[Arnhelm Alt] Frontier Population Growth Revisited

[McEntire]

Frontier Population Growth, Revisited

By McEntire
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5 months ago, when our Frontier was in its infancy, then-Senator upc and I engaged in a dialogue in the Senate regarding our gameside regional population, and the effect that Frontier would have on it. In that discussion, I speculated that our population growth as a Frontier could follow a roughly logarithmic curve, at some point slowing/leveling out. Now we have more information to say what the affect of being a Frontier may be on our regional population, we can assess what the last months may look like and what the future may hold.

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:

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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:

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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:

TL;DR

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.

Now discuss!

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:

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[Josi]

What does that mean? I don't know, it's been years since I was in high school math.

This made me cackle lol

 

[Sopo]

Cool! I don't really know what to make of it, but nice to see the data.

 

[GraVandius]

Given the data, I wouldn’t necessarily expect any additional durable population growth. We seem to have reached an equilibrium between the 1500 and 1600 mark and baring any broad change to nation creation rates, I don’t see any reason to project further growth.

 

[HEM]

What does the linear model think our population will be in 2520?

 

[John Laurens]

This also doesn’t take into account the rise magnetism from other frontiers.

 

[Aexnidaral]

This is good for Blake Masters

 

[McEntire]

Given the data, I wouldn’t necessarily expect any additional durable population growth. We seem to have reached an equilibrium between the 1500 and 1600 mark and baring any broad change to nation creation rates, I don’t see any reason to project further growth.

I’m not sure if this is right. The reason that I did the linear regression on the time between 7/19 and the present is because I was of a similar perception, that growth would probably stagnate and fall into an equilibrium. But the data we have so far indicates a slow upward trend.

Is there some additional statistical analysis I could do to find some kind of margin of error around these growth numbers? Sure. And maybe I will!

I think it’s entirely possible that Frontier has shifted our underlying growth pattern, and will continue to drive a slow increase for years. Clearly, the population boom and subsequent dying-off didn’t behave at all like previous booms, which saw virtually zero nation retention. We’d probably need more data and analysis to understand, but what we have now points to a continuing slow increase.

 

[Rand]

How do you think Delegate endos will follow?

 

[McEntire]

How do you think Delegate endos will follow?

Well that’s really up to us lol. As I said, I’m just talking about regional population. It gets more people into the pipeline from resident>WA member>del endorser. But if the rest of that pipeline isn’t flowing, it won’t have much of an impact at all.

 

[Le Libertie]

This is some interesting data.

Though I'll admit I am far more interested in the Frontier transition's impact (or lack thereof) on the WA resident population than the nation count overall. Especially with the rise of puppet-inflated regions, I don't think nation count is as good of a measure of a region's health as it used to be.

 

[Vor]

Unfortunately, without taking into account the recruitment revamp by UPC and/or separating population increase by foundings v. nations moving in, I can't see this being a useful analysis of the impact that becoming a Frontier had on us. If I recall correctly, UPC's bot began being used very close to the time we transitioned.

Recruitment has too large an impact on region growth to be left out of such an analysis.

Unless I'm missing something?

 

[upc]

Though I'll admit I am far more interested in the Frontier transition's impact (or lack thereof) on the WA resident population than the nation count overall. Especially with the rise of puppet-inflated regions, I don't think nation count is as good of a measure of a region's health as it used to be.

100%. I don't have time to do a deep dive on this at the moment, but some food for thought: the day we became a Frontier, we had 244 WA nations and 185 Delegate endorsements. Just over six months later, we're sitting at 271 WA nations and 201 Delegate endorsements. Obviously there are a ton of other factors that play into this -- we've had a Delegate transition, we're still rebuilding gameside infrastructure, the ERN has a couple of sailors deployed, etc. But the incredible disparity between population increase and WA population increase is very concerning.

Unfortunately, without taking into account the recruitment revamp by UPC and/or separating population increase by foundings v. nations moving in, I can't see this being a useful analysis of the impact that becoming a Frontier had on us. If I recall correctly, UPC's bot began being used very close to the time we transitioned.

Recruitment has too large an impact on region growth to be left out of such an analysis.

Unless I'm missing something?

This is also very correct. There were some early efforts (largely by Gem, shout out to his prescience here) to track foundings vs recruitment, but we didn't have enough bandwidth to get that set up at the time and now most of that data is completely irretrievable.

 

[Le Libertie]

100%. I don't have time to do a deep dive on this at the moment, but some food for thought: the day we became a Frontier, we had 244 WA nations and 185 Delegate endorsements. Just over six months later, we're sitting at 271 WA nations and 201 Delegate endorsements. Obviously there are a ton of other factors that play into this -- we've had a Delegate transition, we're still rebuilding gameside infrastructure, the ERN has a couple of sailors deployed, etc. But the incredible disparity between population increase and WA population increase is very concerning.

Makes sense. Though I do think it’s important to highlight out that at the point right before the Frontier transition, we had an abnormally low number of WAs due to the RSC’s enforcement of the newly established endocaps, which triggered a small exodus of WAs (IIRC, my lowest endocount ever in my tenure as delegate happened then). With that taken in mind, pre-Frontier WA levels seem at least equivalent, if not better than they are now (but like you said, some extenuating factors may be contributing to this state).

I too have been puzzled by the residency/WA discrepancy, and I wonder what could be causing it.

 

[Comfed]

Given the data, I wouldn’t necessarily expect any additional durable population growth. We seem to have reached an equilibrium between the 1500 and 1600 mark and baring any broad change to nation creation rates, I don’t see any reason to project further growth.

I agree with this. I think our standard population is determined by our nation gain rate, the amount of nations that move to or found in Europeia over time, multiplied (roughly) by our retention rate, the proportion of those nations which stay in Europeia without leaving or ceasing to exist. We greatly increased our gain rate (while possibly reducing our retention rate, I'll elaborate later in this post) by becoming a frontier, so my expectation is that our rapid growth was probably our actual population adjusting itself to fit this new standard population.

If we want our standard population to increase, in my view we can either increase our nation gain rate or our retention rate. To increase our nation gain rate, all we can really do is send more recruitment telegrams in a sustained manner; our spawn rate is dependent on the number of new players who create nations over time, and the proportion of those nations we get is literally the highest possible, or at least the highest in the game (3.9). Increasing our retention rate is another matter that many Interior/Outreach advocates have been loudly advocating for for some time now--for good reason, I think.

I too have been puzzled by the residency/WA discrepancy, and I wonder what could be causing it.

Consider two types of nations; nations in the first (type A) always ignore communications from regions, while those in the second (type B) may sometimes read and consider them. We could never recruit the first type with recruitment telegrams and because that was our sole source of mass external recruitment, they would never have formed a significant proportion of our population. Now that we are a frontier, however, we can draw from the second because they do not have to pay any regard to regional telegrams at all to find themselves in our region.

That simplistic hypothetical is to say that while we may overall gain more nations because we are a frontier, it is possible that those nations that passively found in Europeia rather than actively move here after receiving a recruitment telegram are significantly less likely, overall, to be engaged with regional matters. This pattern is reflected in the tendency of feeders to have off-site communities on par with large UCRs despite having nation counts an order of magnitude higher.

This is not to say that there is nothing we can do to increase the number of WAs we have, and the percentage of those WAs who are endorsing the Delegate and RSC. We can and should--and indeed to continue the comparisons to the feeders some feeders (and sinkers) are much better at retaining nations and turning them into WA endorsements than others. However, we might not be able to expect the same efficiency that those efforts could have had in a pre-frontier Europeia.

Though I do think it’s important to highlight out that at the point right before the Frontier transition, we had an abnormally low number of WAs due to the RSC’s enforcement of the newly established endocaps, which triggered a small exodus of WAs (IIRC, my lowest endocount ever in my tenure as delegate happened then).

It is also true that we degraded our base of WAs by enforcing the endorsement cap. A number of WA nations that were solidly in Europeia endorsing the Delegate left because of them (here is an example.) Was it necessary to do so anyways? Likely yes, but ensuring our security did come at the cost of losing a number of WAs that we would have otherwise had (and those WAs are not coming back.)