Mineral Price Equilibrium

I wrote about this in general a couple weeks ago but wanted to lay out the math for posterity, as it were.

There is currently a lot of complaining going around about the mineral prices in Eve. Nullsec people complain about the tepid income. Highsec people complain about the flight to hi-sec manufacturing. No one thinks the mineral prices are "right" (for some definition of right) and we have a wonderfully bitter divide between the l33t SOV owners and the carebear empire dwellers. Both side thinks the other is ruining "their" game.

But looking at the mineral prices, is it possible that we're just victims of the values CCP chose when creating the universe? Rocket scientists don't typically complain about escape velocity because it smacks a little too much of complaining to God about his value for g. This is kind of the same thing.

Here's the exercise that you can do at home as you play along.

Veldspar and Scordite work very well to establish a strong price relationship between Pyerite and Tritanium. If you mine out a belt of random minerals, about half of the Tritanium you mine will be from Veldspar and about 27% will be from Scordite. Scordite will also provide 56% of the Pyerite. So these two ores represent the lion's share of those minerals from mining (though, it's possible, not from all sources... we'll get to that in a minute).

Given that Tritanium forms the backbone of industry, it's not unreasonable to establish everything in terms of Tritanium. Because we know that Veldspar and Scordite are equally ubiquitous (appearing in every system regardless of security status) and they each provide a majority of the two most frequently used minerals (i.e. their demand is very, very high) we should comfortably find that they are worth the same amount. And they're close, Scordite is about 15% more valuable then Veldspar at present (on a per m3 basis which is how mining works). Each m3 of Veldspar makes 30.03003 of Tritanium. Each m3 of Scordite makes 16.67667 units of Tritanium and 8.32833 units of Scordite. We know that these two should be roughly equal so (incoming math!):

30.03003*T = 16.67667*T + 8.32833*P
where T is the value of Tritanium and P the value of Pyerite. By simplifying we get
13.35335*T = 8.32833*P
1.60337*T = P

So the value of Pyerite SHOULD be about 1.60337x Tritanium price

Currently, it's not. It's actually a fair clip off of this but we'll get to that.

You can repeat this for all the ores. As it turns out, Mexallon is largely supplied by Plagioclase (using P = 1.60337*T and plugging in we get M = 9.46514*T) and Isogen comes in decent quantities from Kernite (yielding an implied value of 18.1127*T for Isogen).

Because of the distribution of ores, however, it isn't necessarily fair to group them all together, and here's where it gets complicated. Plagioclase only appears in .9 and lower security systems. That's a very, very minor difference between the availability of Veldspar and Scordite so we can hand wave it away without significant problems. But Kernite is only in .6 and lower space and even then only in about half the galaxy. The other half of the galaxy gets Pyrox. The high-ends become likewise difficult as they have nowhere near the availability of the lower end stuff. So what do we do? Well, Excel and Math (hurray!) have combined to give us a great solution, matrix multiplication. As it turns out, this is simply a difficult algebra problem and matrix multiplication is perfect for that.

I've created an excel sheet with all the ores as well as 9 different bands. Why 9 bands, you ask? Well, it turns out that matrix multiplication needs to be square. There are 15 ores so a full matrix needs to be 15x15 and 9 bands are needed because our inputs are going to be the "band" of the ore and then the price multiplier of the mineral. The astute reader has already noticed that 7 (the minerals) plus 9 (the bands) is 16... not 15. The answer is that we're going to peg everything to Tritanium in value and thus remove it from the equation. Essentially, I've decided by econometric fiat, that I don't care about the value of Tritanium relative to Isk. I only care about Tritanium relative to everything else.

So once you do that, you have to decide what band each ore is in. I established the following:
Veldspar, Scordite, Plagioclase: Band 1. These are ubiquitous and nearly always available.
Pyroxeres: Band 2 (limited to about half the galaxy but still hi-sec available)
Kernite: Band 3 (ditto Pyroxeres comment)
Omber, Gneiss, Spodumain: I know that Omber is a hi-sec ore and Gneiss and Spodumain are not. But the fact is that none of these are worth mining right now. If you replaced every belt in Jita with Omber, Gneiss and Spodumain, you'd probably have Jita asteroid belts stay populated all day. They're just that bad. So they get a band for themselves.
Jaspet, Hemorphite, Hedbergite: These 3 are the "good" low-sec ores. They appear in low, low-sec and are fairly frequent in null-sec. They aren't the "big time" stuff of the ABCs but they're still reasonably valued and mined. They also share duty for supplying the galaxy with Nocxium (and a not insubstantial volume of Zydrine) so they're one band.
Dark Ochre: The forgotten "D" in ABC"D" ores.
Crokite: Band 7
Bistot: Band 8
Arkonor: Band 9

You could argue that at least Arkonor and Bistot should be together as they're kind of polar opposite ores in terms of quantity of Zydrine and Megacyte provided. But there is regionality to them (significantly less now that anomaly mining has become the null-sec norm but regionality nonetheless).

Once you do that, you invert the big matrix, multiply by the Tritanium ratios from the ores and, wa la, you get the expected value ratios for both the minerals AND for the ores.

Mineral (algebraic, idealized ratio to Trit) / [actual ratio to Trit]
Tritanium: (1) / [1]
Pyerite: (1.603365) / [2.174194]
Mexallon: (9.465144) / [10.40688]
Isogen: (11.79592) / [19.22667]
Nocxium: (74.11183) / [105.0475]
Zydrine: (126.7146) / [115.0475]
Megacyte: (368.5216) / [348.904]

Create a spreadsheet that shows all the ores (there are 15, not counting Mercoxit). Some really shocking things are implied by the current prices. Scordite is more valuable than both Bistot and Arkonor. Veldspar is more valuable than Crokite (although that particular result isn't actually that shocking, the algebraic equilibrium had Veldspar 10% more valuable than Crokite anyways). So we have to look at the reasons why this would be. There are two: Bottlenecks and alternative mineral sources. I'll post about those tomorrow.