Post/Author/DateTime	Post
#1 pitiless_interfector Jun 04, 2007 15:04:41	Has anyone ever dissected Vancian spellcasting in depth? If not, here are some observations of mine that I'll chuck out there to get the conversation going: Relative value of spell slots: The Races of the Dragon splatbook features Versatile Spellcaster; a feat that lets a spontaneous caster spend two spell slots of one level to use a spell he knows from a level one higher than the slots expended; i.e., spend two 1st-level slots to cast scorching ray. While it only discusses the prospect in these concrete, limited terms, I'm wondering if it applies in a broader context; i.e., 4 1st-level slots equals a 3rd-level slot, etc. If it does, then each spell level can be broken down by its Cantrip Equivalent Value, or how many 0-level spell slots it would take to cast a spell of that level: 0=1 1=2 2=4 3=8 4=16 5=32 6=64 7=128 8=256 9=512 Seems pretty simple, doesn't it? But, take a look at this: 1+2+4+8+16+32+64+128+256=511 Or, in other words, 1 (cantrip) + 2 (1st) + 4 (2nd) + 8 (3rd) + 16 (4th) + 32 (5th) + 64 (6th) + 128 (7th) + 256 (8th) = 512 (9th) - 1 (cantrip) So, the value of a given spell level is the most infinitesimal fraction higher than the value of all lower spell levels put together. This means that the power of a caster's highest-level abilities doubles every two levels; the same way that two monsters have an EL equal to one monster's EL + 2. Now that we have an absolute value for spell slots, let's compare the various core spellcasting classes and see what we find: Level: Sorcerer total CEV | Wizard total CEV 1: 11 | 5 2: 14 | 8 3: 16 | 12 4: 30 | 18 5: 34 | 26 6: 62 | 38 7: 74 | 56 8: 130 | 80 9: 154 | 116 10: 266 | 164 11: 314 | 236 12: 538 | 332 13: 634 | 476 14: 1082 | 668 15: 1274 | 956 16: 2170 | 1340 17: 2554 | 1916 18: 4346 | 2684 19: 5114 | 3324 20: 6138 | 4092 As you can see, at the beginning of the game the sorcerer has 2.2 times the CEV of the wizard. This becomes 1.75 that of the wizard at 2nd level. From then on, for the majority of the table the sorcerer alternates between 1.33 and 1.66 the CEV of the wizard, with the range being closer to 1.33 when the wizard gains access to a new spell level (at odds) and 1.66 when the sorcerer gains access to a new spell level (at evens). This pattern is exact (i.e., ratios 1.3333333 and 1.6666666) at 3rd and 4th, but afterwards the ratio is always slightly less. The closest they get to ideal after that is at 17th level, when the sorcer CEV / the wizard CEV equals 1.332985386221294. The pattern breaks, though at 19th level (SCEV/WCEV=1.5385078221901324), and at 20th level, evens out perfectly, with SCEV/WCEV=1.5. The sorcerer's CEV increases by approximately x1.2 at all odd levels and at 2nd and 20th level. At others, it increases by approximately x1.8. With the wizard, it increases by approximately x1.44 every level, except at early levels, when it sometimes equals x1.6 or x1.5. Aside from spell slots, one other crucial resource are a spellcaster's actions. Two ways to examine these are by metamagic feats such as Quicken spell, and the arcane fusion spells from Complete Mage. Apparently, a 1st-level spell and a 4th level spell (both with casting times of 1 standard action) cast as a single standard action is equivalent to a 5th level spell, and a 4th level spell and a 7th level spell are equivalent to an 8th level spell. So, a spell of level X and a spell of level X+3 are equal to a spell of level X+4. One notices that the CEV of 2X+3 is always a multiple of 9 (0=1, 3=8, 1+8=9, 1=2, 4=16, 2+16=18, etc.). Of course, this only applies to spells with a casting time of one standard action. What of others? To model those, the best tool is the Rapid Spell metamagic feat. Since a full-round casting time is modeled by a standard action in two consecutive rounds, it would be reasonable to assume that halving the cost in actions would require recompense in the form of doubling the CEV, and this is true: A 3rd and 6th level spell both with casting times of 1 full round are equal in CEV to a 4th and a 7th level spell with a casting time of 1 standard action. Thus, the 3rd and 6th together would require 4 rounds to cast. With Rapid Spell, the CEV is doubled and the time is reduced to 2 rounds. As the 3rd and 6th are equivalent to a 4th and a 7th with a standard casting time, and the 4th and 7th as a single action are equivalent to an 8th as per arcane fusion, it would seem that 4 round's worth of casting in 1 round's time is equivalent to a quadrupling of the total cost as measured by its CEV. Of course, my arguments are based on several assumptions (particularly the last ones on relative value of actions). First of all, metamagic feats are a crude tool for approximation, as the mere act of using them implies an expenditure of money or a feat slot (even more so with sorcerers), and thus they are independent of a simple change to a spell's variables. While the Vancian system is sufficiently stratified to iron out small errors in computation, a system based on CEV would be forced to take into account even the tiniest variables, even those that are so small the current system glosses over them. Which is why I have submitted my argument here, so it may be properly reviewed and discussed.
#2 Kevin_Andrew_Murphy Jun 23, 2007 10:28:39	So basically what you're arguing is that the Sorcerer, with the addition of a single Feat, can turn all their various spell levels into one ginormous spellpool from which to pick and choose, paying instead of in spell levels in CEV? This sounds reasonable, though I'd certainly set a cap where the sorcerer would not be allowed to spend more than a 9th level spell (512 CEV) for any one spell after the various modifications of metamagic feats. Here's an additional question: Would Wizards with access to a PrC with a spellpool--for example, Mages of the Arcane Order or Guild Wizards of Waterdeep--be able to swap spells in the same fashion, presumably after having bought some equivalent Feat? The CEV math seems perfectly applicable to a spellpool.
#3 pitiless_interfector Jun 26, 2007 20:33:08	So basically what you're arguing is that the Sorcerer, with the addition of a single Feat, can turn all their various spell levels into one ginormous spellpool from which to pick and choose, paying instead of in spell levels in CEV? This sounds reasonable, though I'd certainly set a cap where the sorcerer would not be allowed to spend more than a 9th level spell (512 CEV) for any one spell after the various modifications of metamagic feats. Here's an additional question: Would Wizards with access to a PrC with a spellpool--for example, Mages of the Arcane Order or Guild Wizards of Waterdeep--be able to swap spells in the same fashion, presumably after having bought some equivalent Feat? The CEV math seems perfectly applicable to a spellpool. The issue here is that the spell point system already addresses (or tries to address) these complaints. This is more of a design aid; it allows you to measure the power of a creature or spell by comparing it to a set value. It's too complicated [too many big numbers] to be used to its fullest potential in-game.