Frontier Population Growth, Revisited
Of course, all of this comes with the caveat that regional population is not necessarily an indicator of regional health, etc. I am making no claims regarding Frontier overall being good or bad for us, just interested in Frontier-driven population growth.
Also, I am trying to use simple mathematical functions to estimate complicated phenomena. Someone with more statistical knowledge and experience than me could build a model that takes other things into account, including variations in spawn rates, changes in recruitment numbers, and seasonal activity on NationStates. What I am doing is very much an oversimplification.
With that out of the way, and now that we've got more data under our belt, let's see where we're at!
Population Growth - Fitting a logarithmic curve
In order to estimate the function that would best model our growth, I put our daily population data into a spreadsheet and asked it to generate a line of best fit using a logarithmic function. What I got was this:
In this span of time, the logarithmic function that best fit our data is represented by y=185.3ln(x)+669.76. What does that mean? I don't know, it's been years since I was in high school math.
But we can use that function to speculate about where our population might be headed. It seems to fit our growth pattern relatively well, although the initial curve was steeper, the initial spike went higher than expected, then we saw a dying-off that brought the actual curve below the predicted for a time.
If we project this equation out to 1 year as a Frontier, we get this:
This estimate would have us ending our first year as a Frontier with 1769 nations, 252 more than we have now.
Population Growth - Fitting a linear curve
But wait a minute, McEntire, you say. That previous estimation includes the initial spike, which might be influencing the equation. There was too much volatility in those early days, you can't take them into account!
So, what if we assume that our growth since those early spikes is probably about what we could expect in the future? If we look at the portion of the data only after the nations spiked then died off, which I've estimated to around July 19, we see this:
To keep things simple, I've fit this graph with a linear curve, although there's clearly some volatility around that. But assuming that the last three months or so are consistent with what we could see in the future, we get the equation of the line of best fit (which I assumed would be linear rather than logarithmic). And if we project that out to the one year as a Frontier mark, it gets us to a regional population of 1687, or 169 more than we have now.
Comparing the two projections, we get this:
When we look at Europeia's population growth since we became a Frontier, we see a large initial spike, a quick dying off, and then a stabilization resulting in a slower growth rate. When we look to the future, we should see continued Frontier-driven growth, possibly somewhere between 169-252 more nations between today and our first Frontieraversary.
If you want to check my math or look at the data yourself, check out the spreadsheet.
EDIT: One Last Wildly Speculative Scenario
Speculating even further out, the logarithmic scenario sees us plateauing around 2077 nations after 5 years as a Frontier, while the linear scenario would have us grow to 2520 by that time: