Pricing model of equipment according to stats

This game has not been invaded by quants yet, I assume. In this thread, I will attempt to derive a general idea of a pricing model for eqs with respect to their stats.

In this game, the types of scrolls are:

• 100% scrolls, which are absolute junk most of the time
• 60/70% scrolls, which give the same average stats
• 10/30% scrolls, which gives amazing stats
• chaos, ws and css, which complicates everything a little bit

The idea is that we can form equations of value relating stats of eqs and their price. Let f(x, s) be a function of the price of our desired eq, and x is the stat/stats that affect the price of an eq the most, and s is the number of slots left. Also, let p(pct) be the price of a scroll usable to the eq, e.g. p(60% wand ma) = 200k. Let t and t* be the amount of added x when a 60/70% and 10/30% scroll passes respectively. To give an example:

If we are interested in the price of a wand, it is determined by its tma:

• f(x, s) where x = tma
• p(60%) = price of wand ma 60% = 200k, p(10%) = 600k etc
• t = 3, t* = 8, as passing each 60/70% and 10/30% scroll increases tma by 3 and 8 respectively

Then, whenever possible, we can form the following equations:

• f(x, s) + p(60%) = 0.6*f(x+t, s-1) + 0.4*f(x, s-1)
• f(x, s) + p(70%) = 0.7*f(x+t, s-1) + 0.15*f(x, s-1)
• f(x, s) + p(10%) = 0.1*f(x+t*, s-1) + 0.9*f(x, s-1)
• f(x, s) + p(30%) = 0.3*f(x+t*, s-1) + 0.35*f(x, s-1)

And they are for the most basic 60/70/10/30% scrolls. More equations can be formed with the other scrolls. Note that for a piece of stat, there can be many implied prices. I propose that, as a rational maplelegends player, the price of a scrolled equipment would be such that it is the minimum price out of all implied prices:

f(x, s) = min for all scrolling possibilities of f(x, s)

Yea, so that's the basic idea. I do have a spreadsheet made for this, but it's not very complete. Also, a condition for comonotonicity of stats/slots should exist somehow which I do not know of (because I'm getting negative values in my spreadsheet).

Very useful assumptions/extensions when using this model:

• Assume prices as the lowest price such that item sells instantly, and then put a premium on top of scrolled item prices.
• Assume that the prices of scrolls/equipments stay constant and you don't affect the market in any way, or just assume that you do affect the market and input a higher price of the scrolls
• Sometimes prices of equipment are determined by more than 1 stat e.g. dex and luk, a higher dimensional table might be needed, if you're such a nerd like me

That's it for this post, I hope it has a good balance between length/depth (that's what she sa...). Feel free to reach out to me if you have any questions/ideas!