Formula for bonus structure calculations

[FadingSuns]

Snakeye, I'm lovin you man! Finally a formula that makes sense even to someone mathmatically impared like myself. Oh, on an earler message from Slynky: I've got plenty of stats people around me at work too.. none play SE4. What a drag.

[snakeye]

Originally posted by Slynky:
So, did you really use a "real time" example with a real ship? If so, what was the cost of building the ship? Given that, a person could come up with a scale on how many months a person had to have it in service (at the asteroid) at a certain percentage in order for the ship to "pay for itself" and begin "sending back" a profit.

(yeah, I know, I know...git off yer back, right? )

No its ok! I appreciate the comments and suggestions. Cost of building is something I didnt includ in the formulae because there can be no standard relation to cost and profit-over-time. The reason for this is that there are other factors to take into account (productivity, research of new techs that make ship obsolete, accidents, attacks, etc). The formula assumed the ship will be in operation for the end of days. In other words, IF I was to build a ship that would Last forever, be used forever and able to mine forever, what would be the minimum asteroid to mine for the given resource. Since your questions, I started thinking about the initial submitted formula. I think as a general gauge is quite solid! With that, I can calculate quickly how much more I would gain if I installed a system-wide bonus facility, and can use the same formula for research, intel, production. As far as building a remote mining ship goes, then you have to tell me how soon would you like the ship to "pay for itself" as far as the given resource is concerned. If we assume that you would wish to "pay" for the given ship in one turn after its operation then the formula can be modified to:
IF
C=%of bonus from an asteroid
MC=Maintenance cost
BC=Building cost
N=number of miners onboard
A=mining value per turn of miner
then we have
C>(MC+BC)/N*A
Going back to the previous example of the mining ship, if it's cost for minerals is 6500, maintenance is 487 minerals, has 2 mineral miners for 700 per turn each then:

C>(6500+487)/2*700 or C>4.99 or C must be greater than 500%!!! Since there is no asteroid in the game that will have that, we can settle for a ship that will pay for itself in a many turns as it was built. In the case of the above ship, I used a level II shipyard ship to construct my base(yes the ship is actually a base) with rate of 1650 minerals per turn. Substituting this to the above we have:
C>(1650+487)/2*700 or C>1.5264 ~ C>153%
So in order to produce enough to pay for the ship in as many turns as it was built, I will have to aim for any asteroid with a bonus to minerals of 154% or above. You can understand from this formula, that I chose when I want to pay for the ship. This was a choice rather than a rule. Different ppl might have different demands. But by adding the cost in the above equation, we can see quickly if its worth building a mining base with 2 mineral miners or a small ship with one. Hope you find this helpful.

[Loser]

Snakeye you are incredible, I love to see the arithmetically capable do their thing. Your formula for facilities is great.

There are a few more things, however, to take into account where Remote Mining is concerned.

1. Cost of the construction vehicle.

2. Cost to get there. (Turns of movement to proposed station location X construction ship maintenance.)

3. Cost while there. (Turns of station construction X construction ship maintenance.)

4. The value of an asteroid decreases over time. (For this reason it may be a good idea to include a self-destruct device on the mining station, so you can get rid of it when it no longer produces more than it costs in maintenance.)

5. Cost afterward. (Continued maintenance of construction ship until it starts doing something useful again (like heading to the next asteroid, when maintenance should be 'billed' to the next station) Remember to account for taking the construction ship back to a Resupply Depot somewhere in your calculations, if you intend to use the ship for a while.)

This is in addition to those elements you have already isolated.

6. Initial cost of mining station.

7. Maintenance of mining station, a function of 6.

8. Mining station's unmodified production, almost a function of 6. (Really a function of the components of the ship, of which 6 is also a function.)

9. Asteroid's starting production modifier.

After all of this, one could put together a separate formula for the maximum viable distance from planet-side shipyard (or Last station) to proposed station site, maximum construction ship cost, maximum station cost, and minimum asteroid value for any given set of the remaining values, for the proposed station to become profitable at all, ever or to be come profitable in a specified number of turns.

If you have the time, patience, and motivation to put all of this into a spreadsheet (with graphs, in all five involved dimensions, with twenty-four color glossy photos with the circles and the arrows and the paragraph on the back of each one explaining what each one is for), then you are truly an amazing human begin.

If you just want to lay out the formulae for us, with your usual, readable, reasonable explanation then your just a damn cool guy.

So says me.

[Slynky]

Originally posted by Loser:
...twenty-four color glossy photos with the circles and the arrows and the paragraph on the back of each one explaining what each one is for),...

Hey, "Arlo", I think you just showed your true age... .

[Loser]

Originally posted by Slynky:

quote:

---

Originally posted by Loser:
...twenty-four color glossy photos with the circles and the arrows and the paragraph on the back of each one explaining what each one is for),...

Hey, "Arlo", I think you just showed your true age... .

---

Whoa... just because I'm in touch with the past doesn't mean I'm all that old. My real birthdate is in my profile.

I swear, kids these days have no sense of History...

[Slynky]

Originally posted by Loser:

quote:

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Originally posted by Slynky:

quote:

---

Originally posted by Loser:
...twenty-four color glossy photos with the circles and the arrows and the paragraph on the back of each one explaining what each one is for),...

Hey, "Arlo", I think you just showed your true age... .

---

Whoa... just because I'm in touch with the past doesn't mean I'm all that old. My real birthdate is in my profile.

I swear, kids these days have no sense of History...

---

Well ! That'll teach me to make use of my limited detective abilities.

[Stone Mill]

Nice job snakeye. Welcome. This is a solid concept to grasp. I tend to think economics are very critical in SEIV...

[snakeye]

I have finally created a formula to calculate the benefit for remote mining taking into account cost of the vehicle, maintenance of both the constructor and vehicle. I have a excel spreadsheet also for it. Will update forum very soon with my results. My formula calculates the turns before a Remote mine structure or ship pays off all the ovberhead and for how long you can operate it till the overhead from maintenance is more than the profit, and it works for both ships and bases, decaying asteroids or static ones

[Loser]

Originally posted by snakeye:
I have finally created a formula to calculate the benefit for remote mining taking into account cost of the vehicle, maintenance of both the constructor and vehicle. I have a excel spreadsheet also for it. Will update forum very soon with my results. My formula calculates the turns before a Remote mine structure or ship pays off all the ovberhead and for how long you can operate it till the overhead from maintenance is more than the profit, and it works for both ships and bases, decaying asteroids or static ones

Woot.

[snakeye]

Ok here it goes!

Lets assume the following:
Pr=Production of an asteroid at any given time
Ov=overhead for production [total, will explain further below]
A=production of a mining component[for a resource]
N=number of components on board
P=starting percent bonus of asteroid [for a resource, ie 10%=0.1, 150%=1.5]
T=number of turns currently since the remote mining ship was operational
D=degradation degree. Normaly its a steady 0.01 per turn, but it can also be zero or any value for that matter.
Vm=maintenance cost of the vehicle that will perform the mining
Cm=maintenance of the vehicle that will build the mining vehicle, ie for a ship is anything, for a planet is zero
Tm=turns to move construction vehicle to position, ie for a ship could be from 1 to any, for a ship yard is zero
R=rate of building the mining vehicle. Calculations assume a STATIC value! If the contruction is conducted by a ship, then it is a fixed rate by default. If its constructed via a planet assumes a static [max if you like] population has been achieved.
Vc=mining vehicle cost

The overhead discussed above is:
Ov=Cost_to_move+Cost_to_build+Cost_of_remote_miner or

Ov=Cm*Tm+Cm*RNDUP[Vc/R]+Vc

We also assume the following:
-Player has at least one ship with a shipyard component on. The cost and build time of this ship falls outside the scope of the calculations here.
-Player has already built the ship that he is going to construct BEFORE, so the maintenance cost is known. [sorry guys, thats the only way i know how to get the maintenance values. if someone has a better way, please let me know!]

At any given time, the production on an asteroid is:

Pr1=A*N*P1-Vm

next turn it would be:

Pr2=A*N*P2-Vm

On the T turn it would be:

Pr[T]=A*N*P[T]-Vm [1]

Total product would be the total of the two sides of the equation, or:

Pr[total]=A*N*[P1+P2+...+P[T]]-T*Vm [2]

Now the sum P1+P2+...+P[T] is known since P2=P1-0.01, P3=P2-D or P3=P1-2*D, P[T]=P[T-1]-D or P[T]=P1-[T-1]*D. Replacing on [2] we have:

Pr[total]=A*N*[T*P1-[T-1]*D}-T*Vm

The above will give us the total production for a given resource on an asteroid AFTER turns T have elapsed. Since we want to find out after how many turns the output would have paid off the overhead Ov, we have:

Pr[T] must be equal to Ov[T] or more accurately:

A*N*[T*P1-[T-1]*D}-T*Vm must be equal to Cm*Tm+Cm*RNDUP[Vc/R]+Vc. Solving the above we have:

T=[Ov-D*A*N]/[A*N*P-D*A*N-Vm] [3]

After the above turn, the profit will be "clean" and will have paid off the initial cost.

But equation [1] has another use. We can derive the turn T at which the overhead of maintenance [excluding the initial overhead], is greater than the profit, due to asteroid degredation.

From [1] we have:

Pr[T]=A*N*[P-[T-1]D]-Vm must be greater or equal than zero or

A*N*[P-[T-1]D] - Vm >= 0

or A*N*[P-[T-1]D] >= Vm

or

T =< ROUNDUP[[A*N*P+D-Vm]/[D*A*N]] [4]

That is the Last turn that the remote vehicle will give some profit from a degrading asteroid. If the turn calculated by the [4] is less or equal to the turn calculated from the [3] then you have a very unworthy asteroid!!!!! I would upload the excell spreadsheet for all this [ so you guys can just use the thing!] but dont know how and where! Hope someone can help. Hope this is any use to anyone! But I sure had fun working it out, and yes I do use my spreadsheet since I created it! Best regards to all!

[ May 06, 2003, 14:08: Message edited by: snakeye ]