D&D 5E Magic Item Math of 5e

How many magic items should a typical 5e campaign have per PC?

DMG, bottom of page 133:
Over the course of a typical campaign, a party finds treasure 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

DMG, left column page 83:
Party Size. The preceding guidelines assume you have a party consisting of three to five adventurers.
i.e. the average party size for purposes of everything in DMG is 4.

There are 9 Magic Item tables, A-I and we can examine them for permanent items that change resource allocation:
Magic Item Table A has a 2% chance of some minor items. 0-2nd level scrolls.
Magic Item Table B has a 16% chance of permanent items and about a 6% of a meaningful permanent item. 2nd-3rd level scrolls, consumables that can influence a combat such as Potion of Hill Giant Strength or Elemental gem. Goggles of Night stand out here as do a cloak, suit of armor, useful ring, etc...+1 ammo.
Magic Item Table C has a 8% and a 1% of a meaningful permanent item. 4th-5th level scrolls, potion of stone giant strength, Necklace of Fireballs, Periapt of Health. +2 ammo.
Magic Item Table D has a 5% and a 3% 6th-8th level scrolls, +3 ammo
Magic Item Table E has 0%. 8th-9th level scrolls, storm giant strength potions, arrow of slaying.
Magic Item Table F is where +1 items live. About a 3% chance of a relative dud/not typically permanent item. About a 23% chance of a magic weapon in effect. About 11% chance of an implement.
Magic Item Table G is where +2 items live. About a 14% chance of a relative dud/not typically permanent item. About 24% chance of at least a +1 magic weapon in effect. About 22% chance of an implement.
Magic Item Table H is where +3 items live. About a 12% chance of a relative dud/not typically permanent item. About 25% chance of at least a +2 magic weapon in effect. About 22% chance of an implement
Magic Item Table I is where the crazy stuff is. Though no artifacts or sentinent items. About 25% chance of a relative dud/not typically permanent item. 18% chance of an implement.

If, as an example, we have a 4% chance of 1-4 items, that's an average of 2.5 items 4% of the time or essentially an average of 1 item 10% of the time. So what does that mean given what the DMG says is a typical campaign of an average of 4 PCs...

Challenge 0-4: Has a 36% of no magic items, 24% of 3.5 items from Table A(84%), 15% of 2.5 items from Table B(37.5%), 10% of 2.5 items from Table C(25%), a 12% chance of 2.5 items from Table F(30%), and a 3% chance from Table G.
7 rolls = 5.88 items from Table A, 2.63 items from Table B, 1.75 items from Table C, 2.1 items from Table F and 0.21 items from Table G.

Challenge 5-10: Has an 28% of no magic items, 21% of 3.5 items from Table A(73.5%), 19% of 2.5 items from Table B(47.5%), 11% of 2.5 items from Table C(27.5%), 6% chance of 1 item from Table D(6%), a 14% chance of 2.5 items from Table F(35%), a 4% chance of 2.5 items from Table G(10%), and a 2% chance of Table H.
18 rolls = 13.23 items from Table A, 8.55 items from Table B, 4.95 items from Table C, 1.08 items from Table D, 6.3 items from Table F, 1.8 items from Table G, and 0.36 items from Table H.

Challenge 11-16: Has a 15% of no magic items, 14% chance of 2.5 items from Table A(35%), 14% chance of 3.5 items from Table B(49%), 21% chance of 3.5 items from Table C(73.5%), 16% chance of 2.5 items from Table D(40%), 8% chance of 1 item from Table E, an 8% chance of 1 item from Table F, an 8% chance of 2.5 items from Table G(20%), a 10% chance of 2.5 items from Table H(25%), and an 8% chance of 1 item from Table I.
12 rolls = 4.2 items from Table A, 5.88 items from Table B, 8.82 items from Table C, 4.8 items from Table D, 0.96 items from Table E, 0.96 items from Table F, 2.4 items from table G, 3 items from Table H, and 0.96 items from Table I.

Challenge 17-20: Has a 2% chance of no magic items, 12% chance of 4.5 items from Table C(54%), 32% of 3.5 items from Table D(112%), 22% of 3.5 items from Table E(77%), a 4% chance of 2.5 items from Table G(10%), an 8% chance of 2.5 items from Table H(20%), and a 20% chance of 2.5 items from Table I(50% - wow!).
8 rolls = 4.32 items from Table C, 8.96 items from Table D, 6.6 items from Table E, 0.8 items from Table G, 1.6 items from Table H, and 4 items from Table I

How Many Items Per Party?
4th = 5.88 items from Table A, 2.625 items from Table B, 1.75 items from Table C, 2.1 items from Table F and 0.21 items from Table G
10th = 19.11 items from Table A, 11.18 items from Table B, 6.7 items from Table C, 1.08 items from Table D , 8.4 items from Table F, 2.01 items from Table G, 0.36 items from Table H
16th = 23.31 items from Table A, 17.06 items from Table B, 15.52 items from Table C, 5.88 items from Table D, 0.96 items from Table E, 9.36 items from Table F, 4.41 items from Table G, 3.36 items from Table H, and 0.96 items from Table I
20th = 23.31 items from Table A, 17.06 items from Table B, 19.84 items from Table C, 14.84 items from Table D, 7.54 items from Table E, 9.36 items from Table F, 5.21 items from Table G, 4.96 items from Table H, and 4.96 items from Table I


Expected Magic Items per PC?
4th = 1.47 items from Table A, 0.66 items from Table B, 0.44 items from Table C, 0.53 items from Table F and 0.05 items from Table G. 2.53 consumables, 0.62 permanent(0.56 useful, 0.02 duds, 0.04 Table B-D)

10th = 4.78 items from Table A, 2.8 items from Table B, 1.68 items from Table C, 0.27 items from Table D, 2.1 items from Table F, 0.5 items from Table G, 0.09 items from Table H. 9.34 consumables, 2.88 permanent(2.55 useful, 0.14 duds, 0.19 Table B-D)

16th = 5.83 items from Table A, 4.27 items from Table B, 3.88 items from Table C, 1.47 items from Table D, 0.24 items from Table E, 2.34 items from Table F, 1.1 items from Table G, 0.84 items from Table H, and 0.24 items from Table I. 15.36 consumables, 4.85 permanent(4.13 useful, 0.39 duds, 0.33 Table B-D)

20th = 5.83 items from Table A, 4.27 items from Table B, 4.96 items from Table C, 3.71 items from Table D, 1.89 items from Table E, 2.34 items from Table F, 1.3 items from Table G, 0.99 items from Table H, and 0.99 items from Table I. 20.24 consumables, 6.04 permanent(5.01 useful, 0.61 duds, 0.42 Table B-D)

Useful: Items that are good items from the tables F-I. They potentially might be rendered into a dud with additional levels. The guy who finds a +1 Greatsword and then a +2 Greatsword in a party where he's the only Greatsword user. This does not include items from Table B-D
Duds: Usually represent either cursed items, items that might be very difficult to use, items that are better thought of as being consumables, or even items that aren't necessarily strictly better than non-magical items. +1 Scale Mail on Table I, I'm looking at you. The exact number of duds isn't really precise. Quick judgment calls.
Table B-D: Are items from the tables that are mostly consumable items. Usually rather weak, but could help out some builds such as Humans unable to see in the dark or a Paladin who rides a mount.

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Conclusions
PCs typically ought to be finding about 1 consumable each per level.
Note how close the number of useful items per level at 10th, 16th, and 20th per PC is 0.25. i.e. a party should end up finding about 1 useful item each level, with each PC getting 1 useful item every 4 levels.
Levels 1-4 are a little off the curve, representing how fast they ought to happen. Levels 5-10 play catchup.
The idea that magic items aren't taken into account by game mechanics ought to be a false one - there's no assumption that you will have a specific magic item, but a 20th level PC ought to have 5 useful magic items according to what R&D considers a typical campaign.
The amount of gold one gets is approximately 3K per hoard from 5-10, 30K from 11-16, and 300K from 17-20.

I am impressed at the detail of your breakdown, and it's helpful to see in more detail what the DMG considers "typical."

I do think there is a big difference between saying, "over the course of a typical campaign a party finds [5 useful magical items]" and, "over the course of a typical campaign, a party ought to find 5 useful magic items." The former says, "be prepared to compensate in other aspects of your campaign balance if PCs are getting more or less magic items than this." The latter says, "if PCs are getting fewer items than this, give out more, and if they are getting more, stop handing them out."

Obviously, DMs can do Whatever The Hell They Want(tm), but I do think the distinction helps to keep DMs from being pressured into meeting certain treasure expectations if that goes against the feel of their campaign. I'm sure that the obfuscated numbers for "a typical campaign" are part of that — players who pick up the DMG and see, "a 10th level PC should have found 2.5 useful, permanent magic items by now," are more likely to pressure the DM to meet that standard. I can say whatever I want to my players, and I can always tell them that it's my way or the highway, but that's not fun and it's not something I want to have to do unless it's really necessary. In this case, the DMG seems to have opted for a mathematical DIY headache to save DMs from a social pressure headache.

That being said, I do wish there were a little more in the DMG on the various options of magic item economies.

Thanks. I think the other aspect of randomness is that there's a little leeway - it wouldn't be surprising for a 10th level PC to have 1, 2, 3, or 4 permanent items. But 0 or 5 would raise an eyebrow or two.

I think magic item economies tend to be a can of worms. If treasure goes up exponentially and items have a set cost, then you hit a certain point where all kinds of unintended things happen. An example of this is that a level 17-20 challenge ought to provide 280,000 gold's worth of platinum. Which is 5600 healing potions from PHB. Which is then about 50,000 points of healing...

Now of course, any rational DM figures out something to do with all that gold or rules that only so many healing potions can be downed per day. Or something.

I just stumbled upon this thread, and I deem it worth of *resurrection*!!!!

It certainly is useful to have some kind of generic "expected items" amount as a GM if we decide to place items and not roll them...

+1 Scale Mail on Table I, I'm looking at you.

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The existence of such items is a bit baffling, but it possible that at the time the item was made scale mail was the best armor available? Of course, such an item could be easily "spruced up". If I rolled that as a GM, I would perhaps make it of a useful material (say, bone so the druid can wear it), or have a useful minor power.

MwaO said:

Conclusions
PCs typically ought to be finding about 1 consumable each per level.
Note how close the number of useful items per level at 10th, 16th, and 20th per PC is 0.25. i.e. a party should end up finding about 1 useful item each level, with each PC getting 1 useful item every 4 levels.
Levels 1-4 are a little off the curve, representing how fast they ought to happen. Levels 5-10 play catchup.
The idea that magic items aren't taken into account by game mechanics ought to be a false one - there's no assumption that you will have a specific magic item, but a 20th level PC ought to have 5 useful magic items according to what R&D considers a typical campaign.

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Good math! But I have a bit of a problem with your final conclusion.

The fact that the game tells you to provide approximately 5 useful permanent magic items in a typical game need not have anything to do with the (alleged) fact that the game doesn't take magic items into account. Rationally, they are conflicting, but they aren't logically contradictory. It is completely possible to design a game that definitely does give out magic items, but which you refused to factor in the impact of those items on play. I would argue that that is incoherent, in that you are committed to expecting a thing in one sense and committed to *not* expecting it in another, but the two statements can both be true without producing a logical contradiction in the way that, say, "greater than 7 but less than 2" or "an integer which is neither even nor odd" would.

EzekielRaiden said:

Good math! But I have a bit of a problem with your final conclusion.

The fact that the game tells you to provide approximately 5 useful permanent magic items in a typical game need not have anything to do with the (alleged) fact that the game doesn't take magic items into account. Rationally, they are conflicting, but they aren't logically contradictory. It is completely possible to design a game that definitely does give out magic items, but which you refused to factor in the impact of those items on play. I would argue that that is incoherent, in that you are committed to expecting a thing in one sense and committed to *not* expecting it in another, but the two statements can both be true without producing a logical contradiction in the way that, say, "greater than 7 but less than 2" or "an integer which is neither even nor odd" would.

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I actually prefer the approach of giving a completely non-magical baseline and then indicating how to adjust for magic. I think this approach is to be preferred in 5e because of the wide variety campaign scenarios that are possible. If I convert a an old D&D module it will have way more magic than the guideline, or I could simply choose to run a low/no magic item campaign. Additionally a zero-magic baseline with compensating instructions also deals with the inherent variance which was neither calculated nor acknowledged in the original post. A by the books campaign can still end up with no magic at all, or everybody having very rare magic by level 5.

Where 5e actually falls down is that there aren't good guidelines for how to adjust to more or less magic even though that necessity is acknowledged. Fortunately, IME it actually isn't very hard at all to adjust to additional magic in the party (Lvls 1-12), but a good set of guidelines should have been provided without me needing figure out for myself as I go along.

I just posted an analysis on this in another thread here, did not even know this thread existed.

After that post, I worked up some tables for determining random items for higher level pre-generated characters. I plan on posting more in depth on this topic soon.

But in a nutshell, a finite number of rolls are tabled. The items rolled for, consumables of lower tier are considered used. PCs take turns choosing items off the list. Assume for 4-6 PCs, so if you are only creating one character, you can solitaire through the list by making a pick and discarding 4 out of five items. Works well with an actual group, for doing one-shots for instance.

yakuba said:

I actually prefer the approach of giving a completely non-magical baseline and then indicating how to adjust for magic. I think this approach is to be preferred in 5e because of the wide variety campaign scenarios that are possible. If I convert a an old D&D module it will have way more magic than the guideline, or I could simply choose to run a low/no magic item campaign. Additionally a zero-magic baseline with compensating instructions also deals with the inherent variance which was neither calculated nor acknowledged in the original post. A by the books campaign can still end up with no magic at all, or everybody having very rare magic by level 5.

Where 5e actually falls down is that there aren't good guidelines for how to adjust to more or less magic even though that necessity is acknowledged. Fortunately, IME it actually isn't very hard at all to adjust to additional magic in the party (Lvls 1-12), but a good set of guidelines should have been provided without me needing figure out for myself as I go along.

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Both fair points. Honestly, for all the love the 5e DMG gets for its "levers and dials," it seems to leave a lot of...pretty dang important "you might want to change this" parts completely unexplained. "You're the DM, you'll figure it out!" is practically an official line, not just something you hear in lots of 5e advice threads.

Ancalagon said:

I just stumbled upon this thread, and I deem it worth of *resurrection*!!!!

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Two days early.

redrick said:

Obviously, DMs can do Whatever The Hell They Want(tm), but I do think the distinction helps to keep DMs from being pressured into meeting certain treasure expectations if that goes against the feel of their campaign. I'm sure that the obfuscated numbers for "a typical campaign" are part of that — players who pick up the DMG and see, "a 10th level PC should have found 2.5 useful, permanent magic items by now," are more likely to pressure the DM to meet that standard. I can say whatever I want to my players, and I can always tell them that it's my way or the highway, but that's not fun and it's not something I want to have to do unless it's really necessary. In this case, the DMG seems to have opted for a mathematical DIY headache to save DMs from a social pressure headache.

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That's an interesting analysis. I mean, to me knowing that "on average, the party should receive 1 consumable item/player per each level, and 1 permanent item (for the whole party)/level" is quite useful. At the same time, I'm a bit glad that this isn't common knowledge...