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Am I reading these rules right? There seem to be some strange inconsistencies in the benefits some prestige classes grant to the base spellcasting class. Here are some examples, all from the 3.5 DM's Guide (although the inconsistencies continue in other rulebooks).

Archmage (page 178) buffs spells per day and spells known, but doesn't mention caster level:

When a new archmage level is gained, the character gains new spells per day (and spells known, if applicable) as if he had also gained a level in whatever arcane spellcasting class in which he could cast 7th-level spells before he added the prestige class level. He does not, however, gain any other benefit a character of that class would have gained (bonus metamagic or item creation feats, and so on).

Eldritch Knight (page 188) buffs spells per day and caster level but doesn't mention spells known:

From 2nd level on, when a new eldritch knight level is gained, the character gains new spells per day as if she had also gained a level in whatever arcane spellcasting class she belonged to before she added the prestige class. She does not, however, gain any other benefit a character of that class would have gained (bonus metamagic or item creation feats, bard or assassin abilities, and so on). This essentially means that she adds the level of eldritch knight to the level of whatever other arcane spellcasting class the character has, then determines spells per day and caster level accordingly.

Loremaster (page 191) buffs all 3 -- spells per day, known, and caster level:

A loremaster continues training in magic as well as her field of research. Thus, when a new loremaster level is gained, the character gains new spells per day (and spells known, if applicable) as if she had also gained a level in a spellcasting class she belonged to before she added the prestige class. She does not, however, gain any other benefit a character of that class would have gained (improved chance of controlling or rebuking undead, metamagic or item creation feats, and so on). This essentially means that she adds the level of loremaster to the level of some other spellcasting class the character has, then determines spells per day, spells known, and caster level accordingly.

The possibility of prestige classes that buff all 3 is especially odd in the context of Sorcerers; I see no reason to continue leveling Sorcerer once you qualify for a prestige class. A Sorcerer 10/Loremaster 10 character gets the same spells per day, known, caster level, HD, base attack bonus, and saves (actually, slightly better Will) as a Sorcerer 20, in addition to the Loremaster class features. (By contrast, Wizards get bonus feats, which they'd give up by pursuing Loremaster.)

Am I misunderstanding the rules somehow?

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You are reading it correctly, but no one does—or should—rule things that way. Furthermore, it is extremely unlikely that the authors and editors at Wizards of the Coast intended that anyone do so.

Prestige classes that advance spellcasting should advance your Spells class feature, period. Caster level, spells prepared, and spells known, as appropriate. Having a stagnant caster level while advancing spells per day is simply nonsense, that causes all manner of inconsistencies within the system and is actually potentially an avenue for abuse. And having a prestige class that spontaneous spellcasters can enter and benefit from, but they don’t learn new spells, is just an incredible shafting of classes that are already worse off.

Furthermore, it’s pretty obvious that authors routinely filled in the spellcasting feature of prestige classes by copy-and-paste followed by editing the class name as appropriate, with the occasional need to note that the prestige class fails to progress spellcasting at some levels. The failure to advance spells known—or worse, caster level—would be a major aspect of a class that should and would be given due attention—and it is not, in any case. None of these prestige classes note that this is a weakness of the class, not even in the sections of their write-ups dedicated to discussing their pros and cons. This is, quite simply, a failure of editing, and nothing more.

The possibility of prestige classes that buff all 3 is especially odd in the context of Sorcerers; I see no reason to continue leveling Sorcerer once you qualify for a prestige class. A Sorcerer 10/Loremaster 10 character gets the same spells per day, known, caster level, HD, base attack bonus, and saves (actually, slightly better Will) as a Sorcerer 20, in addition to the Loremaster class features. (By contrast, Wizards get bonus feats, which they'd give up by pursuing Loremaster.)

This is mostly true—but it’s a bigger indictment of the sorcerer class than it is of the loremaster. Technically, loremaster does not progress a sorcerer’s familiar, so that is one thing the sorcerer gives up, but that’s minor in the extreme for most sorcerers, and otherwise you are completely correct, loremaster levels are simply flat-out better for sorcerers than sorcerer levels are. Clerics are in a similar boat—prestige classes rarely progress turn undead (though some do), and otherwise they have no class features aside from their spellcasting (some domains depend on cleric levels, but a cleric planning on a prestige class can easily just avoid those). And wizards aren’t far off—bonus feats are nice, but one feat every five levels isn’t terribly impressive; almost any prestige class is going to do better than that. This leads to the general maxim that spellcasters “should” take prestige classes. (Druids, notably, have several separate class features that prestige classes usually miss out on, and so are an exception to this rule.)

This is primarily an issue with the extremely bare “special features” lists of spellcasters, at least in a game where prestige classes exist and can advance the caster’s spellcasting. It’s not hard to do better than “nothing,” which is an accurate description of the cleric and sorcerer progressions, and nearly so for the wizard.

But there is one other thing to consider: despite its lack of class features, in the core game (PHB+DMG), a sorcerer is best off as a single-classed 20th-level sorcerer. Why? Because the prerequisites for all DMG prestige classes are miserable for sorcerers. It is hard to find seven core divinations worth learning as a sorcerer. And with only Knowledge (arcana) in-class, getting two Knowledge skills to 10 ranks is brutal—you can’t do it until 17th level, so you only get to take 3 levels of loremaster anyway. And while metamagic feats are nice for a sorcerer—item-creation feats largely aren’t due to the spell requirements on items—three feats is a lot, especially with no bonus feats. Archmage is better than loremaster—the spell requirements are nicer and the class features are better—but it still requires three (poor) feats, and at any rate it’s only available at very high levels. And every other DMG prestige class forces a sorcerer to miss out on a level of spellcasting, and is therefore garbage.

So prerequisites are often a major consideration for how prestige classes that would otherwise be pure upgrade. There is a lot of opportunity to get “something for nothing” in 3.5e, especially with more supplements, but you have to pay attention and consider your cost–benefit analysis. Importantly, there are almost zero prestige classes in the game that are worth missing out on even a single level of spellcasting—“full” up-to-9th spellcasting is just that good.

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    \$\begingroup\$ Once again, a player forgets that Wizard levels progress their familiars. Those poor rats! They've suffered enough! \$\endgroup\$ – J. Mini Sep 6 at 20:45

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