Equation behind the prices of starfinder gear?

[Michael Haneline]

So, I made a chart of the approximate average price of each level of item in starfinder using both weapons and armor as reference. When I plotted them on a graph, they formed a very clear curve. However, I cannot figure out the equation behind it, and though I used to know how to find that using statistical analysis software in college, I have since forgotten.

What equation to the following prices seem to be following?
1: 250
2: 600
3: 1300
4: 2300
5: 3000
6: 4300
7: 6500
8: 9000
9: 13000
10: 17000
11: 25000
12: 35000
13: 45000
14: 75000
15: 110000
16: 165000
17: 245000
18: 390000
19: 550000
20: 810000

[grudgekeyper]

You could fit the curve to an appropriate polynomial equation however the numbers don't seem to follow a straight forward equation given the difference doesn't increase steadily as seen between values list in 2-5th level

2-3 diff: 700
3-4 diff: 1000
4-5 diff: 700

[J4RH34D]

Fifth Power Series Equation

y = 2.0002x^5 - 68.891x^4 + 908.68x^3 - 5233.2x^2 + 13149x - 9553.2

R² = 0.9997

Exponential Graph Equation

y = 344.41e^0.3891x

R² = 0.991

~~~~~~~~~~~~~~
The R² value is how close the line of best fit plots the data.
99.1% is pretty dame close.
99.97% is even closer

~~~~~~~~~~~~~
If you plot in excel you can get it to give you the line of best fit

[Michael Haneline]

J4RH34D wrote:

Fifth Power Series Equation

y = 2.0002x^5 - 68.891x^4 + 908.68x^3 - 5233.2x^2 + 13149x - 9553.2

R² = 0.9997

Exponential Graph Equation

y = 344.41e^0.3891x

R² = 0.991

~~~~~~~~~~~~~~
The R² value is how close the line of best fit plots the data.
99.1% is pretty dame close.
99.97% is even closer

~~~~~~~~~~~~~
If you plot in excel you can get it to give you the line of best fit

this is exactly what I was looking for, thanks

[NielsenE]

You'd probably get better results, if you don't average different categories of gear together. For instance in Pahfinder, armor and weapons enchantments follow a different progression. I would expect the same to be true here. So your averages get corrupted as the percentage of armor/weapons vary at each level.

[Michael Haneline]

NielsenE wrote:

You'd probably get better results, if you don't average different categories of gear together. For instance in Pahfinder, armor and weapons enchantments follow a different progression. I would expect the same to be true here. So your averages get corrupted as the percentage of armor/weapons vary at each level.

The same is not true in starfinder. Armor of the same level is priced roughly the same as weapons of the same level. Items of the same level aren't priced exactly the same, different weapons of the same level cost more or less than each other, but it seems to just be random variation or something for the sake of making it look more realistic.

[Ravingdork]

Which is hardly realistic at all.

[NielsenE]

I'd still say if you're looking for the underlying cost equation (assuming there is one) you generally need to look at classes of equipment in isolation. The fifth order equation is definitely over-fitting. The exponential doesn't look like like something a game designer would design.

In general, this time of system tends to like n^2 scaling. Figuring out what the 'n' is would be more useful. I doubt its actually the item level -- might be the number of dice for weapon damage, might be modified by the capacity/usage. Crit effects/weapon damage type might be a flat modifier to that as well.

I'd probably start with just one class of weapons (say long arms), fit a simple n^2 for item level and separately for number of dice, and see which is closer/needs fewer tweaks. Then see if the tweaks can be explained by "bad/good" traits/capacity that affect the n up/down.