I'm trying to quantify the correct cost of making certain non-core meta-magic feats able to be infused into meta-magic rods.
A quick comparison of the Pathfinder Core Rulebook reveals that meta-magic rods are priced with a certain discernable logic which appears closely tied to the perceived utility of the base feat whose essence they store. For instance, all meta-magic rods associated with a base feat that requires the spell-caster increase his/her magic by only 1 slot (e.g. Enlarge Spell, Extend Spell and Silent Spell) have a cost array of 1,500 (for their lesser version), 5,500 (for their normal version) and 12,250 (for their greater version).
This same associative logic seems likely to hold true for 2-slot, 3-slot and 4-slot meta-magic rods because Empower Spell (a 2-slot feat), Maximize Spell (a 3-slot feat) and Quicken Spell (a 4-slot feat) all have different price arrays in the rules as written (RAW). (However, I must confess that without at least one other 2-slot, 3-slot and 4-slot meta-magic rod to compare pricing against, this second observation may have keyed in on something purely coincidental and therefore be accidentally false...)
That said, I still feel comfortable assigning rod crafting costs to non-core 2-slot, 3-slot and 4-slot meta-magic feats mirroring what's present in the RAW for core 2-slot, 3-slot and 4-slot meta-magic rods.
Where I've stumbled is trying to calculate the correct pricing for a 5-slot or 6-slot meta-magic feat being crafted into a rod. Since there are no 5-slot or 6-slot meta-magic feats (let alone 5-slot or 6-slot meta-magic rods) nor any rules that I’ve found in the Core Rulebook for pricing such outliers, I thought a good place to start could be interpolating the delta in cost along the continuum started by lesser 1-slot meta-magic rods thru lesser 4-slot meta-magic rods.
Unfortunately, I didn’t find a linear progression via this analysis technique:
Lesser gp_ delta from previous_ delta from origin
1,500_ nill_ nill
4,500_ 3,000_ 3,000
7,000 2,500_ 5,500
17,500_ 10,500_ 16,000
Next, I explored the possibility that each progressively more slot-heavy meta-magic rod might use a simple curve to quantify its pricing. But after crunching the numbers, that too proved patently wrong.
Lesser gp_ factor from previous_ factor from origin
1,500_ nill_ nill
4,500_ x3_ x3
7,000_ x1.56_ x4.67
17,500_ x2.5_ x11.67
Might someone here know the right formula I should be applying? Alternatively (actually, better in my opinion), might you know where I could buy/find RAW from a reputable Pathfinder-friendly publisher for pricing 5-slot and 6-slot non-core meta-magic feats being infuse into rods?
The outlying meta-magic feats I'm looking to make available for rod crafting are both from WotC's Complete Arcane: Energy Admixture and Persistent Spell. And although chapter 5 of the Complete Arcane does price several rods able to store the essence of a few of the non-core meta-magic feats presented in chapter 3, none of them are 5- or 6-slot rods.
That said, I do appreciate the suggestion, Morgen. In pouring over a copy of WotC's Magic Item Compendium tonight, I found a sum of new 13 rods; unfortunately, all of them are spell-based, not feat-based.
So I'm still at a loss. The one ray of shining insight I've been able to glean from this evening's research is that Paizo appears to have abandoned WotC's Complete Arcane/Magic Item Compendium unpredictable magical item pricing convention in favor for continuing the DMG's formulaic pricing.
This lone fact leaves me hopeful that there is a mathematical expression I could use to price meta-magic rods crafted with an infusion of Energy Admixture or Persistent Spell.
Now, just to find it...
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I can't help you out any more except to say one final thing.
Those two items should never exist in any campaign.
Persistent much more then Energy Admixture. You could never possibly make it expensive enough for what it could, nay, will unleash in the game.
Numerous exploits and research was done into how best properly abuse the Persistent meta-magic feat. Character builds abusing loopholes and obscure source book prestige classes and material was cobbled together to get more and more access to persistent spells per day. To simply create a rod that allows access to it 3 times per day is madness to allow, especially knowing the tiers that such rods come in.
If you absolutely must create them, then they should be items only suitable for epic level play when the rules of the game change.
One notes that the price increase from one spell level to two levels is triple, then from two to three is less than double, then from three to four is more than double. Highly inconsistent
So, I threw them into an Excel spreadsheet and calculated forward and I got this:
5 spell levels
20,250
48,500
109,250
6 spell levels
25,300
59,250
133,500
But I don't like those numbers. Mainly because the Quicken rod ruins the pattern (note that for the 1, 2, and 3 level rods, Greater is just over 2x Normal, and Normal is nearly 4x Lesser, but this is not the case for Quicken, where Normal is only barely more than 2x Lesser).
So, if I were to really get serious about pricing these, I would first fix Quicken to match the other three, then the pattern would work better, I think:
4 spell levels (Quicken)
17500
65000
145750
5 spell levels (Energy Admixture)
20250
75250
168750
6 spell levels (Persistent)
25250
94000
210750
Now the formulas are more or less consistent with each other, and the progression is also more consistent, but it's still not great. It's also worth noting that these are crafting costs, which means that the sale price of a Rod of Persistent Metamagic would be 421,500 gp, far more than any item in the book.
If I were the guy making these, I would just make a ring of 3 wishes and wish for three of these rods, it would save a fortune (only cost me 97,000 gp) and would only take 120 days to make three of these babies (as opposed to spending 632,250 gp and 3 years, 6 months of my life to make three Persistent rods).
So, for those interested (which is probably only me, but hey, I was always taught to share):
Being the mathematical nut-job that I am, these prices started to bother me. Why can't we just use a basic formula?
So I started with the simplest of the rods and refactored the prices so that Normal is 3x the price of Lesser, and Greater is 3x the price of Normal. Interestingly, the prices came out fairly close to what's in the book (not exact, but it's fairly clear that the book prices were just spitballed anyway).
Then I applied a simple formula for all the rods that use more than one spell level: price = basic rod x (level increase -1) * 3.
It's an easier formula than it looks. I just multipled the price of the simplest rod x3, x6, x9, x12, and x15 for each more powerful rod.
The weird thing is that some prices came out exactly the same (for example, by the book and by my formula, a normal Rod of Maximize costs 27,000 gp to create). Some rods came out cheaper, and some rods came out more expensive.
/shrug
Since the original numbers don't really follow a pattern, it stands to reason that creating a formula would have its hits and misses.
So, for those who are interested, here is the new math. These are the prices to create the rods. Multiply these numbers x2 for the price to purchase them.
1 spell level
1,500
4,500
13,500
2 spell levels
4,500
13,500
40,500
3 spell levels
9,000
27,000
81,000
4 spell levels
13,500
40,500
121,500
5 spell levels
18,000
54,000
162,000
6 spell levels
22,500
67,500
202,500
... Those two items should never exist in any campaign...
I appreciate the warning. I'll spend some time investigating the details of some of those loophole-abusing character builds you've mentioned for the Persistent meta-magic feat to see if they could/would pose a danger to the balance of our game.
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One thing you need to remember about item creation, the designers themselves did not always stick to the formulas they provided. Sometimes they had to "wing it" and reduce/increase the cost based on their estimation on the utility of the item.
For an example, look in the 3.5 FAQ's where I asked about improving a robe of the archmagi or a ring of wizardy and the cost thereof. I was essentially told that sometimes you just hasve to use your best estimate.
Not a vary satisfying answer for logical types searching for an underlying formula, but there you have it.
My recommendation, ignore Quicken as an exception, and use the formulas you discerned using another +4 slot rod.
FP
So, for those interested (which is probably only me, but hey, I was always taught to share)...
This is perfect! Thanks for all your help with the math.
Not a very satisfying answer for logical types searching for an underlying formula...
Quite right; especially because one of the aspects about 3e/3.5/Pathfinder that I enjoy very much is the linear, formulaic approach used by the designers to quantify many of the mechanical parts of the game. -- With predictable mathematic underpinnings in place for so much of what the folks on either side of the screen have to do to facilitate an enjoyable game session, I often feel that everyone at the table is free to focus on their part of the story-telling process instead of preparing justifications/arguments to support their estimation of the "right" value of any given expression.
** spoiler omitted **
Thanks DM+Blake. I appreciate this.
Consider it yoinked