Reverse Engineering Metamagic Rods

[thorian]

I spent a few minutes and tried to derive an elegant equation which explains how to generate the cost of a metamagic rod. I came up with a simple solution, except there is one rod which doesn’t match up (the lesser quicken rod).

Here is the equation:

((L*2)-1)*(M^2)*300gp

L = the level adjustment of the metamagic feat which the rod duplicates
M = the maximum level of spell which the rod is able to effect

[b][u]type     M   L     cost     Calc[/u][/b]
lesser   3   1     3000     2700
regular  6   1    11000    10800
greater  9   1    24500    24300
lesser   3   2     9000     8100
regular  6   2    32500    32400
greater  9   2    73000    72900
lesser   3   3    14000    13500
regular  6   3    54000    54000
greater  9   3   121500   121500
lesser   3   4    35000    18900 (why?)
regular  6   4    75500    75600
greater  9   4   170000   170100

If anyone can derive a better equation, that would be great. I’d like to see if someone can generate an exact formula.

 

[green slime]

The obvious answer to the "why" you pose, is because some designer realised that 19,000 gp was rather cheap for the ability cast three quickened spells per day, even if they were only 3rd level spells. Compare to the insane prerequisites to access the Sudden Quicken feat from CA, or the limitations placed on caster level for Quicken Spell-like ability.

19,000 gp is available to characters of 7th level....

 

[The Gryphon]

As for pricing the single use metamagic item, I'd divide the cost of the metamagic rod you're trying to duplicate by 6 (3 [reducing the uses from 3 to 1] x 2 [halving the base cost as the item no longer has unlimited use]) and round to the nearest 500gp or 1,000gp if you want to clean the numbers up a bit.

 

[Cheiromancer]

Raise Thread!

If anyone can derive a better equation, that would be great. I’d like to see if someone can generate an exact formula.

I used a slightly different convention when defining the parameters: I set p to be the spell level adjustment of the metamagic feat in the rod (its "plus") and said that x=1 means a lesser rod, x=2 a normal rod, and x=3 a greater rod. My values for lesser rods are off, but the normal and greater ones are right on. At least for p=1,2,3 and 4.

cost = (6p-3)x^2 -(3p-1.5)x +(3.5p-1.5)​

Which yields the following table:

plus	lesser  normal  greater
1	3.5	11	24.5
2	10	32.5	73
3	16.5	54	121.5
4	23	75.5	170
5	29.5	97	218.5
6	36	118.5	267

The costs are in thousands of gp. I added two extra rows for +5 and +6 feats. Anyone know if there is a published source which gives a price for more advanced metamagic rods?

I think if the metamagic feat were epic, there would probably have to be an epic multiplier applied. Like how the ELH multiplies the prices of various items by 10.