Recently, I had a discussion on Twitter (genuinely a discussion, not a fight, a small miracle for the hellish birdsite!) about the often repeated and very rarely sourced notion that the competitive scene is the economic engine behind Games Workshop – basically, that players chasing the meta are the major driver of sales.
I am, admittedly, intensely skeptical that this is true.
But it got me thinking more about how some of these “received wisdom” hobby bubbles form. How everyone you know plays Matched Play 40K, or follows a particular content creator, or uses 3D printed models, or…whatever.
Which means I have an excuse to talk about networks.
We’re going to be talking about networks again fairly soon – but for now, a quick introduction. Networks are just a way that a number of sciences and fields in math – computer science, graph theory, sociology, epidemiology, etc. think about how things are connected together. The things are called nodes and the connections edges. Two computers with a cable between them? Network. Two friends? Network. One podcast giving another a shoutout? Network.
Networks are a useful way to see how communities form and interact with one another.
This post is going to think about how a community forms, in a particularly stylized and hypothetical fashion, using something called a preferential attachment network (or using something called the Barabási-Albert model if one is feeling fancy). Networks are very expensive to collect empirically, involving very sophisticated and expensive survey designs, so we often use models of how networks form to talk about and generate them.
For example, a random model of a network where everyone has a single connection would just…place that connection randomly. The Barabási-Albert model does something slightly different – when a new node is added to the network, the probability of it connecting to each existing node depends on how many other nodes are connected to it. This is a sort of simple heuristic model that occurs – at least approximately – a lot. People want to be friends with popular people. Flights are added to hubs, rather than distant rural airports. It describes a “rich get richer” phenomenon, where well-connected nodes become more well connected.
Let’s think about this in the context of the hobby – say, podcasts, YouTube channels, or just people. There are two groups, Blues and Yellows, and ten people in each group. How might a community form between them?
Well, step one, we’ll connect a Blue and a Yellow together, and then add one new Yellow node. Who does it connect to? Well, right now, there’s a 50/50 chance, so I rolled a d100 and got above 50, so it connects to the Yellow node.
Let’s add another one in now – a Blue node. Now, the central Yellow node is twice as likely to be connected to than the two nodes with a single connection. So basically, it has a 50% chance of being picked, and the other ones have a 25% chance. It’s still random, there’s still a chance, but it’s starting to be weighted.
Despite the odds being (literally) stacked against it, our existing Blue node gets the new connection.
This is going to go on for a bit, and ideally I would have written code to do this for me, but instead I implemented it by hand. This is what we get once we connect every node up in the network:
This isn’t bad! There’s clearly a couple of central hubs in the network, but overall, things look pretty diverse. Of our 20 individuals, only the four Yellow nodes up at the top of the network have few “I know a guy who know’s a guy…” connections to a Blue. And that arises from random chance – the network by design has no build-in communities of just one type of node.
But what if that wasn’t true. Let’s consider a network that forms both with preferential attachment and a preference for homology – nodes connecting to nodes that are like them. Here, we modify the way preferential attachment works – nodes with the same color as the one being added have twice the weight, probability wise. So if we’re adding a Blue node, a Blue node with one connection is worth the same as a Yellow node with two. What do we get if we build this network from the same Yellow-Blue original pair?
This network is a problem y’all. No one is talking to each other. Using the “I know a guy who knows a guy…” metric, most of the yellow nodes know about Blue nodes only through that one linking node. That one link is pretty much what’s keeping these communities from just heading off into two distinct groups that don’t interact. The rest of the diversity of their opposite color comrades is unknown to them. And there’s one poor Blue node, and one Yellow node, both of whom are more than two steps away from any other node of their color – they’re basically the odd-one-out in their respective groupings.
I don’t think this is unreasonable either – homophily is a known property of a lot of networks. And if we think about these groups as people – well, perhaps these are narrative and matched player players, who are more likely to play with like-minded people because there’s the possibility that that’s the way to have the most fun. Or you can think about these as YouTube channels, and things like collaborations – that’s most likely to be between two tactics channels and two terrain making channels than one of each.
Preferential attachment make networks concentrate around a few key actors. Homophily makes them turn into distinct groups.
Now what if we make this slightly worse? Lets say the Blue nodes are less likely to connect at all. Perhaps these are Garagehammer groups, who are just happy to be chugging along doing what they’re doing. Or they’re a different type of social media in the hobby that’s much less likely to link out. Now, each Blue node has a 3+ save vs. just wandering off alone – rolling that out, we lost three.
Here, not only do nodes cluster together naturally with their same types, but the Yellow nodes have an inherent advantage in terms of making those extremely well connected networks. The Blue nodes are forced to the periphery of the core network.
One question here is what the “average node” in this network thinks is the makeup of the community. Lets try that two-step measure again, and ask each node “What % of the nodes are Yellow?” based on this limited picture?
There’s some considerable distortions here. Three full nodes believe there are only Yellow nodes – that Blue is just a figment of someone’s imagination. A lot of the Blue nodes actually think that Blue is more common than it is as well – again, because they connect to each other. And if you did a survey? The most common answer would be 75%, and the mean answer would be 68.4%.
The truth if you can look at the whole network? 58.8%.
The observed percentage of Yellow nodes is off by 9.6%. That’s a little more than one and a half Yellow nodes conjured out of thin air.
What does this mean for 40K?
Warhammer is an inherently social game. It’s built on playing with people, building relationships, and consuming hobby content on various social media sites. We’re subject to the same kinds of phenomena as these simple toy networks.
So the next time you confidently say “Everyone I know listens to Lost to the Nails” or “Competitive players are the majority of players in the hobby”, consider whether you have evidence for this, or if it’s based on your own (including my own), incomplete view of the hobby as a network.
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