SPR: Quantification of the "Theurge-style" PrCls

[Dannyalcatraz]

In several threads here on ENWorld, I've expressed my dislike of the Mystic Theurge-style casting PrCls, but everything up to this point has been opinion or "feel." Until yesterday, I hadn't hit upon a way to quantify my reasons.

The problem is that some spells in a given level are more or less powerful than others of the same level, or have effects that are not measured in hard & fast numbers for comparison. Then there is the question of class features.

So, we need to find a way to find a common basis for comparison across all spells. The closest we come is the Heritage Feats, several of which have assigned a value of 2D6/spell level to all arcane spell slots. IOW, a 1st level spell is worth 2d6 damage. A 3rd level spell is worth 6d6 damage. Etc.

If we then apply this value to each spell a PC of a given level can cast, we find out how many d6 of damage that PC can do in a 24hr period- IOW, what happens if he "goes Nova." Lets call this total his Spell Power Rating, or SPR. Obviously, its not a perfect metric- all of the Heritage feats that grant this type of ability are Area Effect attacks, and we have no way to calculate how many targets get hit, how many made their saves, etc. This is, thus, just a rough baseline comparison.

Ignoring bonus spell slots gained from high characteristics, feats or magic items, we get this:

Wiz20: SPR = 360d6; Avg Nova dmg = 1260hp; Max Nova dmg = 2160hp.

SpecWiz20: SPR = 450d6; Avg Nova dmg = 1575hp; Max Nova dmg = 2700hp.

Sorc20: SPR = 540d6; Avg Nova dmg =1890hp; Max Nova dmg = 3240hp

The "worst case scenario" arcane caster combo
Sorc5/FocSpecWiz5/Ultimate Magus10: SPR = 714d6; Avg Nova dmg =2499hp; Max Nova dmg = 4284hp

Thus we see that the Sorc5/FocSpecWiz5/Ultimate Magus10 does 2x more damage on average when going Nova than a Wiz20 does, and 15% more damage than the Wiz20 maxing out. It also does 33% more damage when maxing out than its nearest competitor doing likewise.

Now, of course as stated before, the SPR does not take into account things like the overall flexibility of the Wizard who has no upper limit on spell selections and a host of bonus feats, the situational flexibility of the Sorcerer who, despite knowing fewer spells, can choose what he wants to cast in real time, or the big difference in the quality of spells as their level increases.

Sure, there are situations where you simply can't solve a problem by slinging damage at it, and that is where the higher level spells earn their keep, and why so many players (not me) bemoan the cost of multiclassing for spellcasters.

But while it isn't perfect, SPR does provide one truly quantifiable basis for comparison.

 

[green slime]

Well, that might or might not be a concern with regads to how you play your game.

But you are significantly ignoring many facts:

1) Your comparison only looks at the very peak; 20th level can hardly be said to be valid for most compaigns.

2) In any given battle, a character only has a certain number of limited actions each round, even with Quicken spell feat, metamagic rods, etc. Thus the character is stymied in the that more of his greater "SPR" is actually tied up in lower level spells, which are easier to save against, and do less damage, and require more time.

No one doubts that the major advantage of the theurges is their staying power: they have a humungous amount of spells in their arsenal. They are, however, less efficient, for the vast majority of their career. You choose to look only at the very peak, and even then, they are still lacking; they have no access to 9th level spells!

I have never had a problem with them in my game.

 

[Dannyalcatraz]

1) Your comparison only looks at the very peak; 20th level can hardly be said to be valid for most compaigns.

True, but I have only so much time.

Choose whatever level you want- the formula is simple:

SPR = A(2d6*1) + B(2d6*2) + C(2d6*3) + D(2d6*4) + E(2d6*5) + F(2d6*6) + G(2d6*7) + H(2d6*8) + I(2d6*9)

or simplified:
SPR = A(2d6) + B(4d6) + C(6d6) + D(8d6) + E(10d6) + F(12d6) + G(14d6) + H(16d6) + I(18d6)

Where the letters represent Spell slots of a given level, (Levels 1-9).

Figure out what level you want, and go from there. (Remember that unlike other MT-style classes, the UM doesn't have a uniform progression...at 1, 4, and 7, only one class gets boosted)

I'm guessing its right as the S/W/UM PC is hitting the real power boost when he first gets access to 5th level spells. (See below.)

Thus the character is stymied in the that more of his greater "SPR" is actually tied up in lower level spells, which are easier to save against, and do less damage, and require more time.

Not quite.

For the base classes, the breakdown is a nice, gently sloping curve.

Wiz20 SPR/level breakdown:
1st 8d6
2nd 16d6
3rd 24d6
4th 32d6
5th 40d6
6th 48d6
7th 56d6
8th 64d6
9th 72d6

a nice, linear progression.

Sorc5/FocSpecWiz5/Ultimate Magus10 SPR/level breakdown:
1st 24d6
2nd 48d6
3rd 72d6
4th 96d6
5th 120d6
6th 132d6
7th 126d6
8th 96d6
9th 0d6

You get a steep curve with an abrupt cliff.

At the peak, a lot of SPR- 378 is grouped not at low levels, but rather at 5-7th level spells. That's right...there is more SPR in those 3 levels than in the entirety of the Wiz 20.

You choose to look only at the very peak, and even then, they are still lacking; they have no access to 9th level spells!

I know that. Like I said, its not a perfect metric. Not all spells are created equal, even within a given level, and across levels, you can get a wildly different potential power. This metric reduces all of those potential variables down to a single, easily measured one.

If it helps, consider this as an extreme abstraction of casters each with access to the best possible spells in identical situations. Since each caster is casting the same spells, we need not consider variables within the mechanics of individual spells. The 2d6/spell level per slot is our common denominator.

But you're still talking more SPR in the S/W/UM PC's 8th level slots than in the Wiz20's 9th level slots. If you look at those 9th level spells, more of them are of the oddball variety- Mass This, Greater That, and of course, Wish. Its entirely probable that most of all results gotten from the casting of a 9th level spell could be gotten from a sufficient number of spells of 8th level.

 

[irdeggman]

I'm not sure but I think the logic here is the same one that people use when they say a warlock is overpowered.

"He can use EB all day long".

People who only look at that miss the fact that they can only do 1 EB per round.

The same logic with psionics (and sorcerers) - they only have a limited number of actions they can do at a time.

A high level raging barbarian with power attack using a full attack action can easily do more damage - all day long. But it is situational - he needs to be in melee and in a position where he can take advantage of his high number of attacks.

Same with MT type casters - their "advantage" is situationally based.

 

[Jhaelen]

If we then apply this value to each spell a PC of a given level can cast, we find out how many d6 of damage that PC can do in a 24hr period- IOW, what happens if he "goes Nova."

I don't quite understand this. For me 'going nova' means to use up all limited resources (in this case casting spells) in a single combat. If I cast one quarter of my available spells in each of four different encounters that's not 'going nova'.

Generally, multi-classed casters have more spells per day as single-classed characters. Since they still cast the same number of spells per round it follows that they'll be able to last through more encounters. That's the only advantage of multi-classes casters - besides the greater flexibility.

Since combats in D&D 3E tend to last only a short number of rounds, the multi-classed caster is at a distinct disadvantage regarding the potential damage output per encounter compared to a single-classed caster.

Or are you talking about something completely different?!

 

[Runestar]

And why are you using direct damage, possibly the most inefficient option available to casters?

Your dual-caster can blast all he wants. My single-classed caster is content with his array of "I-win" spells like gate and disjunction. You will notice that the best spells available to a caster (eg: grease, sleep, colour spray, web, glitterdust, stinking cloud, summon monster, haste, fog spells, evard's tentacles, teleport, shadow evoc/conj, wall of X, forcecage, maze, most 9th lv spells etc just to name a few) are actually not very reliant on caster lv (except to penetrate sr, and even then, many of them actually ignore sr altogether). And with the focused specialist variant from complete mage, I have as many slots as a sorc (and actually more at lower lvs).

Ultimately, it is when you can access the aforementioned spells which is all that really matters, and the sooner the better. And why it is generally such a bad idea to lose a spellcaster lv (or more), much less 3 to enter mystic theurge. You just won't face enough fights to justify having so many slots.

 

[green slime]

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.

3) A single classed character has easier access to supplemental spells: The example wizard is capable of scribing a few 9th level scrolls to have handy. The theurge cannot. If he wishes those, he has to pay a premium price.

4) Most spells allow saves. Casting an 8th level spell instead of 9th level spell means not only is that action that particular round doing less damage (and with a lower max caster level in your example 15th) So 15d6 instead of 20d6 for the 20th level wizard, the theurge will also suffer more opponents to make their saves (Save DC 19+Stat mod vs DC18 + Stat mod).

5) The theurge must choose which stat to concentrate on, the specialist has no such quandries.

6) the Theurge suffers greatly when you start to include Spell Resistance: In your example he is a wopping 5 levels lower! and far less likely to penetrate spell resistance for a level appropriate monster (d20+15 vs d20+20). Against SR 30, for instance, he fails 70% of the time, versus 45%!

All of this show that counting purely "SPR" is a fallacy. Having a large number of 5th level spells available at 20th level in no way will compensate.

IMX, the theurge classes add a lot of flavour to my campaign (they are tied to specific deities and/or organisations), but they are weaker than a dedicated spellcaster in a party situation, similar to the bard: handy to have, if the principle slots have been covered. As such, I'm glad they are around.

 

[Dannyalcatraz]

Lets go with the easier questions first:

And why are you using direct damage, possibly the most inefficient option available to casters?

Because that is the "common denominator." The Heritage feats like Draconic Breath give us the metric for any arcane spellcasting slot of 2d6/spell level.

This is much easier than trying to measure the combat effectiveness of a well cast Illusion, a buff to AC and saves, the value of a movement spell, etc., especially when you can have all of that within a given level of spells. The value of such choices depend greatly upon a variety of variables.

By giving each slot a definite value, the Heritage feats remove almost all of the variables in the equation. In turn, that lets us compare apples to apples, even if the apples are inefficient.

I don't quite understand this. For me 'going nova' means to use up all limited resources (in this case casting spells) in a single combat. If I cast one quarter of my available spells in each of four different encounters that's not 'going nova'.

That's my fault- its the best terminology I could find to say "Casting all of your spells in one day." IOW, using all of your spellcaster's reserves within 24 hours.

Is there a better term or one you'd prefer?

Since combats in D&D 3E tend to last only a short number of rounds, the multi-classed caster is at a distinct disadvantage regarding the potential damage output per encounter compared to a single-classed caster.

Most of your 9th level spells are not really damage spells- many of the best of those reside in that 5-8th level range.

However, it is absolutely true that the lack of 9th level slots does prevent one from using Metamagic on some of your higher level spells that actually do damage.

You just won't face enough fights to justify having so many slots.

and

Since combats in D&D 3E tend to last only a short number of rounds, the multi-classed caster is at a distinct disadvantage regarding the potential damage output per encounter compared to a single-classed caster.

With so many slots, you can be profligate with your use of magic. Such a PC can afford to cast a load of long-lasting buff spells- boosted by whatever Metamagics he has available- and still play artillery when the actual combat rolls around.

Given the standard 4 encounters / day, the most interesting focus should then be on the 24 highest level spells available.

For Wix20, those would be 4 spells each level from 4th-9th.

For the S5/W5/UM10, those would be 11 6th level spells, 9 7th level spells, and 6 8th level spells. While lacking the 4 9th level spells isn't insignificant, the PC has 2 more 8th level spells, 5 more 7th level spells, and 7 more 6th level spells than his Wizardly compatriot in that range, and doesn't have to dip down below that. And if he does, he has 12 4th and 12 5th level spells to boot.

A single classed character has easier access to supplemental spells: The example wizard is capable of scribing a few 9th level scrolls to have handy. The theurge cannot. If he wishes those, he has to pay a premium price.

While it is true that he doesn't have access to 9th level spells at his disposal- and lets face it, that Wizard is probably at an advantage over his Sorcerous rival here too- its arguable that the UM has more access to supplemental spells. He doesn't need to rely on external devices to broaden his repetoir- as pointed out above, he has enough spell slots at any other level to play with that he has all kinds of supplemental spells at his disposal.

Most spells allow saves.

Goodman Games' Power Wizard guide (or whatever its called) points out how one can get around saves, SR, and other defenses to spellcasting. A well designed S/W/UM almost need never worry about it. He can fill his repertoir of spells with those that work in all of the workarounds mentioned in that book.

And that book only deals with the Core 3- there are other ways that have been added in the Completes.

Gotta run- Gustav evacuees need my attention- but I'll be back later.

 

[green slime]

With so many slots, you can be profligate with your use of magic. Such a PC can afford to cast a load of long-lasting buff spells- boosted by whatever Metamagics he has available- and still play artillery when the actual combat rolls around.

Not really, because this is no more of a likely problem than the high level spellcaster actually having access to wands/staves/scrolls.

For Wix20, those would be 4 spells each level from 4th-9th.

For the S5/W5/UM10, those would be 11 6th level spells, 9 7th level spells, and 6 8th level spells. While lacking the 4 9th level spells isn't insignificant, the PC has 2 more 8th level spells, 5 more 7th level spells, and 7 more 6th level spells than his Wizardly compatriot in that range, and doesn't have to dip down below that. And if he does, he has 12 4th and 12 5th level spells to boot.

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. The 20th Level specialist wizard will more likely have 28+ Int (17 starting value, +5 from leveling, +6 item), granting even more spells of all levels (including 9th). So that is 6 9th level spells per day + 6 8th level spells +6 7th level spells +6 6th level spells and easier access to 9th level scrolls. Similarily, the 20th level sorcerer will, with 28+ Cha be able to cast 7 9th level spells per day.

By comparison, the theurge given a 32 point buy:
Stat 1: 17 (13 points) +6 item +3 levelling = 26
Stat 2: 17 (13 points) +6 item +2 levelling = 25

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!
But does calculate all affects for his spells as if he were 18th respective 17th levels. Which means that he has the following spell slots available

0 9th level spells ( -6)
0 8th level spells ( -6)
3 (sorc) +1 (Cha) +2 (wiz) +1(stat) 7th level spells (+1)

How is the UM going to make up for the combine loss of 12 spells of 8th and 9th level?

The (5 Wiz /5 Cleric/10 MT) Mystic Theurge has:

5+10 = 15 for both caster types.
0 9th level spells = (-6)
2 (focwiz) 8th +1 (Int) +1 (Clr) +0! (Wis) +1 domain = -1
3 (focwiz) 7th +1 (Int) +2 (Clr) +1 (Wis) +1 domain = +1
4 (focwiz) 6th +1 (Int) +3 (Clr) +1 (Wis) +1 domain = +4

But he casts as a 15th level spell caster, and has trouble penetrating spell resistance and dispelling opponent magic.

While it is true that he doesn't have access to 9th level spells at his disposal- and lets face it, that Wizard is probably at an advantage over his Sorcerous rival here too- its arguable that the UM has more access to supplemental spells. He doesn't need to rely on external devices to broaden his repetoir- as pointed out above, he has enough spell slots at any other level to play with that he has all kinds of supplemental spells at his disposal.

I'm failing to see how those low level supplemental spells are going to replace astral spell, time stop, mordenkainen's disjunction, and gate. The only way the proposed theurge character is going to be able to access such magic, is through purchasing scrolls.

Goodman Games' Power Wizard guide (or whatever its called) points out how one can get around saves, SR, and other defenses to spellcasting. A well designed S/W/UM almost need never worry about it. He can fill his repertoir of spells with those that work in all of the workarounds mentioned in that book.

What can I say? Not IMX... but YMMV. I don't have access to that book, whatever it is called. SR is a significant factor, as are saves, especially if you are comparing, as you are, pure damage.

 

[Runestar]

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.

Likewise, for a UM, you would be better served by going wizard/beguiler/UM for the int synergy, and beguiler doesn't rely on damage spells (and neither should your wizard). Opting to ignore the realities of spellcasting in favour of convenience is just skewing whatever results you do arrive at, IMO.