The Goal

I paid Ist + Gul + Pul + 28 pgems for a Vex.
Was that a good deal?
It beats the cube recipe...
but I also saw a game "vex 4 gul um" just a couple days ago...

Trading runes in Diablo 2 has always had a funny problem: everyone knows roughly what common trades look like, but comparing two piles of runes is harder than it should be.

2 lem may buy a pul
Pul + lem may buy an um
So um = 1.5pul, right?
But, an um may also command a price of pul + 2lem
I've personally made both trades several times, depending on circumstances.
So... um = 2pul? But no, earlier I showed um = 1.5pul...

The goal of a pgem equivalent value is to turn those common trade patterns into a single number. Instead of asking whether a particular combination of runes feels close enough, we can translate each side into pgems and compare them on the same scale.

Why Perfect Gems?

Perfect gems are small, familiar, and commonly used in rune trades. They are not a perfect currency, but they make a useful measuring stick because many players already understand trades like 40 pgems for a Pul.

Once Pul has a pgem value, nearby trades can help estimate Lem, Um, Mal, Ist, and so on.

The High Level Method

We have a bunch of very believable trades which are mathematically inconsistent:

• 40 pgems = pul
• pul + lem = um
• pul + 2lem = um
• 2lem = pul

So just like in excel, we try to find the best-fit line. But, instead of a line we find the best-fit n-dimensional space. The paper goes in to full detail about the math.

Initial Trade Sample Set

This is the initial set of common rune trades used in the paper. Each row is treated as one relationship the model tries to satisfy.

Initial Pgem Values

The values below are the initial model results from the paper. This example continues with 40 pgems = Pul. The initial sample set starts at Lum, so lower runes are not assigned values here.

The White Paper

If you want the full math, including the example equations and the best-fit linear algebra approach, read the original paper:

On the Calculation of a Perfect Gem Equivalent Value for all Rune Combinations in Diablo 2