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  1. - Top - End - #1
    Ogre in the Playground
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    Default Wealth vs GP [d20 modern & 3.5 D&D - MATH HELP!]

    I'm part of a group running some D&D and d20 modern games, which will cross over regularly. Converting the two systems of wealth measurement (gold pieces in D&D and the abstract "Wealth Bonus" in d20 modern) is not easy.

    (Before you continue, if your opinion is going to be "Why bother?" or "Just guess," or something similar, please don't post it. I'm looking for a mathematical solution that I know is present...)

    In d20 modern, there's a Wealth Bonus (WB) which one adds to a d20 check to see if you can afford stuff (which has a purchase DC).

    As one goes up levels, one can increase this WB by making a Profession check higher than the current WB. I ran some maths on it, and it works out to (roughly) a 1.6 point increase per level. a 20th level character ought to be "very rich" by the terms of the d20 system.

    Now, in D&D 3.5, characters have an expected wealth by level (see page 135 of the DMG). If you look at that table, the increases are very definitely non-linear. I broke out my true geek ability, and took the logarithm of the wealth by level figures, which gave me a nice straight linear increase.

    I remember from my long-past maths and physics studies that I ought to be able to find the equation that ties these two measurements of character wealth together. Can anyone in the Playground help me, please?

  2. - Top - End - #2
    Troll in the Playground
     
    NEO|Phyte's Avatar

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    Default Re: Wealth vs GP [d20 modern & 3.5 D&D - MATH HELP!]

    d20 Future has a Purchase DC/Dollar Value table, for use in determining the final purchase DC of modified/custom starships and mecha. It may not prove to be of any use to you, but it's the only thing I can think of that might help. Since I can't locate locate said table in the relevant SRD, it is seemingly not OGL content, so I can't just link you to it, but it's on page 145.
    Last edited by NEO|Phyte; 2008-11-21 at 07:09 PM.
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  3. - Top - End - #3
    Ogre in the Playground
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    Default Re: Wealth vs GP [d20 modern & 3.5 D&D - MATH HELP!]

    Quote Originally Posted by NEO|Phyte View Post
    d20 Future has a Purchase DC/Dollar Value table, for use in determining the final purchase DC of modified/custom starships and mecha. It may not prove to be of any use to you, but it's the only thing I can think of that might help. Since I can't locate locate said table in the relevant SRD, it is seemingly not OGL content, so I can't just link you to it, but it's on page 145.
    Thanks - I've tried this out now and the values in d20 Future confirm that the WB and purchase DC systems are logarithmically related to actual cash values in the game world.

    However, I still don't know what the step from knowing I have a logarithmic relationship is, to making an equation that changes WB to GP...

  4. - Top - End - #4
    Firbolg in the Playground
     
    Jasdoif's Avatar

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    Default Re: Wealth vs GP [d20 modern & 3.5 D&D - MATH HELP!]

    Hope my memory hasn't failed me in my not-quite-middle age It's been a long time since I've done much with logarithms....But here goes.


    Logarithms basically convert multiplication into addition. log(3)+log(5)=log(3*5), that sort of thing.

    So if the logs of the gold pieces are increasing by adding a set number each level, then the gold piece totals themselves are being multiplied by a set number each level. Divide level 3's WBL by level 2's WBL, level 4's by level 3's, etc.; see if you can determine a factor that fits closely.


    Once you have that, you can tell that every time the Wealth Bonus increases by 1.6, the gold piece total is multiplied by that factor. So if you take 1.6th root of the factor, that's how much the gold pieces are multiplied by each time the wealth bonus increases by one.

    Which is the base for an exponent, something like

    g = k*nx

    Where "g" is the gold piece total, "n" is that last number, "x" is the wealth bonus, and k is...some number we haven't determined just yet. Anyway, that'll be the formula for determining gold pieces from wealth bonus; you'd reverse it to go the other way around.

    As for "k"? Well, the last piece you need is one item/point that you can put a price on in both systems. Plug the gold piece value and the wealth of this in there, and solve for "k". And then that's always "k" in your formula. "k" and "n" will remain the same, only "x" (wealth bonus) and "g" (gold pieces) will be different from then on.
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  5. - Top - End - #5
    Ogre in the Playground
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    Default Re: Wealth vs GP [d20 modern & 3.5 D&D - MATH HELP!]

    Thanks!
    That may work... except XL (which I'm using to graph the results) doesn't seem to have an nth-root function, only a square root function...

    EDIT: d'oh! Found it.

    Doesn't seem to work as yet... I'll get back to you on this.
    Last edited by Altair_the_Vexed; 2008-11-22 at 06:48 AM.

  6. - Top - End - #6
    Firbolg in the Playground
     
    Jasdoif's Avatar

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    Default Re: Wealth vs GP [d20 modern & 3.5 D&D - MATH HELP!]

    Quote Originally Posted by Altair_the_Vexed View Post
    That may work... except XL (which I'm using to graph the results) doesn't seem to have an nth-root function, only a square root function...
    Does it have a power (or exponent) function? You could take it to the power of (1/1.6) for the same result.
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