of course this is true, but what I mean is that is probably doesn't matter that much. So you got an extra +3 to hit. So? The entire encounter system is much flatter in 5e (we'll discuss that in a future post), and it feels like a smaller percentage of a character's capability comes from his or her equipment. And that's likely a good thing. 

The other part of me says this strange dogleg after 17th level might just be the result of a typo in the book. I could try to track down which component of the Challenge 17+ hoard treasure table is likely a typo...perhaps a x1000 instead of a x100 or something. That would be funny if the upper level treasure system was broken by a typo! 

Instead, I decided to fix the system a bit, by ditching the 18th, 19th, and 20th level numbers and generating some new data based on the trend.

Corrected Treasure
When you pitch out the outliers and recalculate the numbers, things look a lot nicer. In the graph below we still see the broken treasure system in blue, the corrected treasure system in orange (toss out 18, 19, 20 and re-calculate), the starting equipment in gray (still very low, comparably). For fun, I also added the XP per level, in yellow. I think all of this shows that the sort of polynomial curves that we see for XP and treasure are on the right path. You could simply give PCs 1 gp for every XP and be in a better place than the broken treasure system as written (at least for high levels).


Average
What still bothers me, of course, is the fact that the "Starting Equipment" level and the "Corrected Wealth by Level" curves are still so different. After some playing around, I decided to split the difference. All of this is informed by a close look at the economy of magic items, of course. That I will save for the next post.



In Table Form
Average Wealth by Level (GPe is 'gold piece equivalent'; the total value of coins, gems, & art)- not including found magic items (which we'll discuss next).








 

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