D&D 5th Edition Let's do math

1. ## Let's do math

So the new October playtest has random magic item generation in it. The tables look pretty wonky so I decided to run them through some good old mathematics.

Before you complain: First, I am running on the assumption that the DM is meant to roll on these magic item tables after EVERY encounter. The fluffy boxes of text hint that magic items should be rare but the tables also have sizable chances of not giving anything at all. Why would a DM roll on them if he didn't intend to give out an item unless it was intended to be a chance of getting an item? So I'm going to run with the idea that you're supposed to roll every time.

Second, I'm working with pure averages here by multiplying the chance of an item by the number of encounters per day to get a rough "items per day" that could be expected.

Third, I'm going to calculate averages using all three tables and the expected adventuring days from Page 11 of the DM Guidelines. So I'll give numbers for a party that fights six easy encounters, a party that fights four average encounters, and a party that fights two tough encounters. Obviously in a real game these would be mixed and matched but you should be able to get a rough estimate of what to expect.

Fourth, I'm making an assumption that the 97-99 slot of the Average Encounter table includes 1d2 rare items. It looks like a typo the way it is.

Example Math:
On the easy encounter table a result of 1-50 results in no magic items. A result of 51-100 will result in 1d2 common items (plus possibly other things but for common items I just care about that 51-100). Thus I can say that there is a 50% chance of rolling 1d2 common items. Thus: 0.5 x 0 + 0.5 x (0.5 x 1 + 0.5 x 2) = 0.75
A party will encounter an average of 0.75 common items per easy encounter.

A party fighting six easy encounters:
Common: 4.5
Uncommon: 0.45
Rare: 0.15
Very Rare: 0.03
Legendary: 0
Artifact: 0

A party fighting four average encounters:
Common: 4
Uncommon: 1
Rare: 0.3
Very Rare: 0.04
Legendary: 0.02
Artifact: 0

A party fighting two tough encounters:
Common: 2.75
Uncommon: 1.1
Rare: 0.5
Very Rare: 0.15
Legendary: 0.04
Artifact: 0.01

Interestingly the level of the adventurer has zero correlation to the power of the items he finds. Level 1 adventurers are just as likely to find a Holy Avenger at the bottom of the goblin hole as world shattering badasses are to find one at the depths of Orcus's palace.

2. Yeah, in my view the distributions are wonky and should vary with both level and difficulty, and be scaled back if they want the economy assumptions -- i.e., it"s hard to both buy and sell magic items because there aren't many and there isn't a "market".

If we assume a 3E spread of 13-15 encounters per level, that's 2-3 times what you've calculated.

If we go by the math in the DM Guidelines (650 XP for level 2, four character party = 2600 XP), that's 6.5 Tough encounters (400 XP) or 16.25 Easy ones (160 XP) to reach level 2 ... which is a lot of magic items by level 2! By the math above, for the "Easy encounters only" party that's ~12 commons, ~1.2 Uncommons, and 0.4 rares by level 2.

3. Originally Posted by n00bdragon
Interestingly the level of the adventurer has zero correlation to the power of the items he finds. Level 1 adventurers are just as likely to find a Holy Avenger at the bottom of the goblin hole as world shattering badasses are to find one at the depths of Orcus's palace.
Probably just because the playtest is 1-5. Maybe when we see 6-10 we'll see new random treasure tables, too? Maybe even a return to treasure types?

4. I agree with @Tony Vargus. Also, if magic items are meant to always be useful do they need to be more frequent at higher levels? PCs will have more magic items just by having had that many more encounters and slowly accruing them.

I'd like to see what the math looks like at each level assuming half the fights needed to level up are average, half are easy, and half are tough. How many items a group would have a such.

5. A quick summary would be that the tables are set up to grant roughly 1 item per party member per day. The majority will be common.

I expect this to in due course come with advice similar to healing for simply setting the dial to lower numbers .

6. A dirt-simple way to scale it by level, along with making low-level types less likely or completely unable to find the real high-end stuff, would be to modify the d% roll by -1 for each level of the party average below 10th. So, if the party average is 4th level all the treasure rolls are at -6%. That said, I'd still keep it that a roll of '00' opens up the high end if the DM so desires.

Lanefan

7. Originally Posted by n00bdragon
Interestingly the level of the adventurer has zero correlation to the power of the items he finds. Level 1 adventurers are just as likely to find a Holy Avenger at the bottom of the goblin hole as world shattering badasses are to find one at the depths of Orcus's palace.
Isn't that how Bilbo found the One Ring? Messing around at the bottom of a goblin hole?

8. Originally Posted by Ultimatecalibur
Isn't that how Bilbo found the One Ring? Messing around at the bottom of a goblin hole?
That's actually an excellent point. Found an artifact at level 1? Plot hook! Spend the rest of the campaign trying to figure out either how to safely hold on to the darn thing, find a safer set of hands for it to fall into, or find some way to destroy it.

... Or just ignore that one roll result if it would unintentionally derail your campaign. Seriously, it's written right at the beginning that these items are all optional, and players are not entitled to them.

9. Originally Posted by cmbarona
That's actually an excellent point. Found an artifact at level 1? Plot hook! Spend the rest of the campaign trying to figure out either how to safely hold on to the darn thing, find a safer set of hands for it to fall into, or find some way to destroy it.

... Or just ignore that one roll result if it would unintentionally derail your campaign. Seriously, it's written right at the beginning that these items are all optional, and players are not entitled to them.

Bingo, dig it.

10. Originally Posted by cmbarona
... Or just ignore that one roll result if it would unintentionally derail your campaign. Seriously, it's written right at the beginning that these items are all optional, and players are not entitled to them.
The ability to ignore bad rules doesn't make them good.