| NationStates Population |
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I believe many of us have wondered about how the population in NationStates works. Based on Ballotonia's observations (here), that I hope and believe are valid one can conclude that the population growth follows a certain pattern the first 21 days, see figure 3 below, resulting in a population of 62 millions. Then the daily increase is a random number: 5, 6 or 7 millions each day. Suppose that the probability of obtaining either a 5, 6 or 7 million increase is equal, then an approximated population number, n, after 21 days is given by
n=62+6(t-21)
where t is the age of the nation in days.
Calculating the population for Sedunn at 430 days age using the equation above yields a population of 2516 millions and the actual is 2533. By using the actual age found for various nations in this region and their date of founding I produced the figure below to see if the equation is valid. [Image: E2qnQG7.png]
Figure 1. Plot of the equation above and a scatter representing actual population. Most of the selected nations' actual populations seem to correspond well with the approximation. I am not sure why there are some 'larger' deviations, but it may be due to inactivity resulting in a pause in population growth. Studying the relative error, see figure below, it seems that the approximation is less accurate for the youngest nations. This might be because not sufficiently many days have passed since the founding resulting in a more uneven distribution of the growth numbers. There are also some 'unexpected' deviations for some older nations that may, as stated before, have been inactive for some time. [Image: 9X5r6P7.png]
Figure 2. Plot of the relative error. For most nations one may expect an error of approximately 1%. Of course much larger amounts of data must be studied, in particular for populations between 9000 - 11000 millions, as they are not represented above. It would be interesting to see if that "triple pattern" in figure 2 would repeat itself. As stated above, the population from day 1 to 21 follows a completely predictable manner. I made an interpolation using the data presented by Ballotonia and plotted it along with the interpolated function, both in the figure below. The figure also shows what one might expect what the growth would be like if it had continued in the same manner after the first 21 days. [Image: MKi0lJE.png]
Figure 3. Population growth for the 21 first days and expected continuous growth. Note the equation of the curve. I am not an expert in this at all, maybe there is someone here how knows more about probability and growth. I hope this is somewhat correct and that someone will find this interesting  What do you think about it?
I'd be interested in testing these theories.
Darkstrait :ninja:
Former Justice, Former Local Councilor, Roleplayer, Former SPSF Deputy for Recruitment, Politically Active Citizen, Ex-Spammer Supreme, and Resident Geek "Hats is very fashion this year."
That would be great
I can create a few puppets for y'alls.
Ah, the wonders of technology. I'm on Tapatalk!
A while back I got together with a few of my friends and we all made nations and made our own region. We all started within about an hour of each other and it didn't take long for them to all be different, I'm talking before we got to 62 million.
Interesting and disturbing observations
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