Help Me With A Math Problem

Something is wrong with my post above. Those polynomials give garbage results. Excel sucks at this kind of stuff.

Ok it is kinda fixed now. I have a third order polynomial fit. You may test it by plugging in your own values into it in the spread sheet at G7 and G8

The sheet is attached below

If somehow I could know exactly how these numbers were generated I could do beter
 

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bolen said:
If somehow I could know exactly how these numbers were generated I could do beter
Both of these books are almost 100% OGL so I think it's OK To post these. Please correct me if I'm wrong and I'll take them down immediately.



Here is the XP-point cost progression that I am using from Buy the Numbers. It shows how much each spell slot costs to buy in XP.

0th-level slots 3 * new total 0th level spell slots
1st-level slots 5 * (new total 1st level spell slots plus 3)
2nd-level slots 10 * (new total 2nd level spell slots plus 6)
3rd-level slots 15 * (new total 3rd level spell slots plus 9)
4th-level slots 20 * (new total 4th level spell slots plus 12)
5th-level slots 25 * (new total 5th level spell slots plus 15)
6th-level slots 30 * (new total 6th level spell slots plus 18)
7th-level slots 35 * (new total 7th level spell slots plus 21)
8th-level slots 40 * (new total 8th level spell slots plus 24)
9th-level slots 45 * (new total 9th level spell slots plus 27)




Here is, from Elements of Magic, the spell point progression of a magic user using the mana point system. This is basically this book's equivalent of a Wizard in D&D.

Spellcaster Level - Maximum Spell MP - Spell Lists Known - Magic Points - Free Cantrips Per Day

1 1 6 5 3
2 2 9 11 4
3 3 11 17 5
4 4 13 26 6
5 5 15 35 7
6 6 17 45 8
7 7 19 56 9
8 8 21 68 10
9 9 23 81 11
10 10 25 95 12
11 11 27 110 13
12 12 29 130 14
13 13 31 152 15
14 14 33 177 16
15 15 35 205 17
16 16 37 235 18
17 17 39 265 19
18 18 41 297 20
19 19 43 332 21
20 20 45 370 22

This list is a bit confusing, so let me explain... the first number is the level of the spellcaster... straightforward enough. The second number is the max amount of mana a spellcaster of that level can spend on a single spell. The third number is the number of "spell lists" known, which replace spells. Spell lists were easy to convert into the Buy the Numbers system so you can ignore those numbers (I'll post the entire conversion later, but for now let's avoid adding extra numbers ;)). The 4th number is the number of mana points a character will have at that level. The last row is unimportant; free 0-level spells per day. But you can see that the 4th column is where I got the X-coordinates from.

I'm converting the spell slot costs into mana point costs.

So I used the buy-the-numbers system to calculate how much XP a regular core rules wizard would spend at each level on his new spell slots. Then I just subtracted to find out how many mana points the EoM wizard gains at each level. Then I divided the XP cost for the stand allotment of spell slots by the number of mana points he would gain at each level to find approximately how much XP he should spend on each mana point when within that level's range of mana points. That's how I got the Y-coordiates.

I'll attach the excell sheet I used to keep track of the numbers I wrote down.

So with x and y, I'm comparing the number of mana points a regular character would gain at each level with the average amount of XP he should be spending on each one (equivalent to how much XP a BtN wizard uses). This way I can hopefully create a decent progression chart that I can show my players to say, "Look, you have 108 mana points, your next mana point costs [certain number] XP to buy."
 

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Another possibility is y=79.4 ln(x) - 71.6. It's almost as good a fit as bolen's (correlation=.958), and I think somewhat simpler than a third-degree polynomial (only two parameters, not four).
 

The Sigil can probably provide something. He's a math geek. One of his books has a logarithm equation in it. A first for a role-playing supplement, I'm sure of it.


I admire your gumption. I was thinking along the same lines as you - that where I wanted to go, d20-wise was to implement both systems, because they allowed the flexibility for the kind of game I wanted to run.

I decided that rather than trying to fix D&D, I'd look elsewhere.

Then I found HARP, and gave up trying to fix D&D.
 

bolen,

Is there a way I can input a number into that excell file to find the value for each integer? This way I can make a chart for my players to show them the progression cost for each mana point.

Thanks for all your help! :-)
 

sure just copy and paste. It bothers me that your numbers fluxuate the way they do (go up go down). This is not random data so why does there seem to be this fluxation. I think my poynomial or the logrithmic fit is a stop gap. If you really want this to be useful, you need to understand why this is.
 

Oh I didn't see the G 7 and 8 fields you made. :-) Thanks ,that works great. I'll make a chart of the conversion between the systems and post it here later on tonight.
 

orsal said:
Another possibility is y=79.4 ln(x) - 71.6. It's almost as good a fit as bolen's (correlation=.958), and I think somewhat simpler than a third-degree polynomial (only two parameters, not four).
This is likely to be as good a fit as any. The system I used in Buy the Numbers was done in increments of 5 XP and so will not track perfectly with a curve, but was meant to be an exponentially increasing system of cost - which means a natural log function (as provided above) should work nicely to marry it to a linear cost system. (It's been so long since I did my hundreds of "trial and error" tests to find a correlation that worked that I forget exactly what formula I finally came up with).

Oh, and I'm actually not a "math guy" but a "physics guy" - which means I would say make y = 80 ln (x) - 70 because it works to sufficient significant digits to keep me happy.


der_kluge
I also think it's funny that "putting a log function in an RPG book" makes me a pioneer of some sort. I don't decide to put them in, they just work and so they put themselves in. ;)

And as others have suggested, I'd love to see the full write-up once this has been done. :)

--The Sigil
 

The Sigil said:
Oh, and because I'm actually not a "math guy" but a "physics guy" - which means I would say make y = 80 ln (x) - 70 because it works to sufficient significant digits to keep me happy.--The Sigil

Where do you work and what do you do?

I teach at Univ of MS and work in GR.
 

bolen said:
Where do you work and what do you do?

I teach at Univ of MS and work in GR.
Heh... I got my degree in Physics at UC Irvine... so naturally, I work in the business insurance industry. ;)

(Hey, it pays the bills and feeds my kids).

--The Sigil
 

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