Spells Known Rule of Thumb?

[Vanye]

My rule of thumb is that an NPC wizard has (Spells per day) x2 in his spellbook, in addition to the starting spells that a wizard gets (3 + Int).

 

[Old Drew Id]

I crunched the math on this, based on NPC starting wealth and the cost to scribe spells into the spellbook, and this is what I came up with:

From the RAW:
A wizard can also add a spell to her book whenever she encounters one 
on a magic scroll or in another wizard's spellbook. 

In most cases, wizards charge a fee for the privilege of copying spells 
from their spellbooks. This fee is usually equal to the spell's level x 50 gp.

A spell takes up one page of the spellbook per spell level. Even a 0-level
 spell (cantrip) takes one page. Materials for writing the spell cost 
100 gp per page.

Also, starting NPC wealth is listed in the DMG and NPC's generally do not spend more than 1/3 of their starting wealth on a single item. That gives you how much money each NPC can spend on spells beyond what they get for free.

So, assuming the wizard goes with scrolls or borrowed books at each level depending on what is most economical, here is the cost for each "purchased" spell:

Spell Lvl  Cost to Scribe (including source)
1	   125
2	   300
3	   450
4	   600
5	   750
6	   900
7	   1050
8	   1200
9	   1350

Assuming the NPC spends no more than 1/3 of his starting wealth on purchased spells, his book of purchased spells will have the following cost and will probably contain the following spells of each level.

LVL	   NPC Starting Wealth		Book Cost	9th	8th	7th	6th	5th	4th	3rd	2nd	1st
1st:		   900			  250  										2  
2nd:		  2000			  625  										5  
3rd:		  2500			  625  									0	5  
4th:		  3300			  925  									1	5  
5th:		  4300			 1225 									2	5  
6th:		  5600			 1675 								1	2	5  
7th:		  7200			 2125 								2	2	5  
8th:		  9400			 3025 							1	2	3	5  
9th:		 12000			 3925 							2	2	4	5  
10th:		 16000			 5125 						1	2	3	4	5  
11th:		 21000			 6775 					1	2	2	3	4	5  
12th:		 27000			 8725 					2	2	3	4	4	5  
13th:		 35000			11125				1	2	3	4	4	4	5  
14th:		 45000			15000				3	3	4	4	4	4	6  
15th:		 59000			19650			2	3	4	4	5	5	5	6  
16th:		 77000			25650			3	4	5	6	6	6	6	6  
17th:		100000			33300		4	4	5	5	6	6	6	6	6  
18th:		130000			43125		6	6	6	6	7	7	7	8	9  
19th:		170000			56450		8	8	8	8	9	9	9	10	10 
20th:		220000			73050		10	11	11	11	11	11	11	12	12

NOTE #1: This assumes to a certain extent that the NPC is going for variety in their spells and not always on just the most powerful spells they can cast. This seems reasonable, because it would not make sense for a wizard to spend too much money on spells for which they do not have enough slots to memorize. In addition, it would be likely that lower level spells are easier to find, and therefore more likely to be written into the spellbook. Finally, I wanted the chart to show a cumulative effect, so even though a starting 5th level wizard could purchase 3rd level spells, the only way that would be possible is if the wizard did not buy as many spells at earlier levels, which would seem irrational. At later levels the starting GP grows faster and this is not an issue.

NOTE #2: The above chart does not include the spells that the wizard learns for free at each level. To include those as well, the TOTAL number of spells in the NPC wizard's book(s) is below:

Lvl	9th	8th	7th	6th	5th	4th	3rd	2nd	1st
1st:									5
2nd:									10
3rd:								2	10
4th:								5	10
5th:							2	6	10
6th:							5	6	10
7th:						2	6	6	10
8th:						5	6	7	10
9th:					2	6	6	8	10
10th:					5	6	7	8	10
11th:				3	6	6	7	8	10
12th:				6	6	7	8	8	10
13th:			3	6	7	8	8	8	10
14th:			7	7	8	8	8	8	11
15th:		4	7	8	8	9	9	9	11
16th:		7	8	9	10	10	10	10	11
17th:	6	8	9	9	10	10	10	10	11
18th:	10	10	10	10	11	11	11	12	14
19th:	12	12	12	12	13	13	13	14	15
20th:	14	15	15	15	15	15	15	16	17

NOTE #3: For each point of Intelligence bonus the wizard has, the spellbook also holds one additional 1st-level spell.

NOTE #4: They start out knowing all 10 cantrips, which takes up 10 pages in the book.

NOTE #5: A spell book is said to contain only 100 pages, so the wizard would need a second book at level 10, a third at level 14, a fourth at level 16, a fifth at level 17, a sixth at level 19, and a seventh spell book at level 20.

SUMMARY:
This is an interesting result, and not really what I would have expected. A mid- to high-level NPC has about 1/3 of the wealth of a PC, and can only spend 1/3 of their wealth on their spellbook, but even with that limitation, they can still have an extremely full and varied spellbook.

 

[Remathilis]

I crunched the math on this, based on NPC starting wealth and the cost to scribe spells into the spellbook, and this is what I came up with:

SUMMARY:
This is an interesting result, and not really what I would have expected. A mid- to high-level NPC has about 1/3 of the wealth of a PC, and can only spend 1/3 of their wealth on their spellbook, but even with that limitation, they can still have an extremely full and varied spellbook.

THAT IS ABSOLUTELY AMAZING! My hat goes off to you.

 

[Patryn of Elvenshae]

NOTE #5: A spell book is said to contain only 100 pages, so the wizard would finally need a second book at level 18 (109 pages.)

They'd need one a lot sooner than that; each spell takes up [Spell Level] pages.

 

[dren]

As per their intelligence number, then with reduced numbers for each additional spell step. A wizard of tenth level with 18 int, will have 18 1st level, 15 - 2nd, 10 - 3rd level, 5 - 4th level...or something along those lines. Clerics are hardly limited and sorcerers, well the whole point of them is their limited selection, so I try to go the middle route with Wizards, ymmv

 

[Mark CMG]

Might want to factor in that half the time that they are exposed to another wizard's spellbook, that wizard might need one of their spells and simply trade for it. Barring that, or including that and more, even if wizards were so mercenary as to always charge, one might have to account for the selling of spells at later levels to offset the cost of purchasing new ones. Just a little more complexity into the mix, as long as others are going there.

 

[Whizbang Dustyboots]

If there's a recurring group of casters, I give them a default list of spells that everyone in that group (Green Mountain Kobolds, the Church of Lothian, etc.) will have access to. For NPCs whose individuality is important, I tweak them from there.

 

[Remathilis]

They'd need one a lot sooner than that; each spell takes up [Spell Level] pages.

So a 20th level wizard in Dre Id's math needs 6 and 8/10ths spellbooks to complete his library.

0 10
1st 17
2nd 32
3rd 45
4th 60
5th 75
6th 90
7th 105
8th 120
9th 126

680 pages, 100/book = 6.8 books. Not a bad library, but not exactly portable...

 

[Destil]

I crunched the math on this, based on NPC starting wealth and the cost to scribe spells into the spellbook, and this is what I came up with:

Yoink, stolen. This is great! Thank you.

 

[dog45]

They'd need one a lot sooner than that; each spell takes up [Spell Level] pages.

Any mid to high level NPC Wizard worth his salt should have a BBB instead of a regular spellbook.