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.
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.
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.
No.It is built into the math of the game and it does assume the players will have this stuff.
I think the simple explanation is that magical items of varying rarity could be found over the course of a tier. In the 5-10 tier, for example, the PCs could find common, uncommon and rare consumable items. Hence, if you line up all the expected magic items by rarity and distribute them evenly, the rarity of the items will not correspond exactly to the tiers.This feels... off somehow.
I would go with the tiers actually used by the game instead of inventing new thresholds.
That is, replacing "every level from 1 to 5" and "every level from 6 to 10" with "every level from 1 to 4" and "every level from 5 to 10". A detail? Perhaps, but since you're doing statistical analysis I would expect you to adhere to the level bands actually used by your source data
There are, of course, many ways to inject more randomness into the distribution of magic items (including actually generating them as suggested by the DMG ), but the intent of this exercise was to establish what magic items a "typical" PC could expect to get, and at what level, similar to the wealth by level guidelines of 3e and 4e. And like those guidelines, individual groups could choose to follow them or ignore them as they wish.For instance, instead of saying "1 legendary permanent item at level 19" I would go with something like...:
each player gets a 25% cumulative chance of getting "their" legendary permanent item from level 17, meaning that if they didn't get it by the time they reach level 20, the chance has reached 100% and they will get it at that level.
I understand that at level 19 the chance is greater of having gotten one, than not getting one, and that this is why you chose level 19. But it invents a new threshold, and means that level 17 no longer is the moment where you can start hoping for your item.