D&D 5E Analysis of "Typical" Magic Item Distribution

[FireLance]

Over the weekend, I entered the magic item tables and the treasure hoard generation tables in the DMG into a spreadsheet to determine what is the expected distribution of magic items that would be generated by what the DMG refers to as a "typical" campaign in the last paragraph of page 133, i.e. 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.

[SBLOCK="General Observations and Comments"]Before I get into the analysis, here are some general observations and comments.

Consumables and Permanent Items
Magic Item Tables A to E tend to produce consumable items (potions, scrolls, ammunition) while Magic Item Tables F to I tend to produce permanent items. While there are exceptions, for simplicity, the following analysis assumes that a roll on Magic Item Tables A to E will generate a consumable item, while a roll on Magic Item Tables F to I will generate a permanent item.

Magic Item Rarity
The tables are more or less grouped by magic item rarity.
Table A has a 90% chance of generating a common item, and a 10% chance of generating an uncommon item.
Table B only generates uncommon items.
Table C has a 96% chance of generating a rare item and a 4% chance of generating an uncommon item.
Table D has a 99% chance of generating a very rare item, and a 1% chance of generating a rare item.
Table E has a 50-50 chance of generating either a very rare or a legendary item.
Table F only generates uncommon items.
Table G has a 98% chance of generating a rare item and a 2% chance of generating an uncommon item.
Table H has a 92% chance of generating a very rare item, a 6% chance of generating a rare item, and a 2% chance of generating an uncommon item.
Table I has an 88% chance of generating a legendary item, a 6% chance of generating a very rare item, and a 6% chance of generating a rare item.
The items of lower rarity on Tables G to I are the higher level armors such as breastplate, half plate, scale mail and plate. For example, +1 plate is one of the rare items generated on Table I. (Table I also lists +1 scale mail. I am assuming this is a typo and that it should actually be +3 scale mail since there is a +1 scale mail on Table G and a +2 scale mail on Table H.)

Terms and Assumptions
For the analysis proper, I will be using statistical terms. For example, a roll on the Challenge 0-4 Treasure Hoard table actually has a 24% chance of generating 1d6 rolls on Magic Item Table A, each of which has a 90% chance of generating a common magic item. However, for the purpose of my analysis, I will say instead that a roll on the Challenge 0-4 Treasure Hoard table has a 76% chance of generating a common consumable.

I also assume that the treasure hoard table rolls are fairly evenly distributed:
One roll on the Challenge 0-4 table at Level 1.
Two rolls on the Challenge 0-4 table at every level from 2 to 4.
Three rolls on the Challenge 5-10 table at every level from 5 to 10.
Two rolls on the Challenge 11-16 table at every level from 11 to 16.
Two rolls on the Challenge 17-20 table at every level from 17 to 20.

I have rounded the numbers in the analysis to keep to whole numbers. Some results are expressed as [N or N+1], which I have used to denote that the expected number is fairly close to [N and a half].

Now, on to the meat of the analysis.
[/SBLOCK]
[SBLOCK="Challenge 0-4 Table"]A roll on the Challenge 0-4 table has a:
76% chance of generating a common consumable.
47% chance of generating an uncommon consumable.
24% chance of generating a rare consumable.
30% chance of generating an uncommon permanent item.
3% chance of generating a rare permanent item.

Hence, over the first four levels, the party is expected to find:
5 common consumables.
3 uncommon consumables.
1 or 2 rare consumables.
2 uncommon permanent items.
[/SBLOCK]
[SBLOCK="Challenge 5-10 Table"]A roll on the Challenge 5-10 table has a:
50% chance of generating a common consumable.
54% chance of generating an uncommon consumable.
26% chance of generating a rare consumable.
6% chance of generating a very rare consumable.
35% chance of generating an uncommon permanent item.
10% chance of generating a rare permanent item.
2% chance of generating a very rare permanent item.

Hence, over levels 5-10, the party is expected to find:
9 common consumables.
10 uncommon consumables.
5 rare consumables.
1 very rare consumable.
6 uncommon permanent items.
2 rare permanent items.
[/SBLOCK]
[SBLOCK="Challenge 11-16 Table"]A roll on the Challenge 11-16 table has a:
32% chance of generating a common consumable.
55% chance of generating an uncommon consumable.
71% chance of generating a rare consumable.
44% chance of generating a very rare consumable.
4% chance of generating a legendary consumable.
9% chance of generating an uncommon permanent item.
22% chance of generating a rare permanent item.
24% chance of generating a very rare permanent item.
7% chance of generating a legendary permanent item.

Hence, over levels 11-16, the party is expected to find:
4 common consumables.
6 or 7 uncommon consumables.
8 or 9 rare consumables.
5 very rare consumables.
0 or 1 legendary consumable.
1 uncommon permanent item.
2 or 3 rare permanent items.
3 very rare permanent items.
1 legendary permanent item.
[/SBLOCK]
[SBLOCK="Challenge 17+ Table"]A roll on the Challenge 17+ table has a:
2% chance of generating an uncommon consumable.
53% chance of generating a rare consumable.
149% chance of generating a very rare consumable.
39% chance of generating a legendary consumable.
1% chance of generating an uncommon permanent item.
14% chance of generating a rare permanent item.
21% chance of generating a very rare permanent item.
44% chance of generating a legendary permanent item.

Hence, over levels 17-20, the party is expected to find:
4 rare consumables.
12 very rare consumables.
3 legendary consumables.
1 rare permanent item.
1 or 2 very rare permanent items.
3 or 4 legendary permanent items.
[/SBLOCK]
[SBLOCK="Overall Treasure"]Over the course of a typical campaign, the party is expected to find [Note: there may be discrepancies from a simple summation of the above breakdown due to rounding]:
18 common consumables
20 uncommon consumables
19 rare consumables
18 very rare consumables
3 or 4 legendary consumables
9 or 10 uncommon permanent items
5 or 6 rare permanent items
5 very rare permanent items
4 legendary permanent items

Assuming a party of four PCs, each PC should obtain:
4 or 5 common consumables
5 uncommon consumables
5 rare consumables
4 or 5 very rare consumables
1 legendary consumable
2 or 3 uncommon permanent items
1 or 2 rare permanent items
1 very rare permanent item
1 legendary permanent item

To translate this into a very even distribution of magic items over all 20 levels, I would probably go with the following approach:
1 common consumable every level from 1 to 5.
1 uncommon consumable every level from 6 to 10.
1 rare consumable every level from 11 to 15.
1 very rare consumable every level from 16 to 19.
1 legendary consumable at level 20.
1 uncommon permanent item at level 4, and another at level 7.
1 rare permanent item at level 10 and another at level 13.
1 very rare permanent item at level 16.
1 legendary permanent item at level 19.
[/SBLOCK]

 

[FireLance]

Something I just thought of, for those of you who like a bit more randomness. Given that Magic Item Tables A to I are more or less grouped by rarity, here is an alternate approach to generate magic items for each PC:

One roll on Table A for every level from 1 to 5.
One roll on Table B for every level from 6 to 10.
One roll on Table C for every level from 11 to 15.
One roll on Table D for every level from 16 to 18.
One roll on Table E for levels 19 and 20.
One roll on Table F at level 4 and again at level 7.
One roll on Table G at level 10 and again at level 13.
One roll on Table H at level 16.
One roll on Table I at level 19.

 

[Eric V]

This is great work, thanks.

This is also a lot more magic per PC than I assumed was the game's philosophy. That's very interesting to me.

 

[Umbran]

Nice analysis!

 

[Remathilis]

Brilliant! This was exactly what I was looking for.

Interestly, the typical PC you outlined gets 19-21 consumables and 5-7 permanents over twenty levels. That's important to people trying to convert older material to 5e, especially since some of those modules are FLUSH with permanent magical items.

I wonder; is a better item worth more lesser items? For example, is a "legendary" item worth 2 very rares or 3 rares? Probably another topic though.

I'd be interesting to see something like this done for "wealth" (Gold, art, gems) to see when the typical PC would start amassing a fortune vs. paying the bills.

 

[DogBackward]

This is great work, thanks.

This is also a lot more magic per PC than I assumed was the game's philosophy. That's very interesting to me.

Keep in mind that this isn't something that's actually built into the math of the game. The game doesn't assume that the players will have this stuff, the tables and whatnot are simply there for those DM's who like the old style of rolling randomly for loot.

 

[Kraydak]

Keep in mind that this isn't something that's actually built into the math of the game. The game doesn't assume that the players will have this stuff, the tables and whatnot are simply there for those DM's who like the old style of rolling randomly for loot.

Whistling in the wind. Gear has a huge effect on character power. The PHB and the DMG make few (not no) assumptions about player gear. The MM makes a bunch of assumptions. Any modules or adventures make lots of assumptions.

 

[guachi]

I did the same thing over the weekend!

Players get lots and lots and lots of potions. I could upload my spreadsheet to GoogleDocs, if someone wanted to look at it. It breaks down the gp treasure and the magic treasure. You can see the % chance of getting any particular magic item on the table in which it appears (some appear on more than one table), the number of times you would roll on that table on average, and the average number of that item you'd expect in a campaign. Some items are so rare you'd only see them in a hoard every 250 campaigns. That's not to say it's that rare. Perhaps that plate +3 isn't found in a hoard but rather being worn by some bad guy.

Number of expected items by broad category over 20 levels:
Armor 3.18
Bags (of all kinds) 1.48
Belts .3
Boots .67
Cloaks .8
Instruments .48
Ioun stones .7
Potions 43.2
Rings 2.01
Robes .52
Rods .99
Scrolls 17.6 (oddly, a party can expect to find more 8th level scrolls than anything but 1st level)
Shields .92
Staffs 1.28
Wands 1.33
Weapons 5.58

CR 17+ Hoards have massive amounts of platinum. By far the largest value of the hoard is just platinum. After every tier but the first, the gems and art are a small portion of the overall value. By the final tier, CR 17+, they are only 7% of the value. It seems really boring considering non cash treasure is so fun.

 

[guachi]

The suggestions are to roll the following number of times for each tier:
0-4 7
5-10 18
11-16 12
17+ 8

If you find one hoard at each CR level (except 0), these are my suggestions for how many times you roll on the respective table. It gives an increasing amount of treasure and somewhat minimizes the jump in treasure from one tier to another. I've arbitrarily decided CR 0 gets no rolls. I'm mean. The total rolls for that tier equal the total suggested rolls.

Tier Rolls
0 0
1 1
2 1
3 2
4 3
5 1
6 2
7 3
8 3
9 4
10 5
11 1
12 1
13 2
14 2
15 3
16 3
17 1
18 2
19 2
20 3

 

[Remathilis]

Whistling in the wind. Gear has a huge effect on character power. The PHB and the DMG make few (not no) assumptions about player gear. The MM makes a bunch of assumptions. Any modules or adventures make lots of assumptions.

So far, the MM has made assumptions on magical weapons, but has failed to mention what type. A +1 sword, a dozen +1 arrows, a frost brand, a holy avenger, or a +3 axe all can it the monster, so a DM could reasonably give out a +1 sword to the fighter and never worry about adding additional bonuses and abilities to it. Additionally, some monsters can be bypassed by adamantine or silver as an option, both of which are rare but non-magical.

That said, its a very big difference than 3e/4e where certain +X bonuses to hit, AC, saves, ability scores, etc were built into the math of the game, making fights harder if you lacked the cloak, ring, armor, and weapon plus.