"Clustering" is a mathematical algorithm by which things are grouped together based on similarities between them. Clustering is frequently used for automated classification of objects, but it is also used for things like data compression.

I've applied various clustering algorithms to board game data a number of times, but recently thought it would be interesting to apply clustering not to the games, but to the gamers.

First, I tried clustering based on user ratings. This worked all right, but the resulting clusters were less interesting than one might hope. The dominant feature distinguished by the clusters was the typical rating a person gave games. That is, the clusters were best described as the "people who rate games highly" cluster and the "people who rate games low" cluster, with otherwise common features. Attempts to normalize the ratings data proved fruitless perhaps in part due to sample selection in what was rated.

Second, I tried clustering based on collections. This didn't work well at all, primarily because the vast majority of collections on BGG have lots of overlap with one another, and where they don't, there isn't a distinctive pattern. Further, comparing collections of dramatically different sizes is hard. If I own 600 games, and you own 25, 22 of which I own, is that a lot of overlap, or a little? At some point, I may revisit this, by trying to normalize collections based on game rarity, but I'm not too hopeful.

Finally, I tried clustering based on "Top 10" lists. These are effectively pre-normalized. There's enough of them to be meaningful. Each person has exactly 10 (well, some don't, but I removed those from the sample, leaving 2700), there's no "ratings" to create an "8 is great" vs. "10 is great" group. Further, there's frequent overlap, but unlike collections there's far from universal overlap. The results were far more compelling than any previous ones.

So, I ended up generating 10 clusters, which is mostly an ad-hoc number, but I may run it with other counts at some later point. The algorithm I used was a straightforward k-means clustering, using probabilities of particular games being present in someone's top 10 as the cluster means. After it settled, I examined the details of each cluster and tried to come up with a compact description that characterizes that cluster.

The resulting clusters, with details below:

Core Eurogamer, Family Euroamer, Heavy Eurogamers,
Dripping with Theme Gamers, Knizia fans, Eclectic Eurogamers,
Classics gamers, Light Minatures Gamers, Wargamers and Mass-market Gamers.

For each cluster, I list

- the name I've given it
- the size, as a percent of the population
- their "touchstone game", typically the one most likely to be on the Top10 list of members
- Other games frequently appearing on the the lists in this cluster