## MER

**Maximum Extraction Rate of Influence Asteroids**

##### Originally developed by protoplanetary (Foreword by Markus Korivak)

###### Asteroid bonuses increase their MER, moving them above the unbonused white line. Graph provided by trevis of Influence Sales.

### Foreword:

#### What is the Best Way to Determine the Value of an Asteroid?

##### Surface Area (or “Size”)

The most basic way of estimating a value is by using the Surface Area. This is very easy to find, and has a huge impact on the utility of an asteroid. Every square kilometre of surface area is the possibility of one more drill, one more building, one more warehouse, one more lease.

No matter how rich a 13km² asteroid is, it can eventually be out-produced by a much poorer asteroid with room for twice as many drills (assuming you can source and ship and run twice as many drills, of course).

##### OBF: Overall Boost Factor (or “Rarity”)

But how do you compare smaller-but-richer asteroids against larger-but-poorer asteroids, then?

This is where the OBF comes in. This is much more complicated than looking up the Surface Area, but there are community tools that will automatically calculate it for you. The math included below is for people looking to understand exactly what is happening behind the scenes. Personally, I am presenting the math exactly as it was presented to me; I am a cartographer, not a mathematician.

The basic idea is that you add the number 1 and all of the bonuses on the asteroid into a single number that is slightly larger than one, which when multiplied by the Surface Area gives you a “Common-Equivalent Surface Area”, or essentially how much larger a Common asteroid would have to be to have the same theoretical resource output.

If that sounds a little complicated, that’s okay. There are tools that will do this for you. And this is the real workhorse piece of MER, since it is allowing us to compare any asteroid of any spectral type, of any size, of any combination of bonuses to any other asteroid with a completely different set of all those variables.

##### MER: Maximum Extraction Rate (or “Utility”)

Okay, a little overwhelmed by that last step? Good news: it gets easier. Here’s the calculation for MER:

MER = Surface Area x OBF

That’s it!

Now, this is a purely hypothetical “maximum”, since it would actually be impossible to have an asteroid where *every* plot had a drill on it, and it does gloss over the boots-on-the-ground level of detail with Traits, Skills, and Core Samples. But that’s okay, because this is about comparing asteroids to each other, not for planning exactly how much cargo space you need to get all your paydirt to market.

##### Utilities (or "I Don't Want to do the Math")

- Influence Sales (https://www.influence-sales.space)
- Influence Sales Data Discord Bot (Influence Sales Discord)
- Tyrell-Yutani Industrial HUB (https://tyrell-yutani.app)

### The Math:

#### How to Calculate the MER for an Asteroid

- Collect your ingredients for the given asteroid: spectral type, surface area, the yield boost, and the five resource-class-specific boosts. These boosts should all be scalars that are 1+. For example, a yield of 6% is 1.06 as a scalar. A Metals boost of 50% is 1.5 as a scalar. If the asteroid doesn't have that resource, just leave it at 1.
- Get the list of abundance factors for each resource class for your asteroid's spectral type from the Spectral Resource Abundance Table (see below). These abundance factors are again scalars, this time between 0 and 1.
- Multiply the five boost factors by the five corresponding abundance factors, and sum the result to one value "Sum of Weighted Boosts" or SWB. (This is the dot product of the two vectors.)
- OBF (Overall Boost Factor) = Yield x SWB.
- MER = Surface Area x OBF.

#### Spectral Resource Abundance Table

Type | -Organics- | -Volatiles- | -Metals- | -Fissiles- | -Rare Earths- |
---|---|---|---|---|---|

C | 0.667 | 0.333 | 0.000 | 0.000 | 0.000 |

Cm | 0.200 | 0.200 | 0.400 | 0.200 | 0.000 |

Ci | 0.500 | 0.500 | 0.000 | 0.000 | 0.000 |

Cs | 0.200 | 0.200 | 0.200 | 0.200 | 0.200 |

Cms | 0.167 | 0.167 | 0.333 | 0.167 | 0.167 |

Cis | 0.167 | 0.333 | 0.167 | 0.167 | 0.167 |

S | 0.000 | 0.000 | 0.333 | 0.333 | 0.333 |

Sm | 0.000 | 0.000 | 0.500 | 0.250 | 0.250 |

Si | 0.000 | 0.400 | 0.200 | 0.200 | 0.200 |

M | 0.000 | 0.000 | 0.750 | 0.250 | 0.000 |

I | 0.000 | 1.000 | 0.000 | 0.000 | 0.000 |

#### An Example

Say I have a 650km² Cm-type asteroid with 3% Yield and a 10% boost to Metals.

- Surface Area = 650. Yield boost = 1.03. Resource-class-specific boost factors: Bo = 1.0, Bv = 1.0. Bm = 1.1, Bf = 1.0, Br = 1.0.
- From the chart for a Cm type asteroid, abundance factors: Ao = 0.200, Av = 0.200, Am = 0.400, Af = 0.200, Ar = 0.000.
- SWB = A•B = 1.0 x 0.2 + 1.0 x 0.2 + 1.1 x 0.4 + 1.0 x 0.2 + 1.0 x 0.0 = 1.04.
- OBF = 1.03 x 1.04 = 1.0712 (= 107.12%).
- MER = 650 x 1.0712 = 696.28.

So, this asteroid of 650km² with bonuses can potentially yield the same amount of resources as a common asteroid of about 700km²

### Appendix A:

#### protoplanetary’s Thoughts on MER

- Maximum Extraction Rate (MER) equals Surface Area times yield times the sum of the spectral abundances for that spectral type, weighted individually by the corresponding boosts for that rock. So basically a measure of the max rate at which you can extract resources, and hence value, from the rock (assuming all resource classes are equally valuable, and that you fully utilize the rock for mining.)
- So when MER/ETH is high, that means you are purchasing a larger amount of possible output for less money, i.e. a better deal. Or put another way, an asteroid is literally a token representing your right to extract resources, and that right has a certain magnitude, which I postulate corresponds more-or-less directly with the token's value (from a utility perspective). And MER is designed to capture the magnitude of that right, and hence the asteroid's value.
- Also of note: MER by far most highly correlates with surface area. Boosts are included at exactly the percentages they say they are, but they turn out to be surprisingly unimportant in the scheme of things. A rock that has just 1.32x the radius of another ( = sqrt(1.15 x 1.5) ) can produce more output than the other,
*even if the other has every single boost at maximum*. - One small but potentially useful addition I might make: define OBF = Overall Boost Factor = SWB x Yield. This dimensionless factor is the closest approximation to how actually boosted an asteroid is, in one number. Of great note, an asteroid's listed rarity is
*not*terribly highly correlated with its OBF, because the listed rarity simply counts the number and level of boosts, not their compounded effect on overall boost, and definitely not how that plays with the spectral type, all of which OBF does.

### Appendix B:

#### trevis’ Explanation of OBF and MER

OBF is Overall Boost Factor, it corresponds to an approximation, based on the data we have and some small simplifications, of the global effectiveness of the rock plots to be mined for their resources. The base value is 1 and can be higher depending on scanning results.

- With a 6% yield boost, it becomes 1.06.
- Or, with a 10% bonus to a resource representing 50% on what can be found, it would be 1.05. MER is the asteroid's Surface x OBF, so it is also measured in km².

Say there are two asteroids of the same spectral type, with all plots occupied by the same buildings and focused only on mining.

- Rock A has 1000 plots (each plot is 1km²) with a 6% yield bonus. MER = 1060.
- Rock B doesn't have any bonuses (so OBF=1) but has a surface of 1060 km². Its MER is also 1060. You can see that even though they have different surfaces, as Rock A is boosted, both asteroids could deliver the same amount of resources per day of mining.

That's why I refer to the MER also in terms of "Effective Surface", and why its dimension is km². To me, the MER is most useful in the context of assessing the price of an asteroid, to calculate cost vs utility in game.

- Sometimes there are "Superior" class asteroids that would have more productive plots than "Exceptional" ones, because their bonuses are a better fit to the rocks available resources. (E.g., +20% of whole rock is better than +50% bonus for a resource found only in 10% of the rock).
- Sometimes a rock is 10% smaller than another one for the same price but with its boosts it would be 10% more productive, and thus probably better. So, with the MER/ETH ratio, you can compare offers more robustly, with respect to in-game utility.

###### Influence is developed by Unstoppable Games. Asteroid data provided by Adalia.info.