I’m going to briefly channel the spirit of Adam Abramowicz of The Best General, and talk about 40K via an extended analogy to an obscure, expensive sport that’s dominated by Europeans. I used to ski race, and one of the great and perpetual questions in the sport is why aren’t the Americans better at it. We have mountains, we have (relatively speaking) a massive skiing population. And yet we’re bad at alpine ski racing. Outside of the occasional star athlete, Team USA isn’t as a team a major contender. I remember one memorable race I watched where the commentators were talking about an Austrian had to shape up and start doing better, or he’d be kicked off the team.

He beat every American in the race.

There are lots of explanations in ski racing, but the frustration with America’s performance speaks to a general concept: In competitions of “Bring your best X competitors”, larger countries should do better than smaller countries.

Is that true for 40K?

The Theory

Imagine that 40K skill is normally distributed – that is, that it follows a bell-curve like distribution, where there are a large number of average players, and a relatively rare number of very good or very bad players. If you have to draw your, for example, eight best players, having more people in that “very good” tail means that you can draw more people from it.

It’s easy to imagine this. For example, consider my local club versus a larger club. Our top eight active 40K players would swiftly consume all our best players, and involve drawing jokers like me, who, as Val Heffelfinger describes it, lost the moment they decided that “The floor is lava” is a useful guiding principle for making an army. A larger team can likely fill out their roster before they hit the thematic narrative players.

But we can also show this theoretically, by drawing a number of hypothetical populations, and then asking what’s the average skill of the players in those groups. Basically, everyone gets drawn from this normal distribution, with an average of 100 and a standard deviation of 30:

As we can see, most players are around an average of 100, with some exceptional players near 200, and some exceptionally poor players near 0.

Now, what we can do is generate populations of different sizes, and ask what the average player score is for the top eight players.

While we’ve talked mostly about normal distributions, if things look more like an exponential distribution (that is, nearly everyone near the average with a very long tail of good players) this general principle holds as well – and can potentially get even more extreme.

So…theoretically, larger populations should result in better teams.

Do the results from the ETC show this?

Of course, we’re talking about the 40K playing population, but since I don’t have access to GW’s marketing data, we’re going to use overall population as a proxy.

The first problem is that the United States is really big. If you look at a histogram of the population in millions of the ETC countries (left), the U.S. is all out on its own. That’s a problem for most statistical methods – a lone country like that, especially if they also won, will disproportionately influence your results.

Taking the log of the population is a common technique to turn data like this into somewhat more amenable forms – that’s the picture on the right.

So, is there any relationship between population size and ETC performance? Looking at scatter plots of either Battle Points or Points (which determined actual placing), it looks like there’s a faint, but definitely there relationship:

Lets take a look at the linear relationships.

There it is. There’s a decided relationship for both, and in both cases, it’s statistically significant. For Battle Points, an increase in the log population of 1 means a predicted 33.51 extra Battle Points. To put that in more realistic terms, lets think about going from Canda’s population to Germany’s. Canada’s population is 36.29 million, for a log-population of ln(36.29) = 3.59. Germany’s population is 82.67 million, for a log-population of ln(82.67) = 4.41, for a difference of 0.82.

Multiplying that number by the predicted 33.51 Battle Points gained from a 1-unit increase in log population gives us: 33.51 * 0.82 = 27.45 more Battle Points predicted to Germany vs. Canada due to population size.

For Points, a 1-unit increase in log-population meant a predicted 0.737 more Points – but given the range of points is only from 0 to 12, that’s significant.

Now, both of those don’t look perfectly linear, and ideally, we’d look at some curved prediction points, but with only 32 teams, we’re already pushing it in terms of sample size. But it does appear there is a weak-but-present influence of population size. This is, of course, not the full explanation of performance. It’s likely that UK-based teams have a much higher percentage of the population that plays 40K than other countries. And there are definitely country-level metas and personalities. And statistics like this certainly aren’t causal – but it does appear that country size confers a slight advantage in terms of being able to draw from a deeper pool of potentially skilled players. We’ll see if this holds up in years to come.

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