SPR: Quantification of the "Theurge-style" PrCls

[green slime]

On a side note, does that UM progression seem erroneous? Unless you use the practiced spellcaster trick (and a liberal mis-reading of the progression rules for UM to allow you to stack all the spellcaster lv increases on wizard), you shouldn't end up with 8th lv spells on both sides, merely 6th at best.

Nah, its 7th, as I noted in my post above.

 

[blargney the second]

It's an interesting way to analyze things, Danny.

You're right that within a spell level, all spells can be considered essentially equal if the casters have equal access to them. However, I see two points where this breaks down:

1) The comparison of one spell level to another. A 9th level spell is worth vastly more than an 8th level spell +2d6. (FWIW, the +2d6 equates to just the increase in caster level required to cast the higher level spell. So the spell level must be adding something more than that.)

2) Unlimited access. Warlocks, reserve feats, and even some magic items turn your equation into infinity, which just ain't right.

-blarg

 

[blargney the second]

Have you read about the Chi/Ro challenge rating system? I think it actually matches up to the core mechanics of 3.5 quite nicely because it is quadratic rather than linear. Along the same lines, you could simplify the math by factoring out the 2d6 because it's a common denominator. With those in mind, here's how I'd be inclined to alter your formula: (x^2 means x-squared)

SPR = A(1^2) + B(2^2) + C(3^2) + D(4^2) + E(5^2) + F(6^2) + G(7^2) + H(8^2) + I(9^2)}

(You can multiply the result by 2d6 if you still want that in there.)

It still doesn't account for characters with unlimited access to abilities, but it does deal better with things like psionic characters who can blow their load of power points on just their highest powers.
-blarg

 

[Dannyalcatraz]

First, let me say that some seem to be treating SPR as if I'm asserting that it should be the ONLY consideration. I'm not.

(2nd, this post is going to be incomplete again- RW time pressures.)

I'm putting it forward as a single metric, just like a baseball player has a batting average, his RBI, a slugging percentage, a RISP rating, an on base percentage, WPA, WPA/LI, Clutch (and probably a few other stats I'm probably forgetting) to measure his value as an offensive force on the diamond.

SR is a significant factor, as are saves, especially if you are comparing, as you are, pure damage.

You're missing the point.

If you look at spells, some have saves, some don't, and there are 3 different kinds of save types. Some are affected by SR, some aren't. Some spells target foes, some allies, some only target you. Some spells are poorly designed and could be considered suboptimal for a given level, others are quite well designed and are arguably designated at a level lower than they should be. Sometimes there are XP costs associated with casting a spell, long casting times, unusually long durations , etc.

That is a lot of variables, making comparison of them head to head virtually impossible.

What filtering all of those spell slots through a Feat like Dragon Breath does is remove virtually all of those variables, leaving only the damage dice. All other variables drop out.

Choosing to ignore as you do, the specialist wiard having actually 5 of each level at 20th level, and the effect of the theurge having to diversify his casting Stats, as opposed to focusing in one stat.

Actually, I originally posted with the Focused Specialist, who has 6 of each spell.

And if you have a problem with diversity of stats, substitute the Beguiler class who has virtually the same progression as the Sorcerer (only losing 1 9th level spell) and still has Int as a casting stat, while remaining a spontaneous caster.

I explicitly left out bonus spells of the equation because:
1) Quality of stats will vary depending upon the method used in the character generation process. A PC with high starting scores in both casting stats would only have a difference of a couple of slots by Lvl 20, not enough to make a significant difference.

I doubted your numbers, so I double checked the Ultimate Magus as described in the Complete Mage, Please correct me if my understanding is incorrect:
The ultimate magus (5/5/10) will have the following actual caster levels:
5+9= 14!
5+8= 13!

To meet the prereqs, a PC could be Sorc1/Wiz3. The UM lets you add to the lowest one, giving us (effectively) Sorc2/Wiz3 at the first UM level. At 4th, Sorc pulls even, and at 7th, pulls ahead (since there is no "lowest" class, its player's choice). Every other level, both classes get bumped.

So its 5+10 = 15; 5 + 7 = 12

(I'm not saying I didn't miscalculate spell slots though- its easy to make mistakes when you're doing this kind of thing on your PDA.)

Don't forget:

1) The UM class has a built in "Practiced Manifester+" effect, casting arcane spells as if he had that feat for both of his classes.

2) I obviously assumed that there would be a balanced approach to taking levels. If, however, you do an unbalanced advancement, you get Sorc7/Wiz3/UM10, which gets you back up.

3) I'm not ignoring the value of an 8th level spell vs a 9th level spell. However, you also have to account that some 8th level spells are nearly as good as average 9th level spells, and some 9th level spells are probably overpriced and should be 8th level spells.

That returns us to why I went through the Feat- it takes spell quality out of the equation.

 

[Dannyalcatraz]

Another quick-strike post here:

1) Yes, I did screw up the math- twice. First, I posted my second stage analysis based on the Beguiler with an uneven progression instead of the balanced progression with the Sorc. Second, I hadn't completed that analysis so it still had the Wiz stats from the previous analysis.

CURSE YOU, CUT & PASTE!

However, in either case, the UM builds still come out ahead in SPR based simply on their sheer number of spells.

Issue of the Beguiler aside, the unbalanced progression will have 8th level spells.
(BTW, a quick question (because I really don't know the answer): the UM's caster level boost...does it stack with Practiced Spellcaster?)

The comparison of one spell level to another.

Again, there really isn't a true consistency of quality within a spell level. If you look at the way powergamers rank spells, you'd see there are spells with potentially drastic differences in effect upon the game within a level.

When you look across the levels, that variable spell quality means that a 9th level spell may not be as good as the top 8th level spells, and the worst 8th level spells may only be equivalent to one of 7th level. Or worse.

And the best 9th level spells may truly be worthy of bumping up a level.

So this metric simply uses the Heritage Feat valuation- all questions of quality are eliminated.

2) Unlimited access. Warlocks, reserve feats, and even some magic items turn your equation into infinity, which just ain't right.

Yet more reasons why SPR isn't, should never be, and was never suggested to be a sole metric.

Just to pull an item out of the stack, consider a UM with a Ring of Wizardry (4th level)- that's an additional 12 spells for an SPR boost of 48d6

(You can multiply the result by 2d6 if you still want that in there.)

I kept that 2d6 in there despite its being a common factor because it puts it in units of a particular game mechanic anyone can understand rather than just a raw number.

beguiler doesn't rely on damage spells (and neither should your wizard).

Again, you're missing the point.

How do you quantitatively compare the value of an illusion spell to a stat-draining spell to a shapechanging spell to a polymorph spell to a buff spell to a damage spell with a save to a save-or-die spell?

The answer: you can't until you find a common denominator.

The problem is that by their nature, those spells don't have a common denominator that can be expressed in numbers...until filtered through something like Dragon's Breath.

I'm not saying that a PC needs to just blast away. I'm just saying that SPR lets us look under the hood in a different and quantitative way.

Look at it this way. All programs boil down to 0 and 1s eventually, but comparing the most current version of Microsoft Office to the original Sim City on a quantitative level is impossible...except by examining program size: how many bits of info does each program use? That they use their bits differently is without question, and looking at bit size doesn't suggest that all programs should be like one or the other, it doesn't tell you which is better. It just tells you which is bigger. And a bigger program has potentially more power as well as potentially more errors.

SPR doesn't tell you what path to go down. It is an observation of the raw potential energy within the framework of a particular build.

It doesn't address any other details of a build at all- a Wizard or Sorcerer with poor spell & feat selection could be worse than useless in the face of a UM run by a top player.

The (5 Wiz /5 Cleric/10 MT)

For the record, I actually stayed away from the classic MT because WotC has not, AFAIK, supplied a Feat or ability that works for Divine spell slots the way the Heritage feats work for Arcane slots.

We can extrapolate, yes, but I leave that to others.

 

[Jack Simth]

1) Given that most fights at the level being discussed are over in three rounds or less, in any given one fight, the most spells caster is going to unleash during a battle is not expected to exceed 6, ignoring prep.

2) Given the standard 4 encounters / day, the most interesting focus should then be on the 24 highest level spells available. If you add more, you are deliberately slighting the comparisson in favour of the theurge. But this is more of a campaign specific trait, and is easily controllable by the DM.

... you have long fights for the number of spells you're throwing around.

If you're optimized enough that you're spitting out two spells per round, every round, at 20th, the majority of your battles will be over (one way or another) in one round; with a small number of them taking two rounds and a very rare three.

If you're not optimized to the point where 20th level such that you're still averaging three rounds per battle, you're likely only zapping away with one spell per round.

With my perspective, at 20th, you shouldn't be comparing the top 24 spell slots - you should be comparing the top six to twelve spell slots (especially in the case of a Sorcerer, which has can't Quicken in Core).

 

[green slime]

I realize your SPR is only one metric. But because it is so simplistic, we also need to have the other qualifiers onboard, in order to see the whole picture. This "SPR"-metric concept (albeit named differently) has been around before, right from the beginning of 3e: comparing Sorcerer vs wizard, psion vs wizard, etc.

Other metrics we need are:

Total number of spells
Total number of Low level spellslots (1st-3rd level)
Total number of Medium Level spellslots (4th-6th level)
Total number of High level spellslots (7th-9th)
Total number of Epic Level spellslots (10th level+)

Expected number of spells known (based on wealth)

Quality of Expected Primary Stat(s)
Expected Save DC
Expected Spell Resistance Penetration of =CR & CR+4

Actual casting Level (with regards to range, damage, and other spell effects).

Any restricted school access (which schools are banned/unavailable to the character).

Feats slots and any special abilities compared.

And we should compare across a wide range of character levels, in order to see the whole picture: 5th, 10th, 15th, 20th, & 25th. Alternatively 7th, 14th, and 21st.

Finally, we should compare with other viable PrC for single classed spellcasters as well: Red Wizard, Guild Wizard of Waterdeep, Loremaster, etc.

The uneven UM suffers by having only the 8th & 7th level spells from a single class, so are also going to be fewer in number than the single classed Wizard, who will gain more by dint of being a higher level. The large number of 6th level spells will hardly make up for all those lost spell slots.

 

[green slime]

... you have long fights for the number of spells you're throwing around.

If you're optimized enough that you're spitting out two spells per round, every round, at 20th, the majority of your battles will be over (one way or another) in one round; with a small number of them taking two rounds and a very rare three.

If you're not optimized to the point where 20th level such that you're still averaging three rounds per battle, you're likely only zapping away with one spell per round.

With my perspective, at 20th, you shouldn't be comparing the top 24 spell slots - you should be comparing the top six to twelve spell slots (especially in the case of a Sorcerer, which has can't Quicken in Core).

Mr Smith.... Surely you understand the concept of erring on the side of caution? By allowing the top 24, there is large room for manuever and to allow for various styles of play.

And the sorcerer has access to Quicken, surely, via the use of Metamagic Rods? I suppose there is some debate about the details of their use. But as we are talking about Beguilers and Ultimate Mages, I don't think we are restricting this discussion to core only

 

[irdeggman]

And the sorcerer has access to Quicken, surely, via the use of Metamagic Rods? I suppose there is some debate about the details of their use. But as we are talking about Beguilers and Ultimate Mages, I don't think we are restricting this discussion to core only

I could be wrong but I don't think a spontaneous caster can ever apply the quicken spell feat to their spells. If the metamagic rod descriptin specifically states otherwise then IMO it is broken - but the RAW on Quicken Spells say that it can't be applied, IIRC.


The text on applying metamagic feats to spontaneous casters is that it is always a full round action (or longer) - hence quicken does you no good at all since you can't get two spells per round that way.

 

[Runestar]

The metamagic specialist sorc variant from PHB2 lets you apply metamagic feats to spells without increasing their casting time, which would let the sorc quicken his spells.