How much do the bonus spells from a high INT/WIS/CHA matter?

[Unbeliever]

Why are they more valuable to Specialists than non-specialists? 

Double the focus, double the fun?

Because the number of normal slots they have are less than a non-focused specialist. So more normal slots give you better versatility.

I guess I would have thought about it differently.  If I have only very few slots of X level, then the marginal benefit 1 more slot is really valuable.  If, for example, I've only got a single 4th level slot, then having a high enough stat to get a second one is a big boon, it doubles the amount of Solid Fogs or whatever I can cast.   If, however, I've got a ton of slots anyway, to the point where I'm unlikely to run out of sweet awesome spells to cast, then the bonus ones aren't all that valuable to me. 

I view specialists as more quickly falling into the second camp.  Sure, you lose out on versatility, but usually there are enough awesome spells in your specialty school that you're still casting great stuff each round, even if you don't always have the exact right tool for the job (though some specialists can swing that, too).  If there weren't enough great spells of a school to fill up a lot of your slots, you wouldn't have bothered specializing in it in the first place -- hence the quantity of Conjurers and Transmuters at gaming table and the dearth of Enchanters. 

[Redeemer of Ogar]

I view specialists as more quickly falling into the second camp.  Sure, you lose out on versatility, but usually there are enough awesome spells in your specialty school that you're still casting great stuff each round, even if you don't always have the exact right tool for the job (though some specialists can swing that, too).  If there weren't enough great spells of a school to fill up a lot of your slots, you wouldn't have bothered specializing in it in the first place -- hence the quantity of Conjurers and Transmuters at gaming table and the dearth of Enchanters. 

Specialists, yes. I said FOCUSED specialists, who lose one general spell to gain 2 extra specialty spells.  What that means in practice, is once you run out of bonus spells, your general slots start coming a level late. Where an 11th Wiz Specialist would have 1 6th gen and 1 6th conj, your 11th Focused Specialist will have NO 6th gen, but 3 6th conj.  That is one of the reasons you hear people saying focussed specialist is better for low-mid campaigns. My GM is being stingy with stat items higher than +2, and I'm going to be vaguely annoyed if I can't nudge my INT to 24 by the time I get to 13...

[Hand_of_Vecna]

I would have to say those slots are less valuable, otherwise they wouldn't be focused specialists.

[rasmuswagner]

True. The problem is that Spellcasting Prodigy only treats your casting stat as 2 higher for the sake of calculating bonus spells. That's at most a 1st level and a 4th level spell, or a 2nd level and a 5th level spell, etc. Those bonus slots don't travel upwards with level, only if you manage to boost your casting stat. So if you have Int 18 and Spellcasting Prodigy, you'll rejoice when you reach Wizard 9, because Spellcasting Prodigy immediately grants a bonus spell/day from your current highest level. As you level up, though, that bonus spell/day stays locked in 5th level, so it becomes much less exciting once 6th and 7th level spells come online.

But boosting your casting stat is the expected standard, not the anomaly. Assuming an 18 Int at level 9, getting to Int 22 by level 13 is not at all unreasonable. Lo and behold, Spellcasting Prodigy once again gives you a bonus spell slot of your highest level.

[awaken DM golem]

Bookending the possibilities ... in the range of 4th level spells:



Wilder gets 1 Known with Max (or recharge!) Uses.

Sorc gets 4 Known with 6 Uses.
Wiz gets 6+ Known with 4 Uses.

Genie gives Max "known" via Limited Wish, but with only 1 Use.



The boards rather clearly come down on the side of Wiz over Sorc.
The exact tipping point between Wiz and Genie, is rather unexplored.

Bonus Slots as compared to More Options, moves a Sorc toward a Wilder.
imho