| T O P I C R E V I E W |
| xaeyruudh |
Posted - 03 Feb 2013 : 03:54:29
I'm pretty stumped.
"+1" metamagic feat: 3000 for spells up to 3rd level, 11000 for up to 6th level, 24500 for up to 9th level.
"+2" metamagic feat: 9000 for up to 3rd level, 32500 for up to 6th level, 73000 for up to 9th level.
"+3" metamagic feat: 14000 for up to 3rd level, 54000 for up to 6th level, 121500 for up to 9th level.
"+4" metamagic feat: 35000 for up to 3rd level, 75500 for up to 6th level, 170000 for up to 9th level.
It's use-activated but it's not a Spell Effect... but metamagic isn't listed under the nonspell effects on table 7-33. Treating it as a spell effect results in values that go way over the given prices.
I'm looking for patterns and coming up blank. Anyone have the answer? |
| 30 L A T E S T R E P L I E S (Newest First) |
| GameVortexGeck0 |
Posted - 19 Aug 2013 : 21:29:37
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 |
| Ayrik |
Posted - 09 Feb 2013 : 03:49:37
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. |
| xaeyruudh |
Posted - 08 Feb 2013 : 19:18:49
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. |
| Ayrik |
Posted - 07 Feb 2013 : 05:06:14
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. |
| sleyvas |
Posted - 07 Feb 2013 : 03:47:47
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. |
| xaeyruudh |
Posted - 06 Feb 2013 : 04:42:35
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. |
| xaeyruudh |
Posted - 06 Feb 2013 : 03:46:51
I'm in agreement that we're not going to come up with a formula that gives us the numbers in the DMG. I'm going to stick with my equations (which I'll try to clarify in the earlier post) for now; they feel the most cohesive to me... my only unexplained anomalies are the infamous 35000 in the DMG and the prices of the +0 metamagic rods from Complete Arcane.
Thank you for the input, and especially for your effort Ayrik! If anyone else wants to chime in, at any point in the future, please do. |
| sleyvas |
Posted - 05 Feb 2013 : 23:08:50
Are you by chance trying to figure out a price for a metamagic rod of persistence (i.e. +6 spell level)?
the rough formula is this as I see it
the 1st - 3rd lvl a set price
4th - 6th lvl 4 times set price
7th - 9th lvl 9 times set price
Where did I get this?
The +1 metamagic feat has a "set price" of 2750 that they rounded up to 3000
the +2 metamagic feat has a "set price" of 8125 that for some reason was rounded to 9000
the +3 metamagic feat has a "set price" of 13500 that for some reason was rounded to 14000
Then it all breaks at +4 for the 1st-3rd lvl range only.... because the "set price" there works only if its 18875. But assuming that set price for the 1st-3rd stuff, then the 4th-6th and 7th-9th follow the same pattern as previous. However, it is interesting to note that exactly 16000 (bonus is +4 and 4 squared is 16) is added to the set price here.
What's the rough formula for raising the "set price" add 5375 gp per +1 past the initial +1 (so 2750 (+1), 8125 (+2), 13500 (+3), 18875 (+4)). Note that 2750 is a slightly "rounded up" half price of 5375 (i.e. half price would be 2687.5)
So, for a metamagic rod of persistence (+6), "set" price for 1st-3rd lvl would be 29625, then 4th-6th lvl would be 118500, then 7th-9th lvl would be 266625. However, just to model it on what they did for +4, I'd recommend adding an additional 36,000 to the 1st-3rd lvl (to make it 65625), and I'd continue that trend upwards as well for the more powerful rods by adding a multiple of that bonus such that at 4th-6th lvl you add 36,000 X 2 (i.e. 72000)..... for a final price of 118500 + 72000 = 190500. Then for 7th-9th lvl, add 36,000 x 2 x 2 (i.e. 144,000)... for a final price of 410625.
Why do I not recommend following this odd pattern at the end? Essentially, those high level metamagic rods are more and more doing things that only extremely powerful epic mages can do (i.e. persisting a 9th lvl spell is like casting a 15th lvl spell). The higher you go, the more insane the requirements should be to make those really epic items. Hell, I'm not even sure if those amounts I added are truly enough, but I think its headed in the right direction. |
| Kentinal |
Posted - 05 Feb 2013 : 20:32:20
I was considering this, because greater or lessor does not require the same level it is possible part of the price is based on level of builder. |
| Ayrik |
Posted - 05 Feb 2013 : 20:00:50
It is always possible they used a progression beyond the ability of my "real math skills" to decipher. I'm pretty inclined to say no single formula was used because the MATLAB crunch is definitely correct and I basically worked through all (3^4=81) allowable permutations without forming any kind of overall pattern. |
| xaeyruudh |
Posted - 05 Feb 2013 : 17:58:04
Bummer. I liked your initial formula idea. It's possible that they did use that, and arbitrarily knocked 500/1000/1500 gp off the +2/+3/+4 numbers.
Thanks for tackling it with real math skills. I've tended to assume the formulas will be relatively simple, which isn't really fair.
The item they really just picked numbers out of the air for is the bag of tricks. |
| Ayrik |
Posted - 05 Feb 2013 : 10:55:11
After some serious attempts, I cannot reduce the matrices with any single f(x,y) expression. Heh, in fact, I think I've inadvertently worked out a formal mathematical proof that no single function was used.
I am forced to conclude that either a deviously complicated (or miscalculated) function is involved or the values for each of the "+N" tiers were produced through differing methods. In short, I can produce a formula duplicating each tier of results (as I already did for the first tier), but I cannot do so in any manner which expands into any kind of logical pattern/progression. I think WotC basically just made numbers up which "looked good". |
| Kentinal |
Posted - 03 Feb 2013 : 20:02:23
Hey just make one with all of them, it appears only can be used three times a day, though if spending more could use 5 or 10 times a day *EG* Likely would need to be made by level 30 caster that was bored and very rich.
|
| xaeyruudh |
Posted - 03 Feb 2013 : 19:38:36
quote:
Originally posted by Kentinal
consider that WotC did not believe these rods should ever be made.
Yea, this was my conclusion. But it seems odd, so I think I'm adding them to my own table... along with rods for some of the metamagic feats in other sources.  |
| xaeyruudh |
Posted - 03 Feb 2013 : 19:37:10
Hm... I may not be smart enough to do anything with it in that form. |
| Kentinal |
Posted - 03 Feb 2013 : 19:36:05
Hmm, This quote:
Lesser and Greater Metamagic Rods
Normal metamagic rods can be used with spells of 6th level or lower. Lesser rods can be used with spells of 3rd level or lower, while greater rods can be used with spells of 9th level or lower.
Indicates that feats are used for these Rods. Listed rods include.
Metamagic, Empower
Metamagic, Enlarge
Metamagic, Extend
Metamagic, Maximize
Metamagic, Quicken
Metamagic, Silent
Those of Heighten Spell, Still Spell and Widen Spell are not lisited. You might be able to compare costs of existing rods and apply to rods of these types, or might consider that WotC did not believe these rods should ever be made.
|
| Ayrik |
Posted - 03 Feb 2013 : 19:18:12
Haha, well MATLAB decided to solve the formula by treating each dataset as a vector set; so "+1" = data vector A1, "+2" = data vector A2, etc, yielding:
500 * ((16*A1) - (31*A2) + (14*A3) + (A4)) = 0
I could work out the linear function for you, if necessary. |
| xaeyruudh |
Posted - 03 Feb 2013 : 19:08:58
As far as I can tell, there's nothing in the DMG about figuring the price of items that duplicate feats.
...and I'm not going to justify the existence of metamagic feats... except to say that wizards and to a lesser extent sorcerers are like sprinters. They're good for one or two combats, but then they need a night's rest. Your fighter can keep dealing 2d6 damage on every hit, all day long, because there's no mechanic to address the issue of arms getting tired. And, depending on your DM, the fighter probably doesn't have to worry about his sword breaking either. After his combat spells are gone, though, your wizard is utterly useless for anything other than target practice. Even a fighter with a broken sword can still pull out his shortsword or dagger and go on causing damage... a wizard in melee will look pathetic in comparison. And not all of the wizard's spells will cause damage, because spell selection is a juggling act of buffs, debuffs, general usage, and damage spells. The wizard doesn't know at the beginning of the day how many fights there are going to be... and he really needs that information. The fighter has no reason to care how many fights there will be, because he can swing as many times as he needs to. I'm sure others can chime in that wizards are super-uber-powered, but that's only true for the first combat of the day... and even then only if the enemy is vulnerable to the damage spells the wizard chose.
All of that has been true in every edition... except maybe 4th where it seems everybody is a little more wizard and the wizard is a little less wizard, but I haven't played it so I'm not really gonna go there. Metamagic feats make a 3rd ed wizard's spells more efficient in certain circumstances. They're "expensive" in terms of getting limited feat slots, and there are a whole lot of feats to consider. Overall, assuming that the party has 3, 4, or more encounters in a day (not unusual at all), their impact seems minimal to me.
Plus, metamagic feats are of limited value because of their drawback: they take up higher level spell slots. So, sure, I could maximize a magic missile and be sure of dealing 5 damage per missile... but it becomes a 4th level spell, so I have to be a 7th level wizard or 8th level sorcerer before I can do that, and by that time I could have 4 or 6 regular 1st-level magic missiles that (statistically) will deal more damage than the maximized one, even if it does take longer to cast them all. Just one example, and we can probably find examples to serve either point. My point is just that the apparent increase in power offered by metamagic feats is illusory, and the flexibility comes at a high price.
Everyone's experience may be different though. |
| The Masked Mage |
Posted - 03 Feb 2013 : 12:08:36
I've been starting to read the 3rd e rules, and I got to say, I'm not much of a fan of all the metamagic "feats". If done "right" they make mid level wizards cast spells like archmages.
More importantly, they are simply not necessary. Learning to live with and conform to the parameters of spells is part of what makes being a wizard's player interesting. And if you REALLY want to change something - do a little research and change the darned spell. |
| Ayrik |
Posted - 03 Feb 2013 : 11:52:16
Does the DMG doesn't provide formulae for other feats? It would save time to know Wizbro's algebraic mindset at the time, I suspect that computations would apply a consistent approach across the board.
[Edit]
Is there any correlation with the 3E character experience charts? |
| xaeyruudh |
Posted - 03 Feb 2013 : 10:33:58
Yea, all that needed to happen was lowering the +2 values by 500, +3 by 1000, and +4 by 1500... and verifying that the 9000 and 35000 values in the DMG are typos. Maybe it's even in the errata; I haven't checked. Or maybe a new formula will iron out those kinks too.
No matter what we end up with, though, there's no doubt that the DMG just leaves us hanging when it comes to magical items with feats. |
| Ayrik |
Posted - 03 Feb 2013 : 10:27:23
Well, as I said above (after some editing) ... the expression (N^2) was just a quick assumption and should be replaced by a A((B*N)^(C/D)) ... which isn't as ugly as it looks since it will simplify if any of the [A,B,C,D] variables = 1
You're right, M probably = 500 for them all while the extra multiple is applied somewhere within the N expression.
I think the summations are correct, as they seem to closely approximate the pattern. |
| xaeyruudh |
Posted - 03 Feb 2013 : 09:40:05
I'm totally in favor of letting computers do the work. Speaking of which, I noticed that each row and column of GP values involves at least one "500" so I'm guessing M should stay 500 for all of them. Using goal seek in Excel gives N all sorts of weird values. But I'm curious to see what your script churns up. No rush or anything though... I don't want to be responsible for anyone losing sleep! |
| Ayrik |
Posted - 03 Feb 2013 : 09:27:34
Haha, I used to enjoy scribbling pages and pages of math. Now I'm lazy and let the machines do the crunching while I hang out at Candlekeep. |
| xaeyruudh |
Posted - 03 Feb 2013 : 09:23:22
Okay... sounds like a headache to me, but I'm guessing you enjoy that kind of thing. |
| Ayrik |
Posted - 03 Feb 2013 : 09:18:29
I'll script up a brute force Fourier transform in MATLAB tonight, it should be able to provide an *exact* (to like 32 significant digits) formula with the dataset. Or it'll spit out an error because the dataset is arbitrary beyond acceptable error tolerances. I'll do three runs to assume error margins of +/- 250, 500, and 1000 XP. |
| xaeyruudh |
Posted - 03 Feb 2013 : 09:18:24
One thing I don't like about the way these numbers seem to have been generated is that there's no provision for metamagic feats which don't change the spell level. Eschew Components and Energy Substitution are useful! And the rods would be comparatively cheap... but I don't see there being room for these rods to exist. Which is a bummer, imo. |
| xaeyruudh |
Posted - 03 Feb 2013 : 09:13:26
None taken, I'm open to other possibilities. Your idea has merit too, but I don't see it yielding the values in the DMG either. Although I'm keeping things simple, and if you have a program to churn through numbers to generate an equation I'm sure you'll get a better match than I am.
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. |
| Ayrik |
Posted - 03 Feb 2013 : 08:20:49
Hmm, no offense intended, but I think it's better to assume the calculated approximation is wrong, not the given data. Although your approximations are fairly good (at least on the middle and high values).
I'm on a mobile without Excel or MATLAB installed, but at a closer glance I'm thinking the sequence resembles a summation plus an exponent or slope curve (truncated or rounded to < +/- 500 precision).
For example, the "+1" dataset approximates well with
M*((N^2)+1+2+3)
M*((N^2)+1+2+3+4+5+6)
M*((N^2)+1+2+3+4+5+6+7+8+9)
for tier multiplier exponent N = 0,1,2 and XP multiplier constant M = 500
while the "+2" dataset approximates well with, say, a higher N sequence and M = 1500, etc ... perhaps what I called (N^2) takes the form of A(BN^(C/D)), where [A,B,C,D] each = 0, 1, or other integer values
(Sorry, too lazy to determine the precise function, but I think it's a better overall pattern approximation.)
Remember, of course, that the Wizbro 3E team may have used mathematical nerd power or may have arbitrarily invented/massaged the numbers to better fit some other purpose. I suspect their proprietary formulae are designed with an eye towards obscuring the math a little, specifically so it's harder to calculate "precise" values whic extend the sourcebook progressions.
... asterisks * indicate multiplications, carets ^ indicate exponents, extra/redundant parenthesis provided to clarify order of operations
... integer summations can always be simplified with a Riemann sigma formula: additive total of all integers from 1 to N = N*(N+1)/2 |
| xaeyruudh |
Posted - 03 Feb 2013 : 07:17:09
Ayrik: The numbers (especially that 35,000) looked weird to me so I was just trying to figure out where they got them from, since they weren't supported by the item pricing tables in the DMG. I thought of exponents first too, but it seems it was less/more complicated than that. Yay for puttering around in Excel! |
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