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 3.5e metamagic rods - cost calculation?
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sleyvas
Skilled Spell Strategist

USA
11719 Posts

Posted - 07 Feb 2013 :  03:47:47  Show Profile Send sleyvas a Private Message  Reply with Quote
quote:
Originally posted by xaeyruudh

For me, sleyvas, I hadn't considered the +6 category yet. I had seen persistent spell written as a +4 metamagic feat, so that's where I'd stuck it in my table. I wanted to expand the metamagic rod listing to include other spell levels, rather than just 3/6/9, and make rods with more/less uses per day. So that's why I wanted to understand where they got the numbers from... just so I could pick it apart and add my own custom items.

In general I like your idea. There are two small problems though. Not trying to be a jerk, at all. Just saying we don't have the right formula yet. All of us have good ideas for ballpark estimations though, and that's really what counts.

1. If the set price for +1 metamagic rods is 2750, then the 9th level rod would be priced at 9x2750: 24750. There's never going to be a good reason for that to get rounded down to 24500. And other values need to be rounded up to reach the DMG numbers, so it's not a matter of consistently rounding down. But my idea kinda relies on WotC having made some rounding errors too, so of course I think this is a pretty small problem. Ayrik gets brownie points though, for bringing something that wouldn't require rounding because it's built into the formula.

Now I want brownies. Or fudge. Or both.

2. Does a 4th level +1 rod have the same price as a 6th level +1 rod? Ideally the formula could differentiate each spell level.

2-and-a-half. The only way to end up with a set price of 35000 for the +4 rods is by adding 16000 to your calculated 18875. Not that there's anything wrong with higher cost accompanying higher power, but why do we add to +4 (and higher) rods but not the lower rods? It's the most powerful (published) rod but that seems like a pretty flimsy reason for WotC to artificially inflate the prices. They did it on a grand scale with epic items in the ELH, but that's a demerit for their mathemagicians rather than a gold star. I think, and I admit that this is probably just my bias, there should be some consistent way to come up with all the factors that go into the equation.

We seem to have approached the formula from opposite directions. I see the lower level rods as offering some fraction of the full-power item's power, meaning that the formula would be based on the level 9 items. You're coming at it from the other direction, using the 3rd level item as a base and multiplying by a factor for the higher level items. I'm not calling either one a mistake or anything; I just think it's cool that we're covering the bases and coming up with ideas from both directions.



Yeah, I know my math's not perfect to match theirs exactly, but then again, I truly think whoever did the math... they were drinking something. The anomalous +16000 on the +4 rod though they may have thought.... hmmmm, +4 spell lvls on spells 3rd lvl or lower.... I'm going beyond the spell level that the person is even casting... better add more money.... hmmm, 1000 gp x lvl squared.

Alavairthae, may your skill prevail

Phillip aka Sleyvas
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Ayrik
Great Reader

Canada
7974 Posts

Posted - 07 Feb 2013 :  05:06:14  Show Profile Send Ayrik a Private Message  Reply with Quote
Alright, final computations, graphing optimal "best fit" matrices which cannot be reduced to any simple f(x,y) format:

+0: 1000, 4500, 12000
+1: 3000, 11000, 24500
+2: 9000, 32500, 73000
+3: 14000, 54000, 121500
+4: 35000, 75500, 170000
+5: 56000, 110000, 194500
+6: 90000, 152500, 245000


Sorry I couldn't find any references to confirm, but the calculated values for +1 through +4 tiers match perfectly* so I have high confidence the others will as well.

* "perfectly" meaning with such uncanny mathematical precision that (even though my approach differs) it must essentially be the same method used by WotC. Incidentally, the dubious +4/35K value seems accurate.

I did find this page, which reports nice-looking values of 50000, 150000, 250000 for a +5 Metamagic rod. However, I don't think it's canon/SRD material.

Also, Pathfinder uses values of 1500, 5500, 12250 for +0 Metamagic rods (Elemental Metamagic rod, and many other examples). I suspect these are just "halved" numbers rather than global-formula values. I extended my chart down to +0 for comparison.

And just for completeness, a "Creating rods..." thread at EN World with some excellent ideas and approximations.

I still cannot help but notice a strong resemblance to Fibonacci numbers (1,1,2,3,5,8,13,21,34,55,89,...), suggesting a comparatively simple summation or prime-number formula was used, even though it has thus far eluded analysis (also suggesting my calculations are wrong because they break the pattern).

Finally ... (two-click linky) ... the values are remarkably similar but not quite identical to mine. Non-canon, and note the comments about how these values were generated.

[/Ayrik]

Edited by - Ayrik on 07 Feb 2013 08:17:18
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xaeyruudh
Master of Realmslore

USA
1853 Posts

Posted - 08 Feb 2013 :  19:18:49  Show Profile  Visit xaeyruudh's Homepage Send xaeyruudh a Private Message  Reply with Quote
Interesting... good to know that others have been thinking about it as well, and they haven't found "one equation to rule them all" either.

At first glance, I like your numbers Ayrik, but my brain needs them to work together. A solid (and obtainable/understandable without advanced math) way to get each number in the line, and to get from one line to the next. I'm picky.

But I'm not trying to convince anyone; we should each go with what works best for us. I would guess that most people are happy with the DMG values. For me, the problem with that is that I like to make new items.
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Ayrik
Great Reader

Canada
7974 Posts

Posted - 09 Feb 2013 :  03:49:37  Show Profile Send Ayrik a Private Message  Reply with Quote
I know you wanted a nice function with one or two inputs and a single output, with some direct correlation between proportion and symmetry and pattern. "+5 Metamagic for 4th level spell" etc ... sorry, there's just not enough numbers to refine the broad generalities to exacting specifics, there just isn't enough precision to eliminate the paths you don't want.

[/Ayrik]
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GameVortexGeck0
Acolyte

USA
1 Posts

Posted - 19 Aug 2013 :  21:29:37  Show Profile  Visit GameVortexGeck0's Homepage Send GameVortexGeck0 a Private Message  Reply with Quote
quote:
Originally posted by xaeyruudh


N can remain 0,1,2
M=500,1500,2500,3500

For "+1" I get 3000,11000,24500... cool.
For "+2" I get 9000,33000,73500... the second and third values are off by 500. Not a huge discrepancy but it gets bigger.
For "+3" I get 15000,55000,122500... consistently "over" by 1000 and I don't see a way to lower all the values by the same amount using your formula.
For "+4" I get 21000,77000,171500... which appears to be high by 1500... at least our ideas agree on one point: the 35000 in the DMG has to be wrong. :P

Feel free to correct me if I'm doin' it rong.

I'm not dismissing the idea that the formula could be something like this, or at least more complicated than what I have above. I'm just not seeing the right numbers yet.



So, if +1 looks good, +2 is off by 500 (too high?), +3 is too high by 1000 and +4 is too high by 1500, then the equation is over by ((SL-1)*500)

Simply subtract ((SL-1)*500) from your equation and you should be good...

+1: -((1-1)*500) = -(0*500) = -0
+2: -((2-1)*500) = -(1*500) = -500
+3: -((3-1)*500) = -(2*500) = -1000
+4: -((4-1)*500) = -(3*500) = -1500
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