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.