Formula for bonus structure calculations

[snakeye]

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.

[dogscoff]

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.

[snakeye]

Originally posted by dogscoff:
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.

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!?)

[Slynky]

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.

[FadingSuns]

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

[Slynky]

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

Well, kind of...

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 )

[dogscoff]

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.

[snakeye]

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! ( )

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

[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? )

[Fyron]

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.