Wealth Model

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Has anyone teased out the math involved in the standard wealth-by-level
model? Also, is that table in the SRD?

--
^v^v^Malachias Invictus^v^v^

It matters not how strait the gate,
How charged with punishment the scroll,
I am the Master of my fate:
I am the Captain of my soul.

from _Invictus_, by William Ernest Henley

 

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Out from under a rock popped Malachias Invictus and said

> Has anyone teased out the math involved in the standard wealth-by-level
> model? Also, is that table in the SRD?

I've always found that it's best to use carets to tease wealth monsters out
from under the table.

--
Rob Singers
"All your Ron are belong to us"
Credo Elvem ipsum etiam vivere

 

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In article <U_KdnZXJx4-jw7_fRVn-hQ@comcast.com>,
Malachias Invictus <capt_malachias@hotmail.com> wrote:
>Has anyone teased out the math involved in the standard wealth-by-level
>model?

There doesn't seem to be a simple formula. See below.

> Also, is that table in the SRD?

I'm fairly sure it's not. I created a file of "stuff not in the SRD" for
creating characters online; here it is.

PC Wealth (GP): DMG 135
1: 0 2: 900 3: 2,700 4: 5,400 5: 9,000
6: 13,000 7: 19,000 8: 27,000 9: 36,000 10: 49,000
11: 66,000 12: 88,000 13: 110,000 14: 150,000 15: 200,000
16: 260,000 17: 340,000 18: 440,000 19: 580,000 20: 760,000

It looks like it's regular only in chunks. The first 4 are 900*(level^2).
The next few increase by 4k, 6k, 8k, then 11k, 13k, 17k, 22k, 22k, 40k, 50k,
60k, 80k, 100k, 140k, 180k. So it's vaguely quadratic in shape. We could fit
a 20th degree polynomial to any set of 21 numbers, but that's likely to be
unusable.
--
"Yo' ideas need to be thinked befo' they are say'd" - Ian Lamb, age 3.5
http://www.cs.queensu.ca/~dalamb/ qucis->cs to reply (it's a long story...)

 

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"David Alex Lamb" <dalamb@qucis.queensu.ca> wrote in message
news:cvuva6$nmi$1@knot.queensu.ca...
> In article <U_KdnZXJx4-jw7_fRVn-hQ@comcast.com>,
> Malachias Invictus <capt_malachias@hotmail.com> wrote:
> >Has anyone teased out the math involved in the standard wealth-by-level
> >model?
>
> There doesn't seem to be a simple formula. See below.
>
> > Also, is that table in the SRD?
>
> I'm fairly sure it's not. I created a file of "stuff not in the SRD"
for
> creating characters online; here it is.

If definitely isn't.

> PC Wealth (GP): DMG 135
> 1: 0 2: 900 3: 2,700 4: 5,400 5: 9,000
> 6: 13,000 7: 19,000 8: 27,000 9: 36,000 10: 49,000
> 11: 66,000 12: 88,000 13: 110,000 14: 150,000 15: 200,000
> 16: 260,000 17: 340,000 18: 440,000 19: 580,000 20: 760,000

Thanks. I keep meaning to write this table down because the values come up
in discussion quite a lot.

> It looks like it's regular only in chunks. The first 4 are
900*(level^2).

Nit (probable typo): 900*((level-1)^2)

 

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In article <42230dd3$0$26734$cc9e4d1f@news.dial.pipex.com>,
Symbol <jb70@talk21.com> wrote:
>
>"David Alex Lamb" <dalamb@qucis.queensu.ca> wrote in message
>news:cvuva6$nmi$1@knot.queensu.ca...
>> PC Wealth (GP): DMG 135
>> 1: 0 2: 900 3: 2,700 4: 5,400 5: 9,000
>> 6: 13,000 7: 19,000 8: 27,000 9: 36,000 10: 49,000
>> 11: 66,000 12: 88,000 13: 110,000 14: 150,000 15: 200,000
>> 16: 260,000 17: 340,000 18: 440,000 19: 580,000 20: 760,000
>
>Thanks. I keep meaning to write this table down because the values come up
>in discussion quite a lot.
>
>> It looks like it's regular only in chunks. The first 4 are
>900*(level^2).
>
>Nit (probable typo): 900*((level-1)^2)

Thanks for the correction. Thanks also for the charitable interpretation, but
it was a thinko. I looked at the 0 and thought "oh yeah, starts at zero".
--
"Yo' ideas need to be thinked befo' they are say'd" - Ian Lamb, age 3.5
http://www.cs.queensu.ca/~dalamb/ qucis->cs to reply (it's a long story...)

 

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In article <slrnd26l63.7pg.keith.davies@kjdavies.org>,
Keith Davies <keith.davies@kjdavies.org> wrote:
>Still not right, though:

I need to stop calculating in my head. It's not reliable enough anymore.
--
"Yo' ideas need to be thinked befo' they are say'd" - Ian Lamb, age 3.5
http://www.cs.queensu.ca/~dalamb/ qucis->cs to reply (it's a long story...)

 

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"Keith Davies" <keith.davies@kjdavies.org> wrote in message
news:slrnd26l63.7pg.keith.davies@kjdavies.org...
> Symbol <jb70@talk21.com> wrote:

> >> It looks like it's regular only in chunks. The first 4 are
> > 900*(level^2).
> >
> > Nit (probable typo): 900*((level-1)^2)
>
> Still not right, though:

I blame David!

> 1: 0 * 900
> 2: 1 * 900
> 3: 3 * 900
> 4: 6 * 900
> 5: 10 * 900
>
> that makes an interesting pattern -- sum(0..(level-1)) * 900
>
> The next two steps I'm willing to see as rounding differences; following
> the pattern above, you'd have
>
> 6: 15 * 900 == 13,500 (they use 13,000)
> 7: 21 * 900 == 18,900 (they use 19,000)
>
> (notice that they only go to two significant figures above)
>
> After that it goes loopy altogether.

It could well be a function of treasure gain/encounter difficulty related
to average encounters.

 

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In article <422454aa$0$26714$cc9e4d1f@news.dial.pipex.com>,
Symbol <jb70@talk21.com> wrote:
>
>"Keith Davies" <keith.davies@kjdavies.org> wrote in message
>news:slrnd26l63.7pg.keith.davies@kjdavies.org...
>> Symbol <jb70@talk21.com> wrote:
>
>> >> It looks like it's regular only in chunks. The first 4 are
>> > 900*(level^2).
>> >
>> > Nit (probable typo): 900*((level-1)^2)
>>
>> Still not right, though:
>
>I blame David!

As well you should.

>>[beginnings of a pattern]
>> After that it goes loopy altogether.

>It could well be a function of treasure gain/encounter difficulty related
>to average encounters.

I think it's just plain poorly designed. It would make sense if the
difference between one increment and the next kept increasing [I mean D2
below], but sometimes it is zero and sometimes negative.

Here's a simple spreadsheet. L is level, DMG the DMG wealth entry for that
level. D1 is the difference betwen adjacent DMG entries. D2 is the
difference between adjacent D1's; it would be constant if a quadratic formula
represented the data well. L2 is L(L+1)/2, the sum of the levels to that
point. The next formula is meant to be Keith's -- L2 for the PREVIOUS line,
time 900. Like Keith said, there is a good match up to level8, but then it
goes wonky.

L DMG D1 D2 L2 L2[l-1]*900
1 0 0 0 1 0
2 900 900 900 3 900
3 2,700 1,800 900 6 2,700
4 5,400 2,700 900 10 5,400
5 9,000 3,600 900 15 9,000
6 13,000 4,000 400 21 13,500
7 19,000 6,000 2,000 28 18,900
8 27,000 8,000 2,000 36 25,200
9 36,000 9,000 1,000 45 32,400
10 49,000 13,000 4,000 55 40,500
11 66,000 17,000 4,000 66 49,500
12 88,000 22,000 5,000 78 59,400
13 110,000 22,000 0 91 70,200
14 150,000 40,000 18,000 105 81,900
15 200,000 50,000 10,000 120 94,500
16 260,000 60,000 10,000 136 108,000
17 340,000 80,000 20,000 153 122,400
18 440,000 100,000 20,000 171 137,700
19 580,000 140,000 40,000 190 153,900
20 760,000 180,000 40,000 210 171,000

It might be possible to fit a quadratic curve (or, yuck, cubic) to D2 -- it
would be off for most numbers but might make some kind of sense. It can make
sense to escalate the treasure at higher levels, but there's no rhyme or
reason to what they've got (other than D2 is nonnegative).
--
"Yo' ideas need to be thinked befo' they are say'd" - Ian Lamb, age 3.5
http://www.cs.queensu.ca/~dalamb/ qucis->cs to reply (it's a long story...)

 

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"David Alex Lamb" <dalamb@qucis.queensu.ca> wrote in message
news:d024i0$f9f$1@knot.queensu.ca...
> In article <422454aa$0$26714$cc9e4d1f@news.dial.pipex.com>,
> Symbol <jb70@talk21.com> wrote:
> >
> >"Keith Davies" <keith.davies@kjdavies.org> wrote in message

> >> > Nit (probable typo): 900*((level-1)^2)
> >>
> >> Still not right, though:
> >
> >I blame David!
>
> As well you should.
>
Just kidding. I'd eyeballed the first couple of numbers for which it was
right. I'm just as guilty!

> It might be possible to fit a quadratic curve (or, yuck, cubic) to D2 --
it
> would be off for most numbers but might make some kind of sense. It can
make
> sense to escalate the treasure at higher levels, but there's no rhyme or
> reason to what they've got (other than D2 is nonnegative).

Nerdish confession. I tried to solve the formula with simultaneous, cubic
equations but there are some pretty arbritrary jumps going on. As someone
has now confirmed Bradd spotted that it is a function of average treasure
from typical encounters.

 

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Symbol wrote:
> "Keith Davies" <keith.davies@kjdavies.org> wrote in message
> news:slrnd26l63.7pg.keith.davies@kjdavies.org...
>
>>Symbol <jb70@talk21.com> wrote:
>
>>>>It looks like it's regular only in chunks. The first 4 are
>>>
>>>900*(level^2).
>>>
>>>Nit (probable typo): 900*((level-1)^2)
>>
>>Still not right, though:
>
> I blame David!
>
>>1: 0 * 900
>>2: 1 * 900
>>3: 3 * 900
>>4: 6 * 900
>>5: 10 * 900
>>
>>that makes an interesting pattern -- sum(0..(level-1)) * 900

900.N(N-1)/2 where N=(level-1) here.

>>The next two steps I'm willing to see as rounding differences; following
>>the pattern above, you'd have
>>
>>6: 15 * 900 == 13,500 (they use 13,000)
>>7: 21 * 900 == 18,900 (they use 19,000)
>>
>> (notice that they only go to two significant figures above)
>>
>>After that it goes loopy altogether.
>
> It could well be a function of treasure gain/encounter difficulty related
> to average encounters.

Bradd's figured it all out IIRC, perhaps he'll turn up. The basics
are derived from 13.33 encounters per level, though I'm not sure if they
used the suggested EL rates (15% hard, 50% standard...)

PC Wealth (GP): DMG 135
1: 0 2: 900 3: 2,700 4: 5,400 5: 9,000
6: 13,000 7: 19,000 8: 27,000 9: 36,000 10: 49,000
11: 66,000 12: 88,000 13: 110,000 14: 150,000 15: 200,000
16: 260,000 17: 340,000 18: 440,000 19: 580,000 20: 760,000

EL Average treasure awards (GP): SRDTreasure.rtf
1: 300 2: 600 3: 900 4: 1,200 5: 1,600
6: 2,000 7: 2,600 8: 3,400 9: 4,500 10: 5,800
11: 7,500 12: 9,800 13: 13,000 14: 17,000 15: 22,000
16: 28,000 17: 36,000 18: 47,000 19: 61,000 20: 80,000

wealth - previous(wealth + 3* treasure)
2: -foo 3: -0 4: -0 5: -0
6: -800 7: -0 8: +200 9: -1200 10: -500
11: -400 12: -500 13: -7400 14: +1000 15: -1000
16: -6000 17: -4000 18: -8000 19: -1000 20: -3000

So, they've basically assumed you'll collect up standard treasure
less 10% (13.33 / 4, -10% = 3). Then they've rounded down each step to a
neat number, accounting for another 4% loss.

Of course, you're supposed to get about 30% "easy" encounters, and
20% "hard", and then you're supposed to run from maybe half the hard
ones, which makes it ever more complicated... hard wins screw you out of
cash, and then there's the defeated NPCs who have about tripple standard.
I've not checked it, but I presume all the various monster types
otherwise even out with some having double standard treasure and others
havng none. Perhaps you actually need a good few NPCs to keep enough
treasure coming, especially fighting alot of animals and zombies.


As to why they didn't make the treasure awards scale the same as
the XP table (double every two levels): well, they'd have to give DMs
something to remove *far* more treasure; more like 60% than 15%.
If you could remove more like 75%, you could have NPCs and PCs with
the same wealth, aswell as treasure that scaled properly.

--
tussock

Aspie at work, sorry in advance.

 

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Keith Davies wrote:
>
> Now, I wonder how difficult it would be to render the entire thing
> linear. A +4 item costs *twice* what a +2 item does, rather than the
> current four times. Right now it seems (loosely) assumed that when you
> have four times the money you'll have items of double the power. What
> if we could say that when you have items at double the power, you have
> double the money? I imagine it'd make a lot of things simpler.
>
>
> Keith

The current system exists because they started with a linear wealth
system and saw the problems with it.

The non-linear wealth system also has some interesting trade-offs. You
can buy that +2 sword, or you can buy a +1 sword, +1 Shield, +1 Armor,
and still have cash left over for a few potions. Which is more
attractive? How much is that +2 worth? What about a +3? This system
de-emphasizes weapon bonuses a bit, and also encourages equipment
diversity. That's good, IMHO.

There's also a different psychology with items at x4 cost over x2 cost.
This emphasizes to both GM's and players that a +2 is, in game terms,
far more important than a +1.

CH

 

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"Clawhound" <none@nowhere.com> wrote in message
news:WujVd.2730$Ny6.4756@mencken.net.nih.gov...

> The non-linear wealth system also has some interesting trade-offs. You can
> buy that +2 sword, or you can buy a +1 sword, +1 Shield, +1 Armor, and
> still have cash left over for a few potions. Which is more attractive? How
> much is that +2 worth? What about a +3? This system de-emphasizes weapon
> bonuses a bit, and also encourages equipment diversity. That's good, IMHO.

That is, honestly, one of the things I *don't* like about D&D: the crazy
amount of magic item proliferation. It is one of the reasons I like the
Sculpt Self feat (you can spend 1/5 the non-slotted cost of a magic item to
have its effect as a supernatural ability), and one of the reasons I
encourage signature items.

--
^v^v^Malachias Invictus^v^v^

It matters not how strait the gate,
How charged with punishment the scroll,
I am the Master of my fate:
I am the Captain of my soul.

from _Invictus_, by William Ernest Henley

 

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Malachias Invictus wrote:

> "Clawhound" <none@nowhere.com> wrote in message
> news:WujVd.2730$Ny6.4756@mencken.net.nih.gov...
>
>
>>The non-linear wealth system also has some interesting trade-offs. You can
>>buy that +2 sword, or you can buy a +1 sword, +1 Shield, +1 Armor, and
>>still have cash left over for a few potions. Which is more attractive? How
>>much is that +2 worth? What about a +3? This system de-emphasizes weapon
>>bonuses a bit, and also encourages equipment diversity. That's good, IMHO.
>
>
> That is, honestly, one of the things I *don't* like about D&D: the crazy
> amount of magic item proliferation. It is one of the reasons I like the
> Sculpt Self feat (you can spend 1/5 the non-slotted cost of a magic item to
> have its effect as a supernatural ability), and one of the reasons I
> encourage signature items.
>

I'll have to look at that. Thanks.

In many ways, I agree. Mostly, I dislike how wealth affects gameplay.
I'm always interested in how others have solved this problem. Has anyone
tried D&D with the D20 Modern wealth sysem?

As for a wealth system for a magic rich world, I am happy with the
current system. Move gameplay to magic poor world, and the current
system does not work.

CH

 

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In article <42258356$0$26724$cc9e4d1f@news.dial.pipex.com>,
Symbol <jb70@talk21.com> wrote:
>Nerdish confession. I tried to solve the formula with simultaneous, cubic
>equations but there are some pretty arbritrary jumps going on.

I think you'd need to do curve fitting (means and standard deviations and all
that stuff I've forgotten from college math).

> As someone
>has now confirmed Bradd spotted that it is a function of average treasure
>from typical encounters.

How clever. But doesn't that just mean that the average treasure data is
arbitrary, too?
--
"Yo' ideas need to be thinked befo' they are say'd" - Ian Lamb, age 3.5
http://www.cs.queensu.ca/~dalamb/ qucis->cs to reply (it's a long story...)

 

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Keith Davies wrote:
> tussock <scrub@clear.net.nz> wrote:
>
>> As to why they didn't make the treasure awards scale the same as
>>the XP table (double every two levels): well, they'd have to give DMs
>>something to remove *far* more treasure; more like 60% than 15%.
>> If you could remove more like 75%, you could have NPCs and PCs with
>>the same wealth, aswell as treasure that scaled properly.
>
> I'm becoming more and more inclined to revise the treasure
> determination. Right now things are somewhat quadratic, as are item
> costs. Happy situation: if you have two similar quadratic (or
> logarithmic, for that matter) systems, you can usually convert them into
> something more or less linear without breaking *too* much.

That's only true if those are the only things you effect. However,
to produce a linear increase in wealth by level you need a fixed income
per level: i.e. meet 1 ogre at 2nd level, get 100gp, meet 8 ogres at
level 8th level, get 100gp, meet a great wyrm red dragon at 23rd level,
get 100gp.
That would break the XP system quite badly, and characters would
still have vastly more wealth than NPCs. I guess you could just work on
destroying nearly all the accumulated treasure every level, but that can
get pretty silly.

Having a linear scale on items breaks all the limited slot and
stacking bonus effects, which relies on two +2's being cheaper than a
+4, even when one of the +2's is double normal price.

Characters are supposed to be twice as powerful every two levels,
so they should have at least the same progression in wealth, and much
higher than that if you're being realistic.
The game picked a slower progression, presumably to make sure the
"bonus squared" item costs don't overpower the spellcasters.

--
tussock

Aspie at work, sorry in advance.

 

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Keith Davies wrote:

>
> 'Linear' was a very poorly-chosen word, especially since it wasn't what
> I meant to say. I'd intended 'proportional to XP'.
>
>
> Keith

That's a very interesting little system. I wish I was running a game to
test it out.

CH

 

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Malachias Invictus wrote:
> Has anyone teased out the math involved in the standard wealth-by-level
> model? Also, is that table in the SRD?

Many models are wealthy, and most of them are teases.

- Ron ^*^

 

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Keith Davies <keith.davies@kjdavies.org> wrote in message news:<slrnd2cka2.7o3.keith.davies@kjdavies.org>...
> tussock <scrub@clear.net.nz> wrote:
<snip: Linear=bad>

> Linear isn't *quite* right. An additive system (similar to the XP
> system) looks like it may be workable, though.

That's a square too, or rather, a 2nd order polynomial. It's
definately a parabola, albeit squished and shunted left and down.

> estimated value
> bonus current additive
> +1 1C 1C
> +2 4C 3C
<...>
> +9 81C 45C
> +10 100C 55C

(Current + bonus) /2 = "additive"; which, as you can see,
approches current/2, but starts at current. You're effectively just
doubling the relative cost of +1 items for high level characters.

> ... where C is the multiplier for item type.

Which would all have to be made similarly closer to each other, so
as to not price the higher multipliers out of existance.

> Expected Wealth
> Level experience PC/DMG 90% XP
> 1 0 0 0
> 2 1k 900 900
<...>
> 19 171k 580k 153.9k
> 20 190k 760k 171.0k

Note: You've done the wrong order of transformations here. The
core rule wealth is a function of N^level (N ~=1.3), whereas core
costs are a function of level^2. Your new costs are still basically
level^2, but so is the wealth.


> Now, if we look at when a character could afford to buy a +n weapon
> (ignoring anything else that may be wanted), we get:
>
> Core Additive
> bonus Value Level Value Level
> +1 2k 3 2k 3
> +2 8k 5 6k 5
<...>
> +9 162k 15 90k 15
> +10 200k 16* 110k 17

It's the ignoring everything else that'll change the game in ways
you might not have expected. Currently, a character of 8th-12th level
is best off having a whole lot of trinkets (+1's, on to +2's, in every
slot), you might just push the balance into characters with all thier
eggs in one basket.
The rules are balanced for everyone having magic weapons, and
armour, and save boosters, and stat boosters, and something for
mobility, and whatever else they need at high level.

Is halving the number of trinkets (or more if players choose
better ones) of high level PCs a good idea?

--
tussock

Aspie at work, sorry in advance

 

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In article <f95318ef.0503031814.42791b5b@posting.google.com>,
tussock <scrub@clear.net.nz> wrote:
> Note: You've done the wrong order of transformations here. The
>core rule wealth is a function of N^level (N ~=1.3), whereas core
>costs are a function of level^2. Your new costs are still basically
>level^2, but so is the wealth.

Are you sure that is the right exponent? When I correlate DMG wealth with
L^1.3 I get the following. There is no linear relation as you suggest. It's
little better with L^2.3, and better than that with 3.3, which is flat in the
middle, but strange before and after. I suppose this might mean there are
some L^2 or L terms involved.

L DMG DMG/L^1.3 DMG/L^2.3 DMG/L^3.3
1 0 0.00 0.00 0.00
2 900 365.51 182.76 91.38
3 2,700 647.30 215.77 71.92
4 5,400 890.67 222.67 55.67
5 9,000 1110.66 222.13 44.43
6 13,000 1265.75 210.96 35.16
7 19,000 1514.00 216.29 30.90
8 27,000 1808.62 226.08 28.26
9 36,000 2069.13 229.90 25.54
10 49,000 2455.82 245.58 24.56
11 66,000 2922.36 265.67 24.15
12 88,000 3479.74 289.98 24.16
13 110,000 3919.82 301.52 23.19
14 150,000 4854.28 346.73 24.77
15 200,000 5917.13 394.48 26.30
16 260,000 7073.22 442.08 27.63
17 340,000 8548.61 502.86 29.58
18 440,000 10270.66 570.59 31.70
19 580,000 12619.68 664.19 34.96
20 760,000 15469.44 773.47 38.67
--
"Yo' ideas need to be thinked befo' they are say'd" - Ian Lamb, age 3.5
http://www.cs.queensu.ca/~dalamb/ qucis->cs to reply (it's a long story...)

 

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David Alex Lamb wrote:
> In article <f95318ef.0503031814.42791b5b@posting.google.com>,
> tussock <scrub@clear.net.nz> wrote:
>
>> Note: You've done the wrong order of transformations here. The
>>core rule wealth is a function of N^level (N ~=1.3), whereas core
>>costs are a function of level^2. Your new costs are still basically
>>level^2, but so is the wealth.
>
> Are you sure that is the right exponent? When I correlate DMG wealth with
> L^1.3 I get the following.

Not L^(1.3), but (1.3)^L. It can't be made to fit perfectly; it's
off at zero, but close enough for go'm'nt work.

base *4k -6k
1.3 5.2 -0.8
1.7 6.8 0.8
2.2 8.8 2.8
2.9 11.4 5.4
3.7 15 9
4.8 19 13
6.3 25 19
8.2 33 27
10.6 42 36
13.8 55 49
17.9 72 66
23.3 93 87
30.3 121 115
39.4 157 151
51.2 205 199
66.5 266 260
86.5 346 340
112.5 450 444
146.2 585 579
190.0 760 754

Hey, look 't that, close indeed.

PC Wealth (GP): DMG 135
1: 0 2: 900 3: 2,700 4: 5,400 5: 9,000
6: 13,000 7: 19,000 8: 27,000 9: 36,000 10: 49,000
11: 66,000 12: 88,000 13: 110,000 14: 150,000 15: 200,000
16: 260,000 17: 340,000 18: 440,000 19: 580,000 20: 760,000

--
tussock

Aspie at work, sorry in advance.

 

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Malachias Invictus wrote:
> Has anyone teased out the math involved in the standard
> wealth-by-level model?

I nearly figured it out. I couldn't reproduce the recommended gear table
exactly, but I found a formula that comes very close (accurate for all
levels except 8th-12th).

The total wealth level is related to the average treasure per encounter.
Essentially, it's the sum of all treasure earned minus a small fraction
for waste (expendable items, expensive spells, theft, living expenses).

I did find a formula that exactly predicts treasure per encounter:

Let L be effective character level,
round(x) = round to 2 significant digits.

Te(L) = L in [1,4]: 300L,
L > 3: round(1200 x 1.3^(L-4))

In plain English: Through 4th level, expected treasure per encounter is
300 gp per level. After that, each level is worth 1.3x the previous
level. Round the final result to 2 digits to get the values on the
table.

To get total character wealth, add up the treasure amounts for all
encounters (13.33 per level) and subtract a fraction for waste. For the
first 6 levels, waste is 10% of treasure earned. After that, the waste
at each level is very close to 1090 x 1.25^(L-6). Again, round the total
to 2 significant digits.

Here's a table of the results:

sum round book calc calc round
L T/E T/L T/PC T T W waste W W
1 300 3999 1000 0 0 0 0 0 0
2 600 7998 2000 1000 1000 900 100 900 900
3 900 11997 2999 3000 3000 2700 200 2700 2700
4 1200 15996 3999 5999 6000 5400 300 5399 5400
5 1600 21328 5332 9998 10000 9000 400 8998 9000
6 2000 26660 6665 15330 15000 13000 1090 13240 13000
7 2600 34658 8665 21995 22000 19000 1363 18542 19000
8 3400 45322 11331 30660 31000 27000 1703 25504 26000
9 4500 59985 14996 41991 42000 36000 2129 34706 35000
10 5800 77314 19329 56987 57000 49000 2661 47041 47000
11 7500 99975 24994 76316 76000 66000 3326 63044 63000
12 9800 130634 32659 101310 100000 88000 4158 83880 84000
13 13000 173290 43323 133969 130000 110000 5198 111341 110000
14 17000 226610 56653 177292 180000 150000 6497 148167 150000
15 22000 293260 73315 233945 230000 200000 8121 196699 200000
16 28000 373240 93310 307260 310000 260000 10151 259863 260000
17 36000 479880 119970 400570 400000 340000 12689 340484 340000
18 47000 626510 156628 520540 520000 440000 15862 444592 440000
19 61000 813130 203283 677168 680000 580000 19827 581393 580000
20 80000 1066400 266600 880451 880000 760000 24784 759892 760000

T/E is treasure per encounter.
T/L is treasure per level for the whole party.
T/PC is treasure per level for each PC.
Sum T is the total treasure earned (per PC) through that level.
Round T is sum T rounded to 2 digits.
Book W is the recommended PC gear as printed in the rulebooks.
Calc waste is my estimate of the "wasted" loot.
Calc W is all treasure earned minus all waste.
Round W is calc W rounded to 2 digits.

As you can see, round W is identical to book W for most levels.
Unfortunately, it's pretty far off for 8th-12th level. I wasn't able to
find any simple formula that matched exactly at all levels.

If you just want a rough estimate, use 85-90% of sum T (which is easy to
calculate from the SRD "Treasure" rules).
--
Bradd W. Szonye
http://www.szonye.com/bradd

 

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tussock wrote:
>> Note: You've done the wrong order of transformations here. The core
>> rule wealth is a function of N^level (N ~=1.3), whereas core costs
>> are a function of level^2. Your new costs are still basically
>> level^2, but so is the wealth.

David Alex Lamb wrote:
> Are you sure that is the right exponent? When I correlate DMG wealth
> with L^1.3 I get the following ....

1.3 is the base, not the exponent. The average treasure per encounter is
proportional to 1.3^level (at 4th level and above; below that, it's
linear). Also, the average expenditure per level is roughly proportional
to 1.25^level (again, only at medium to high levels). The formula for
total wealth is a series computed from those two functions. As far as I
know, there's no simple way to express it, but IIRC it also ends up
being close to 1.3^level.
--
Bradd W. Szonye
http://www.szonye.com/bradd

 

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Symbol wrote:
> Nerdish confession. I tried to solve the formula with simultaneous,
> cubic equations but there are some pretty arbritrary jumps going on.
> As someone has now confirmed Bradd spotted that it is a function of
> average treasure from typical encounters.

I used the very nice curve fitter at
http://members.aol.com/johnp71/nonlin.html

At first, I was also stumped by the arbitrary-seeming jumps from level
to level. However, I eventually realized that the weirdness was caused
by rounding error. All results are rounded to two significant digits. In
a couple of places, that makes it seem like wealth increases unusually
quickly or slowly, because the rounding error is large.
--
Bradd W. Szonye
http://www.szonye.com/bradd

 

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On Wed, 02 Mar 2005 01:02:40 GMT, Keith Davies
<keith.davies@kjdavies.org> wrote:

>I'm becoming more and more inclined to revise the treasure
>determination. Right now things are somewhat quadratic, as are item
>costs. Happy situation: if you have two similar quadratic (or
>logarithmic, for that matter) systems, you can usually convert them into
>something more or less linear without breaking *too* much.
>
>I think a big part of the reason they go with escalating costs is to
>prevent low-level characters from being able to afford the big items...
>but then have to escalate the expected equipment total in order for the
>higher-levels to be able to afford them.
>
>Now, I wonder how difficult it would be to render the entire thing
>linear. A +4 item costs *twice* what a +2 item does, rather than the
>current four times. Right now it seems (loosely) assumed that when you
>have four times the money you'll have items of double the power. What
>if we could say that when you have items at double the power, you have
>double the money? I imagine it'd make a lot of things simpler.

(Sorry about the late reply, I've been out of town.)

I don't think it's possible.

The problem is that if you make it linear you permit more
concentration of power. The fighter type probably has a +2 melee
weapon and a +2 ranged weapon. He can't quite trade them in for a
single +3 weapon as it stands now. Under a linear system he can trade
them in for a +4 weapon--something he will probably do.

Personally, I have my doubts about the quadratic curve even. My
inclination is that things might be better if the curve were cubic.
(Note: This would also scrap the x10 epic pricing, which seems to me
to be a kludge for the quadratic curve being too shallow.)