Help Me With A Math Problem

osarusan

osarusan

Explorer
For my game I'm combining EN World's Elements of Magic: Revised with S.T. Cooley Publishing's Buy the Numbers system. I've got almost all the kinks worked out but I'm having a bit of trouble figuring out an equation to convert the magic point system from EoM to the point buy system of BtN. The BtN system basically lets players spend XP to buy abilities, spell slots, feats, you name it rather than gaining levels. I wanted to make EoM compatible with this point-buy system. It's been four years since I took calculus and I don't remember how to do this kind of math problem. :confused:

I need someone to help me find the curve equation for the following points:

(5, 15.2)
(11, 12.3)
(17, 23.3)
(26, 24.4)
(35, 33.3)
(45, 51)
(56, 53.6)
(68, 76.7)
(81, 76.9)
(95, 89.3)
(110, 76.5)
(130, 95.5)
(152, 94.8)
(177, 114.8)
(205, 109.3)
(235, 125.3)
(265, 128)
(297, 149.1)
(332, 127.1)
(370, 132.2)

What the points represent is the number of magic points a spellcaster should have at each level (1-20), by the cost-per-point that I calculated from the tables in EoM and BtN. When I can find an equation that fits this set of points, that equation can be used to calculate the cost of each magic point the player wants to buy (where x=the number of points the player will have, and y=the cost of that point).

I know these points will not make a very good curve... in fact just picturing it in my head I can tell that it's going to look really really strange. But if someone who is decent in math can find an equation that at least comes near to this one, I'd be really grateful. :heh:
 

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B

bolen

First Post
Couple of questions

Is (0,0) a point?

What order polynomial are you looking for? (I just tried 4th for the hell of it)


Ignore the previous polynomials they are trash
 
Last edited:

osarusan

osarusan

Explorer
Yes, (0,0) is a point.

Basically, I'm trying to make a table of costs for mana points in an XP-based point-buy system. The cost to buy a mana point increases depending on the number of mana points that you have, so when you only have a few mana, you don't spend as much XP to buy the next mana point as you would if you had many many.

It's based off of a point-buy system where Wizards could buy their spell slots with XP points, thus customizing how many slots they had. I'm converting that system over to the Elements of Magic system, and converting slots into MP is where I've hit the snag.

(I really hope this makes sense... it's hard to know if I've explained that sufficiently, so please tell me if I need to clarify it more.)

For what I've calculated (from the two books I mentioned above which I am using to make this list), (x,y) x= the total number of mana points purchased, and y= the cost to buy 1 mana point at that level: Therefore, when you want to have up to 0 mana points, you spend 0 XP. When you want to have up to 5 mana points, you spend 15.2 on each one. When you want to have between 56 and 68 mana points, you would be spending 76.7 XP on each one. That progression is very jumpy and I'm looking for a simpler way to express it. (I know that the points are not good enough to make a decent curve. It will have to be simplified or smoothed into a decent-looking progression.)

I used Excell to plot the numbers, but basically that's all I know how to do in Excell. I know it probably the program I need to be using, but I'm not sure how to do it.

I hope this all makes sense... I'm trying to explain this at 2 am. ;-) One last run through: I'm making a conversion of Elements of Magic's mana-point casting system into the Buy The Numbers XP-based point-buy character creation/levelling system. I got these numbers by calculating the XP a BtM Wizard spends on his spell slots at each level and equating it to the amount of Mana Points an EoM Wizard would have at the same level (since these variant Wizards are roughly equal in power to eachother). What I want to do with these numbers now is figure out a general XP-cost progression for each mana point so the characters can buy as little or as many mana points with their available XP as they want.

What I've got so far would look like this:

1st mana point costs: 15 XP
2nd mana point costs: 15 XP
3rd mana point costs: 15 XP
4th mana point costs: 15 XP
5th mana point costs: 15 XP
6th mana point costs: 12 XP (weird little jump in the graph here, I know)
7th mana point costs: 12 XP
.
.
.
242nd mana point costs: 125 XP
243rd mana point costs: 125 XP
244th mana point costs: 125 XP

but I'd like to have something that looks more like this:

1st mana point costs: 10
2nd mana point costs: 11
3rd mana point costs: 12
4th mana point costs: 14
5th mana point costs: 17
...and so on.

The problem is that it needs to roughly follow the plot of points that I've listed in order to maintain game balance.

I hope this makes better sense. Sorry to ask such a confusing problem... :-S
 

E

Eltern

First Post
If/when you figure out this conversion SEND IT TO ME! :D I, too, have wanted to run a game with Buy the Numbers and Elements of Magic.
 


B

bolen

First Post
So if you accept a bit of error you should be able to use the equations that I generated above and do just that so use the 2nd equation and plug in your x values and out will pop y.

If you want to do something like this yourself just plug the numbers into excel and plot them. Then use regression analysis (it will ask you what order polynomial you want, just tell it)

Hope that helps, the equations above should be correct to around 1%. I should know exactly but I always have to look stuff like that up.

If I am talking mumbo jumbo, I am sorry and will try to explain better in the morning (It is late here)
 

osarusan

osarusan

Explorer
bolen, thanks for your help, although it's late here too so I'm not quite able to follow.

Er.. well... I understand what you're saying but I don't know how to do it, since I am an excell dummy (and its too late for me to be capable of figuring it out right now).

Perhaps tomorrow you could email me an excell file that's ready to go... or give me instructions on how to do this?

Btw, thanks so much for the really fast replying. My game is tomorrow afternoon and you're going to make my players so happy! :)
 



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