Geeky math question re: Shadow Evocation and saves

This topic applies to 3.x and Pathfinder, so I figured I'd stick it here.

I'm playing a 9th-level illusionist who's considering tracking down Shadow Evocation. Certainly the spell is worthwhile for its flexibility (blast, wall of ice, or resilient sphere, to name a few different uses), but it occurs to me that it may actually be a better blast spell than the evocation spells, under certain circumstances.

With my feats, I've got +2 to illusion saves. Assuming that I find a fourth-level 1d6/level, reflex-half blast spell (e.g., Dragon Breath, from Pathfinder), I'd normally require a reflex save DC 20 (+6 int, +4 spell level). If I cast it under Shadow Evocation, I'd require a Will save and a Reflex save, both DC 23 (+6 int, +5 spell level, +2 illusion).

My question is, under what circumstances would victims take more damage on average from the Shadow Evocation than from the straight-up spell? That is, what would their saves have to look like such that it'd be harder to make two DC 23 saves (one will, one reflex) than to make one DC 20 reflex save?

I really have no idea, but it'd be difficult to gauge since the reflex and will saves will be different values. Also, in order for SE to have any chance of doing more damage than the normal spell, failing the will save seems pretty much required. 20% is a pretty small sliver. Even if it did more damage, it's at least 1 spell level higher than what the evocation would be, is this factoring into your math at all, what the evocation spell could look like using that same spell level slot w/ metamagic?

Also, a side note: SE is HORRIBLE for nondamaging evocations. If they make the will save, it does't matter what % reality it is, they completely ignore the effect, even if it's 100% or more (it's possible!) "real". And objects always make thier will save.

The math isn't as bad as some scenarios.

Let r be the fraction of the time the enemy makes a DC 23 reflex save, and w be the fraction of the time he makes a DC 23 will save. (I'm going to ignore corner cases, like only failing on a 1 or only making on a 20.) Let d be the damage on a failed save.

The expected damage from Shadow Evocation is:

d_SE = d * (0.2 w + (1-w)) * (0.5 r + (1 - r)) =
d * (1 - 0.8 w) * (1 - 0.5 r)

The expected damage from the 4th level evocation spell is:

d_E = d * (0.5 (r + 0.15) + (1 - (r + 0.15)) =
d * (0.925 - 0.5 r)

You want d_SE >= d_E, or

(1 - 0.8 w) * (1 - 0.5 r) >= 0.925 - 0.5 r

-0.8 w >= (0.925 - 0.5 r) / (1 - 0.5 r) - 1

w <= 5/4 ( 1 - (0.925 - 0.5 r) / (1 - 0.5 r))

Putting some numbers in:

r=0.5 (decent reflex save modifier of +12):
w <= 0.125 or Will save mod +4 or less

r=0.8 (good reflex save modifier of +18):
w <= 0.15625 or Will save mod +5 or less

r=0.2 (bad reflex save modifier of +6):
w < 0.104167 or Will save mod of +4 or less

In short, unless you are fighting someone with or horrible will save, this isn't going to be a good idea. The 20% on a successful will save basically means that failing the will save is nearly required. As the enemy's reflex save improves, the +3 on the save DC becomes more important, so giving up a bit on the will save is worth it to increase the chance that he will fail the reflex save.

Where this spell shines is when you factor in "resistences". Whereas some creatures would be resistent to say, fire damage... just change your attack to a lightning bolt.

Illusion is among the most powerful schools of magic, up there with conjuration and transmutation easily.

Pielorinho said:

This topic applies to 3.x and Pathfinder, so I figured I'd stick it here.

I'm playing a 9th-level illusionist who's considering tracking down Shadow Evocation. Certainly the spell is worthwhile for its flexibility (blast, wall of ice, or resilient sphere, to name a few different uses), but it occurs to me that it may actually be a better blast spell than the evocation spells, under certain circumstances.

With my feats, I've got +2 to illusion saves. Assuming that I find a fourth-level 1d6/level, reflex-half blast spell (e.g., Dragon Breath, from Pathfinder), I'd normally require a reflex save DC 20 (+6 int, +4 spell level). If I cast it under Shadow Evocation, I'd require a Will save and a Reflex save, both DC 23 (+6 int, +5 spell level, +2 illusion).

My question is, under what circumstances would victims take more damage on average from the Shadow Evocation than from the straight-up spell? That is, what would their saves have to look like such that it'd be harder to make two DC 23 saves (one will, one reflex) than to make one DC 20 reflex save?

Click to expand...

What Dandu is saying is that the Shadowcraft Mage(Races of Stone) takes the spell you mentioned and other image illusion spells and gives scaling damage based upon what level it is. Dragon-blooded, heighten spell, earth spell, and accelerate metamagic automatically casts 10th level spells giving you a 100% base at its third level. It gains another 20% at its final level and you add the basis of this at its fifth. So, you cast at 140% of the real spell even if they disbelieve. Plus there are other illusions in which other effects are rigged in the spell making it one of the most feared blaster/control builds in the game.