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Sometimes when designing a prestige class for a spellcaster, you run into the problem where if you advance its spellcasting ability in addition to other special abilities the class gets, it's too powerful. One option is to grant +1 spellcasting every other level. Unfortunately, that makes the prestige class much less desireable because advancing spellcasting at every level is part of the fun of "leveling up" a character, and not getting to advance your spells for a level sucks. :(
As an alternative, I suggested a "fractional spellcasting progression," which would allow you to grant a partial increase to spellcasting and still give cool special abilities without overpowering the class or forcing the character to wait for every other level to advance spellcasting. How this works is you insert half-levels into the wizard spell progression chart, so instead of 1, 2, 3, the rows are 1, 1 1/2, 2, 2 1/2, and so on. Then you can have a prestige class that grants "+1/2 level of spellcasting in an existing class."
These modified spells per day tables and spells known table are open game content as defined by the Open
To properly balance this sort of progression, you have to do some weird things with the gaining of spell slots. For example, the only difference between a wiz4's spellcasting and a wiz5's spellcasting is the one 3rd-level slot that the viz5 has and the wiz4 doesn't. What do you give the wiz4 that advances to wiz4.5 (wiz4-and-a-half)? Well, since you can always use higher-level slots to prepare lower-level spells, in a way that 3rd-level spell slot the wiz5 gets is really a 2nd-level spell slot that can do a little bit more than a normal 2nd-level spell slot. So, what we do is give the wiz4.5 an extra 2nd-level slot ... which, upon reaching wiz5, magically turns into a 3rd-level slot. This means you're going to see weird places on the table where a character's spells per day for that spell level goes up one level and down another; that's okay, they're not actually losing anything.
Finally, you get some weirdness in the last few levels of the class. If you look at wiz18-wiz20 in the Player's Handbook, you see that the spell progression for 8th and 9th-level spells doesn't follow the pattern established in the other spell levels. That's because at wiz19 you would normally get a 10th-level spell slot (and another at wiz20), but because there are no 10th-level spell slots (not counting epic-level rules), the wizard would be hosed out of some extra spell slots if you exactly followed the pattern, so the PH gives them extra 9th-level spell slots instead. Now because of this distortion in the PH pattern, you're going to get some distortion in the fractional spellcasting progression pattern as well. Again, that's okay, they're not actually losing anything.
As with all things D&D, you round fractions down, so if you're a wiz9.5 casting a fireball, your caster level is effectively 9, likewise if you're trying to dispel something with dispel magic.
I'll get around to doing this for the other spellcasting classes later, and maybe even do a 1/3 level progression, which I know is going to be a real pain.
A thought just hit me. NPC classes are weaker than PC classes. Perhaps a 1/2 spellcaster level progression added to them would make them appropriate for PCs. Thus, a cleric that wanted a little more martial ability at the expense of some spell progression could multiclass as a warrior with +1/2 spellcaster level, or a sorcerer who wanted to be more sage-like could multiclass as an expert with +1/2 spellcaster level. Obviously this wouldn't work for the adept, but I think it would work fine for aristocrats, commoners, experts, and warriors. Feel free to post on my boards with comments on this idea.
In response to several emails over the past couple of months, I felt I should post some clarifications about certain things.
Question: Why not instead set up the table to give the wiz 4.5 (for example) a 0 as their 3rd-level slot, so that a wizard with a bonus spell from Int would get a 3rd-level spell at class level 4.5?
Answer: For two reasons. (1) It lets someone have access to spells of a higher level before the game expects them to. That can throw the balance out of whack for some encounters (for example, an encounter for level 4 characters that expects them to not have access to the fly spell yet. Not a super big issue, but still worthy of noting. (2) Doing it that way means that a wizard who doesn't have a bonus 3rd-level spell gains nothing for going from level 4 to level 4.5. :( That defeats the purpose of providing fractional spellcasting at all (you might as well give the character +1 level every other prestige level since they wouldn't be getting anything every other level anyway).
Question: What about a wizard's 2 free spells per level she adds to her spellbook? Should she get 1 free spell at each half-level?
Answer: Sounds like a perfect solution to me. :)
Question: What if a wizard 9/prestige 1 (effective wizard level 9.5) decides to take 1 level in wizard instead of the prestige class (probably because she wants that bonus feat at wiz10)? Would she end up a wizard 10/prestige 1 (effective wizard level 10.5)?