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There's been some concern by the Sorcerer loving crowd that Wizard spell flexibility, especially in the context of the Quick Preparation feat, is unfair given equal spell slots and spells known/prepared for each class. A sorcerer can learn 4 spells per level, plus some flexible heightening, a Wizard gets four (5 for a specialist) free spells per spell level 2-9 and has to pay for the rest.
How many more can they realistically buy, and how wide a toolset can they have for their broader flexibility?
Here's a comparison of the cost to scribe a new spell in your spellbook (pg 146) to the total currency a character is expected to earn (pg 347) over the two character levels where that is your highest spell level. Format is spell level, spell learning/scribing cost, expected earnings over two levels, and percentage of those earnings that single spell of your max level costs. For 9th I've only included two levels, 17th and 18th, for 10th I included 19th and 20th, even though that's frontloading when you get 10th level spells
1 - 2 gp - 24 gp - 8.3%
2 - 6 gp - 80 gp - 7.5%
3 - 16 gp - 205 gp - 7.8%
4 - 36 gp - 430 gp - 8.4%
5 - 70 gp - 850 gp - 8.2%
6 - 140 gp - 1700 gp - 8.2%
7 - 303 gp - 3750 gp - 8.1%
8 - 650 gp - 8250 gp - 7.9%
9 - 1500 gp - 19500 gp - 7.7%
10 - 7000 gp - 45000 gp - 15.6%
If we assume a Wizard is willing to spend around 25% of his currency (which is also going to extra magic items and consumables) on spell book improvements, and maximizing his highest level spells with that budget, we can expect him to buy 3 per spell level (except for 10th), for a total of around 7 (8 for specialists) spells of levels 2-9, and 4 total for 10th level spells.
Of course, at higher levels he can also spend a smaller relative percentage to fill out some of those lower levels. If you spent up to 10% of your available (dual character level wealth) to buy more spells 2 levels below your maximum spell level you'd add this many additional spells:
1 - 10
2 - 7
3 - 5
4 - 4
5 - 5
6 - 5
7 - 6
8 - 6
So as an example, a 10th level universalist Wizard about to reach 11th level and spending about 30-35% of his income on spell expansion would have this many spells in his book:
1 - 25
2 - 14
3 - 12
4 - 7
5 - 7
That's honestly better than I thought it would be, but it's not completely dominant at higher levels, and I'm not sure a Wizard will actually want to spend this much on spell acquisition costs. Fewer high level spells might be more reasonable as a tradeoff between spell flexibility and available magic equipment.
In any case, I thought this would help the debate going forward.
The second group of numbers, spending 10% of your coin wealth on spells 2 levels below your max, should match up pretty well with someone archetyping into Wizard and wondering how cheaply they can fill out their spell book. Pretty cheaply, given that you can only only prepare 1-2 of those anyway.
Bards with a spellbook probably only want to buy one or at most two high level spells.
We also have to consider which levels the most utility spells are found. I haven't gone through the list to much yet but there seem to be larger cluster of situational utility in slots 1-3 than anywhere else.
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I'm not sure I really like this analysis.
We have to keep in mind that with heightening of spells, most spells are now of a lower level.
I really repeat part of the analysis I made previously here:
Here is the number of arcana spell for each level: (XH means that X number of spells have heightened effect).
1st level: 35 common (20H), 1 uncommon (1H)
2nd level: 35 common (22H)
3rd level: 23 common (8H), 3 uncommon (1H)
4th level: 24 common (13H), 7 uncommon (2H)
5th level: 18 common (10H), 7 uncommon (2H)
6th level: 16 common (9H), 3 uncommon (2H)
7th level: 8 common (5H), 7 uncommon (2H)
8th level: 11 common (3H), 3 uncommon (1H),1 rare
9th level: 7 common(2H), 2 uncommon (1H)
10th level: 3 uncommon
Without having to pay to learn new spells, Wizards will naturally learn half of the 7th and 9th level spells, a third of the 8th and 1st level spells and a quarter of the 6th level spells.
That means most of the spell you want to learn will be of the 2nd to 4th spell levels. (where most spells that can be heightened are)
Lots of those spells will be quite useful since most heightenable spells are of level 1 and 2.
Trying to learn all of your highest level spell is a very bad strategy and investment, the wizard should always focus on investing into lower level spells.
That means that at lower level, a Wizard and sorcerer are in fact really close to one another. It's only after level 7 that I think we will begin to see the wizard shine over the sorcerer, since he will finally have enough slots and spell levels to make his utility tool kit work. And the higher level the wizard will be, the better his toolkit will become.
Quick Preparation doesn't shine when switching your highest level spell for another. It shines when you use all of your lower level spells and their heightened version in order to solve your issues. And most of the utility spell are of lower levels.
One issue holding the Wizard's spell book (and Quick Preparation) in check is that learning your highest level of spells has a 30-35% failure rate across your entire career, and if you fail you can't try again until you gain a level unless you pay a skill feat tax (Magical Shorthand). One out of three spells a Wizard wants at his peak power level he can't have.
Sorcerers will have the same problem learning uncommon/rare spells, but better because it won't come up very often, but worse because they have an attribute handicap on their magic skill and may not be investing as much in a boosting item.