Cost of Spell DC Increase

[Cheiromancer]

Well, the rods are usable only three times a day. So they've been multiplied by 3/5 to express the reduction of costs. So for a unlimited use per day (but otherwise as a minor rod) the cost would be:

(2x-1) * (9000)

Minor rods only affect up to 3rd level spells. If n is the highest level spell affected by the rod, then the cost for all three rods can be expressed as:

(2x-1) * n * n * 1000

 

[kreynolds]

Ability scores are 2000 x bonus squared

Nope. They're 1000 x bonus squared.

 

[da chicken]

Nope. They're 1000 x bonus squared.

Right. It's just bad game design to do them in anything but even increments.

Cheiromancer:
Thanks. I knew a 3/5 had to figure somewhere in there. I was trying to find it before I found the (2x-1).

So, it is 3/5*(2x-1)*n^2*1000, where x is the heighen bonus and n is the highest spell level.

[rant]
Why the heck does T&B tell us to divide by a fraction? Must you make the math randomly more arcane than it already is?
[/rant]

[Edit: Missed the 1000 in the formula. ]

 

[kreynolds]

It's just bad game design to do them in anything but even increments.

Did somebody do them in uneven increments?

[rant]
Why the heck does T&B tell us to divide by a fraction? Must you make the math randomly more arcane than it already is?
[/rant]

You don't divide by a fraction. If the power is fireball, unlimited charges, but only useable 3 times per day, the formula looks like this: 3 (spell level) x 5 (caster level) x 2,000gp / 1.66 (5 divided by 3) = 18,072gp. I use two decimal points in the times-per-day number to get a more accurate price.

 

[Marshall]

Minor rods only affect up to 3rd level spells. If n is the highest level spell affected by the rod, then the cost for all three rods can be expressed as:

(2x-1) * n * n * 1000

Cool! So they hand me the rod AND pay me a 1000gp to take a Rod of Eschew Materials or a Rod of Energy Substitution(Sonic)... Sign me up!

 

[da chicken]

Did somebody do them in uneven increments?

No. But it answers the implicit question about 2,000 vs 1,000, and answers why the original poster was mistaken.

You don't divide by a fraction.

Uh, I don't know what book you're reading, but my copy of T&B says "Divide by (5 / charges per day)" on Table 4-3. That, like THAC0, is needlessly complicated. It should say "Multiply by (charges per day / 5)."

And yes, division is more complicated than multiplication. That's why you learn multiplication first. What they did is even called a complex fraction.

Cool! So they hand me the rod AND pay me a 1000gp to take a Rod of Eschew Materials or a Rod of Energy Substitution(Sonic)... Sign me up!

No, you use a different constant for +0 items, just like for every other formula for items involving a zero. A metamagic rod of substitution costs 2,700 gp, 10,500 gp, and 24,300 gp.

The formula is 3/5*(2x-1)*n^2*1000, where x = level bonus and n = maximum level spell.

Solve for x | n = 3 and F(x) = 2700:

3/5*(2x-1)*9*1000 = 2700

9*3*1000 = 27000, so:

(2x-1)/5 = 0.1

2x-1 = 0.5

2x = 1.5

x = .75

 

[kreynolds]

Uh, I don't know what book you're reading, but my copy of T&B says "Divide by (5 / charges per day)" on Table 4-3.

What's your point? Mine says the exact same thing, but that's not a fraction, regardless of what you think it is. You divide 5 by the number of charges per day, then divide the cost of your item by that number.

 

[Staffan]

Nope. They're 1000 x bonus squared.

And that works out to 4000 x ability modifier bonus squared. A pair of gauntlets of ogre power gives +2 to Strength, which means +1 to Strength modifier. Since the ability bonus is twice that of the ability modifier bonus, and the whole thing is squared, the cost for an ability modifier bonus is four times that of an ability bonus.

Now that that bit of math is out of the way... an item that increases save DCs of one type of spells (I would limit it to the spells from one class list - clerics, druids and wizards would all use different items) is less useful than one that gives a bonus to the whole ability score, so it should definitely not cost more than 4000 x bonus squared. If it could stack with ability enhancement bonuses, I would probably price it at 3000 - I've seen one wizard with ridiculously high DCs, and I wouldn't want to make it too easy to push them up even higher. If it doesn't stack with ability enhancements, I'd probably price it at half that, 1500.

 

[Kae'Yoss]

Unfortunately, it will stack with the bonus provided by, say, a headband of intellect: the headband will give you a +4 (e.g) to int. Because of this, the int mod, and the wizard spell DC's will improve by 2. But that's no enhancement bonus to DC, the DC was determined normally. If you now have a thing of spell power +2, it's enhancement bonus will increase the DC's by 2. Together with the headband, this will actually be +4 reached via enhancement bonuses, but two enhancement bonuses to different values.
Come to think of it, it's like a Belt of Giant Strength and a Magic Weapon: you'll get +2 to hit and damage from the belt (indirectly through the enhancement bonus to str) and +2 to hit and damage because it's a +2 weapon.

If you want the new item's boost and the boos of ability-score-increasing items (headband of int, periapt of wis and so on), you'd have to introduce weird house rules. I'd not do this. If you don't want them to stack, just forget the new item.

If it's OK for you that Spellcasters can further increase their DC with magic items, a formular similar to that of magical weapons should be appropriate, since those essentially are "weapons" for spellcasters: a tool to make their attacks more dangerous.


Now, those items should have a formula of

bonus^2 *2000gp

maybe even

bonus^2 * 4000gp

because I recon it's even more dangerous than a weapon's enhancement bonus.

So, you could put that into a ring or something, but especially for humanoid (i.e. PC race-) spellcasters (especially wizards), it would be far more stylish if you put it into their magic staff. Create a magic staff that improves their save DC's. That would be in line with all the magic staves you see wizards use in all the fantasy stories: they do their magic themselves, but the staff makes the magic stronger (as opposed the staffs/wands we already have, that just enable the wizard to use some spells for free). It would be a nice version of a rod. Rod of Spell Power.

Or you create a weapon special quality: spell power. (Maybe it works only for the quarterstaff). For +2 market price you get DC +1 (It's like an item that doesn't use up an item slot, so double price. You could even argue that's +4 for +1, when you are for bonus^2*4000 for an item that does use up a slot). +1 and +2 would be normal, and +3, +4 and +5 (and theoretically more) would be epic!

 

[las]

Make em epic.