#### FireLance

##### Hero

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.

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.

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.)

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]

[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]

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