The 10 Types of Gamers (Clustering Analysis)
Matthew Gray
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"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
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1. Board Game: Puerto Rico [Average Rating:8.05 Overall Rank:15]
Matthew Gray
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Core Eurogamer
Size: 38%
Touchstone: Puerto Rico (85%)
Other games: Power Grid (43%), E&T (37%), Caylus (35%)

By far the largest group, this group's top 10 is quite comparable with
the overall BGG Top 10.
 
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2. Board Game: Ticket to Ride [Average Rating:7.46 Overall Rank:130] [Average Rating:7.46 Unranked]
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Family Euroamer
Population: 18%
Touchstone: Ticket to Ride (60%)
Other games: Settlers (62%), Carcassonne (51%), Puerto Rico (32%)

The other big group, but still under half the size of the core
cluster, this is dominated by the lighter Eurogames.
 
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3. Board Game: El Grande [Average Rating:7.78 Overall Rank:57]
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Heavy Eurogamers
Population: 9%
Touchstone: El Grande (72%)
Other games: E&T (51%), Princes of Florence (24%), Age of Steam (20%)

The games are heavy, not the gamers. I almost called this the "Puerto
Rico Dissenters" because the fact that they don't include Puerto Rico
on their Top10 seems to be the main distinguishing feature. In
contrast, "Core Eurogamers" include El Grande 23% of the time and
"Family Gamers" include it 6% of the time. Heavy Eurogamers never
include Puerto Rico. Other "heavier" games make prominent appearances
here, such as Goa and Wallenstein.
 
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4. Board Game: War of the Ring (First Edition) [Average Rating:7.79 Overall Rank:83]
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Dripping with Theme Gamers
Size: 6%
Touchstone: War of the Ring (43%)
Other games: Arkham Horror (38%), Twilight Imperium 3e (33%), Descent (19%)

Again, it's the games that are dripping with theme, not the gamers. I
almost thought this was an additional miniatures gaming cluster, but
looking at some other matches (Game of Thrones, Runebound, RoboRally)
I think it's more about theme, than the miniatures, but a lot of them
sure do have miniatures.
 
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5. Board Game: Ra [Average Rating:7.47 Overall Rank:136]
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Knizia Fans
Size: 6%
Touchstone: Ra (59%)
Other games: E&T (28%), Samurai (25%), Through the Desert (24%)

The fifth game in this cluster is also Knizia (Amun-Re), but after
that several non-Knizia games appear (Princes of Florence, Acquire,
Age of Steam) in addition to more Knizia games.
 
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6. Board Game: Carcassonne [Average Rating:7.43 Overall Rank:141] [Average Rating:7.43 Unranked]
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Eclectic Eurogamers
Size: 5%
Touchstone: Carcassonne (94%)
Other games: Puerto Rico (19%), Memoir '44 (18%), Ticket To Ride Europe (14%)

Other than Carcassonne, little unifies this group other than a slight
bias toward lighter games.
 
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7. Board Game: Catan [Average Rating:7.21 Overall Rank:293] [Average Rating:7.21 Unranked]
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Classic Gamers
Size: 5%
Touchstone: Settlers of Catan (73%)
Other games: Magic The Gathering (19%), Acquire (18%), Risk (14%)

This group is dominated by games published over 10 years ago. A few
newer games (War of the Ring, Citadels) appear at the 8% or 9% level.

 
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8. Board Game: Memoir '44 [Average Rating:7.55 Overall Rank:117] [Average Rating:7.55 Unranked]
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Miniatures Gamers
Size: 5%
Touchstone: Memoir '44 (65%)
Other Games: Heroscape (31%), SpaceHulk (15%), Battle Cry (13%)

When you get further down the list, some non-miniatures games appear,
but not a lot. (Does Formula De count as a miniatures game? It's on
the list) Bang is the most common unambiguous-not-a-miniatures-game
game on the list.
 
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9. Board Game: Hannibal: Rome vs. Carthage [Average Rating:7.82 Overall Rank:150]
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Wargamers
Size: 5%
Touchstone: Hannibal Rome v Carthage (24%)
Other Games: Paths of Glory (23%), ASL (21%), Twilight Struggle (17%)

As you can see from the percentages, this group doesn't even really
have a single touchstone. But, the games on the lists in this cluster
are almost exclusively wargames and a few civilization games,
including Civilization.
 
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10. Board Game: Chess [Average Rating:7.09 Overall Rank:416] [Average Rating:7.09 Unranked]
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Mass-market Gamers
Size: 2%
Touchstone: Chess (27%)
Other Games: Axis and Allies (27%), Munchkin (18%), Shogun (12%)

The lists in this group are an odd mix, also with no real touchstone,
but the theme seems to be "Was it available in the mass market?"
 
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