Formula for bonus structure calculations
 

Hi all,

This is my first post to the forum, so a big hello. May I take this opportunity to say how great game this is.

Anyway, the other day when I was playing, I noticed that my research started discovering structures that give bonuses to Research, Mining, Intelligence, etc. But I thought in order to build them on a planet I have to waste 1 facility. So I was looking to find after what number of those facilities, one can add a bonus facility and get a better output in research, production, intelligence, etc, than if he simply had one of those facilities instead. So i developed a formula ( yes I am that sad, but it was fun):

Lets say you have a planet that has mineral, organics and radioactive production >100%. So you decide to make this a research planet, full with research centres. If the number of available facility slots is N then your research production on the planet BEFORE any racial bonuses would be RESEARCH_POINTS_PER_FACILITY X N. So far so good, right? Lets say you have a facility that gives you a bonus in reseach on the planet, ie 20%. You want to know whether by replacing one reseach station with one of these would give you more, less or the same. Cut long story short, the formula to calculate this is:

N=number of facilities set aside for research
B=number of facilities slots LOST due to building of bonus structures
C=percent of the bonus all bonus facilities give on the planet.

N>(B*(C+1))/C

Can you see something strange on the above? It matters NOT whether your facility gives you 600, 800 or 100000000 points! What matters is how many facility slots you will loose by constructing bonues structures in their place and the TOTAL percentage of the benefit.

For the above example if we assume that we have research centre II (600RPs) and a central computer complex (30% to research on planet)then we will have:
B=1 we loose one facility slot to the central computer complex
C=0.3 (30%)

N>(1*(1+0.3))/0.3 or N>4.33333, ie N>4. We must therefore have atleast 5 research centres in the planet BEFORE we can build a bonus structure and get more than what we would normaly get by just adding another research centre.

As you can see from the above, the formula can be used for anything and not just research. And since the percentage of bonus and number of facilities if seperate, you can use it to calculate the same N for 1,2... bonus facilities and their bonuses.

Hope this wont get me flamed and I dont know if anybody has said/used/posted this before. Hope it helps.

Re: Formula for bonus structure calculations
 

Good calculations Snakeye, welcome to the forums.

We do get a few number-crunchers in here who have come up with similar things in the past, but it's always good to be reminded.

Where it gets complicated is with the resource production multipliers, when you factor in the cost of the thing vs the extra resources it produces, and the time spent building it vs the time you could have spent mining if you'd put a producer there instead.

Re: Formula for bonus structure calculations
 

<font size="2" face="Verdana, Helvetica, sans-serif">AGHHHHHHHHH! DAMN YOU ARE RIGHT! Apologies! The reason for this is because I developed the formula for research and applied to production. For research, maintenance cost doesnt matter since it doesnt affect research points. But if you were to apply this to production, you will have to take into account the maintenance! Well spotted and corrected! BACK TO THE DESIGN BOARD! Thank you! (will still use it for Intelligence and Research since it applies though. Will you think I am ultra sad if I was to say I have a spreadsheet with it already!?)

Re: Formula for bonus structure calculations
 

Yeah, snakeye, get busy and develop one for remote mining that factors in building costs of the ship, maintenance cost of the ship, supplies (if applicable), and the minimum percentage an asteroid belt has to be before there is any mining advantage/gain. http://forum.shrapnelgames.com/images/icons/icon10.gif

Re: Formula for bonus structure calculations
 

Slynky, I know you are just pulling his leg, but you know.... a formula like that about mining really would be helpful!

Re: Formula for bonus structure calculations
 

<font size="2" face="Verdana, Helvetica, sans-serif">Well, kind of... http://forum.shrapnelgames.com/image...s/rolleyes.gif

But, like you said...it would be nice to have. I just thought I would "throw" something complicated at him in case he was a diehard bean-counter. (we have an office of bean-counters and one statistician but, wouldn't you know it, NONE of them play SE4 http://forum.shrapnelgames.com/images/icons/icon9.gif )

Re: Formula for bonus structure calculations
 

before anyone puts too much work into this (unless you really enjoy this kind of thig snakeye) I would suggest a quick search of the forums. I know for a fact that much of this work has already been done.

Re: Formula for bonus structure calculations
 

Well!!!! Let it not be said that I am a guy that does not enjoy a challenge! Here are my latest findings.

I thought that structures have maintenance cost but apparently they dont. So the initial formula will work for every kind or production, be it Mineral, intelligence or Research! ( http://forum.shrapnelgames.com/images/icons/icon7.gif )

Now! You guys gave me an idea about Remote mining. In the past I used to build Remote mining ships only for asteroid belts with Resource_PCT > 100%. Since I read your post, I thought to examine if my assuption was logical. This is what I found. I normaly build mining bases rather than ships, but what I will say applies to either.

In order to determine whether is beneficial to build on an asteroid or not, one can look to the individual resource (ie minerals) or the total. After examining this fact, I came to the conclusion that taking the total of an asteroid is pointless and not really useful. For example I might be mining on an asteroid with 135% Mineral, 50% Organic and 10% Radio. I know my ship needs radio to maintain, but I dont care spending it since I am after the 135% mineral bonus. In view of that, it would be safe to assume we would need a formula to calculate what would be the ideal % of an asteroid before we place a REMOTE MINER COMPONENT to harvest the particular resource. Lets assume we have an asteroid belt with stats:
135% Mineral, 40% bio, 60% Radio.
I would like to know IF its worth sending a ship with a Mineral mining component on to harvest minerals and what would be the min % bonus I would require (did i undestand your request successfully?). So here it goes:

if C = the bonus in percent
MC = maintenance cost of the ship AS FAR AS the resource harvested is concerned
and A = the amount of material produced by the component AS FAR AS the resource harvested is concerned
and N = number of such components on the ship
we have:

C>MC/(N*A)

This means that in order to gain advantage of an asteroid the % bonus for the material has to be greater than its MaintenanceCost divided by the product of components with their output. One can verify the formula roughly like so: if we increase the number of components N then the product of N * A becomes larger, but MC/N*A becomes smaller, hence a smaller percentage is enough to give us profit from the mining.

Real game example:
I have a ship that containts 2 mineral miners, 1 organic and 1 radio. The maintenance of the ship is 487mineral, 59 organic, 71 radio. Whats the ideal asteroid for my ship?

Answer:
Using the above formula I have:
C(mineral)>MC(mineral)/N*A

since i have 2 components N=2 and they give me 700 each in minerals. So i have:
C> 487/1400 or C>0.34 or C>34%. In otherwords, I will have profit from the asteroid as far as minerals go, for as low bonus as 35%. To verify this we have 1400 * .35 = 490 which is greater than 487. Of course, building the ship would require time and materials so something as low as that its not really viable, but gives you an idea on how low it can be before you actually make profit on it. It came as a surprise to me since I never build on anything less than 100% bonus

Re: Formula for bonus structure calculations
 

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? http://forum.shrapnelgames.com/images/icons/icon12.gif )

Re: Formula for bonus structure calculations
 

There is no maintenance cost for any facilities. DS just meant the build cost. But, that is not a good way to compare them, because the increased production rates offset the build cost of Robotoids and such very quickly. You lose at most 4 turns of production from a mineral miner when building a planetary Robotoid, and System Robotoids provide so much of an increase that the extra build time is even more irrelevant in most situations. The build cost of the facility is really only a major issue in Proportions mod. http://forum.shrapnelgames.com/images/icons/icon7.gif

Re: Formula for bonus structure calculations
 

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.

Re: Formula for bonus structure calculations
 

<font size="2" face="Verdana, Helvetica, sans-serif">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.

Re: Formula for bonus structure calculations
 

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.

Re: Formula for bonus structure calculations
 

<font size="2" face="Verdana, Helvetica, sans-serif">Hey, "Arlo", I think you just showed your true age... http://forum.shrapnelgames.com/images/icons/icon12.gif .

Re: Formula for bonus structure calculations
 

<font size="2" face="Verdana, Helvetica, sans-serif">Hey, "Arlo", I think you just showed your true age... http://forum.shrapnelgames.com/images/icons/icon12.gif .</font><hr /></blockquote><font size="2" face="Verdana, Helvetica, sans-serif">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... http://forum.shrapnelgames.com/images/icons/icon7.gif

Re: Formula for bonus structure calculations
 

<font size="2" face="Verdana, Helvetica, sans-serif">Hey, "Arlo", I think you just showed your true age... http://forum.shrapnelgames.com/images/icons/icon12.gif .</font><hr /></blockquote><font size="2" face="Verdana, Helvetica, sans-serif">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... http://forum.shrapnelgames.com/images/icons/icon7.gif </font><hr /></blockquote><font size="2" face="Verdana, Helvetica, sans-serif">Well ! That'll teach me to make use of my limited detective abilities. http://forum.shrapnelgames.com/image...s/rolleyes.gif

Re: Formula for bonus structure calculations
 

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

Re: Formula for bonus structure calculations
 

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

Re: Formula for bonus structure calculations
 

<font size="2" face="Verdana, Helvetica, sans-serif">Woot.

Re: Formula for bonus structure calculations
 

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 ]

Re: Formula for bonus structure calculations
 

I forgot to thank Loser for his/her motivation for me to do this. Took me back to my school days and was a nice trip down memory lane. Thank you again bud. I dont have the graphs on the spreadsheet you requested, but would be nice to create them.

Re: Formula for bonus structure calculations
 

http://forum.shrapnelgames.com/images/icons/shock.gif Christ in Drag! http://forum.shrapnelgames.com/images/icons/shock.gif

Snakeye you rock! This verbose post belongs in the FAQ, I'd think. I am ecstatic to have this lengthy and complete explanation and even more pleased that you enjoyed pursuing my suggestion. You are more than welcome.

I'm sure someone can tell you where and how to upload that spreadsheet, and I was just joking about the graphs and the rest of the Alro Guthrie gibberish.

Re: Formula for bonus structure calculations
 

Rock! Now this is what I'm talking about, math finally coming in handy for something other than figuring out all the deductions out of my paycheck. Snakeye, this really should go into the FAQ, you've just solved one of those questions that everyone has sooner or later about remote mining. Great job http://forum.shrapnelgames.com/images/icons/icon12.gif

Re: Formula for bonus structure calculations
 

<font size="2" face="Verdana, Helvetica, sans-serif">Start at 25%. Subtract your maintenance reduction racial characteristic. (Commonly boosted to 20%; 25%-20% = 5%)
This is your actual maintenance cost per turn.

Multiply you ship's build cost by the above maintenance rate.
If you are looking at a base, rather than a ship, divide by 2.

If you have a crystalline restructuring plant in the system, take off another 5 to 15% depending on tech level.

This is how much you spend each turn for maintenance.

Re: Formula for bonus structure calculations
 

<font size="2" face="Verdana, Helvetica, sans-serif">That isn't very common, as it is extremely expensive to do that, esp. in 2000 point games. http://forum.shrapnelgames.com/images/icons/icon7.gif

Re: Formula for bonus structure calculations
 

anybody knows where i can upload a spreadsheet that has the formulae already in? Would be helpfull i think for anybody to use. As far as the maintenance is concerned, I think leaving the maintenance cost as a figure is less complicated.

Re: Formula for bonus structure calculations
 

Go to the main Intel Forums page, and click on the Scenario/Mods Upload Category (first one). Upload it to the appropriate SE4 thread in there (probably Other Helpful Tools/Information).

Re: Formula for bonus structure calculations
 

As promised, the excel file that utilises the formulae mentioned in the thread. I took the liberty and put some sample data into it to aid the understand of its functionality.

1053087403.zip

ENJOY!

[ May 16, 2003, 13:18: Message edited by: snakeye ]