GWS 2024: Games of a Feather...Group Together
By Jon Freitag
When respondents to the Great Wargaming Survey are asked to list their Top 3 wargaming periods (see Wargaming Period Preference), the counts of wargaming periods from most to least popular are as shown in Figure 1 below:
The previous analysis examined a selection of demographic attributes shown to hold some influence on wargamer's choice in periods. Relying on aggregated counts only, descriptive statistics were utilized in making inferences on general tendencies. In today's analysis, we drop the path to descriptive statistics and examine period preference using predictive analytics through the lens of cluster analysis.
What is cluster analysis? Simply put, cluster analysis constructs a grouping of objects (period preference) so that objects in the same group (cluster) are more similar to each other than to those in other groups.
Cluster analysis is a statistical technique used to identify and classify homogeneous groups of similar objects or data points into clusters based upon their characteristics or attributes. Such objects within the same cluster are more similar to each other than to those data points in nearby clusters. Cluster analysis is an unsupervised machine learning technique. "Unsupervised" reflects that analysis results do not rely on any predefined labels or categories. Instead, machine learning techniques "discover" patterns and structures present within the data itself. Cluster analysis can provide a powerful exploratory data analysis tool capable of revealing hidden structures and patterns even within complex datasets.
What are some questions that cluster analysis may answer? For me, a few questions to consider are:
- Using only gaming period choice, do distinctions between historical and non-historical gamers emerge?
- Do some game periods tend to cluster together? If so, which ones?
- If distinct groups emerge from clustering, are these distinct groups intuitive?
The first step in cluster analysis (after wrangling the data into shape for analysis) is figuring out an optimal number of clusters. With 5,995 respondents having up to three period choices each, these resulting responses are aggregated and classified using cluster analysis. Only respondent choices are utilized in building this model. Figure 2 illustrates the initial dendrogram showing how each of the twenty wargaming periods group.
What does Figure 2 suggest? The answer depends upon the number of clusters chosen but clear clustering emerges nonetheless. What can we infer from this initial dendrogram? Without examining the dendrogram more closely, it may be difficult to identify any meaningful inferences at a glance. This is where identifying the number of clusters comes into the analysis.
Starting from the right-hand side of the chart and drawing a vertical line down through the first two branches of the dendrogram tree identifies two clusters of gaming periods (see Figure 3). This is the two-cluster solution. The two, distinct clusters are highlighted. What does this first and primary division suggest?
The two-cluster solution clearly and cleanly bifurcates the twenty wargaming periods into two, distinct groups. The two groups identified, with no ambiguity, cleave the Historical periods from Non-Historical periods. Well, perhaps there is a bit of ambiguity. Pulp falls into the non-historical grouping. Perhaps that makes sense since Pulp identifies with a wide genre of adventure/RPG gaming, including a broad brush of character-driven adventure gaming with Steampunk, Horror, Gangster, Back of Beyond, etc. Notice that Pulp groups with the non-Warhammer Fantasy/Sci-Fi periods.
The result illustrates that historical wargamers generally tend toward historical gaming while non-historical gamers generally tend to remain within non-historical genres. Notice within Non-Historicals that the Games Workshop Warhammer settings show distinct separation from other Fantasy/Sci-Fi periods.
What if we want to see more granularity instead of the very high-level, two-cluster solution? We move the vertical bar to the left and cut across the dendrogram a second time. Moving the vertical cut to the left, the dendrogram is bisected across three branches to identify a three-cluster solution as shown in Figure 4. Note that the three-cluster solution keeps Non-Historicals separate and intact. Historicals, however, are split further. As seen in the two-cluster solution, the split in the three-cluster solution is intuitive in that the Historical groupings are clearly split between Modern and Ancients wargaming periods. Interesting that the Ancients gamers tend to separate from the Modern gamers with seemingly little interaction between the two groups.
Staying with the Ancients Historical Gaming Periods for a moment longer, Figure 1 shows that the Ancients, Medievals, and Dark Ages wargaming periods hold ranks 7, 8, 9 in the period popularity summary. As a test of data reliability, I was curious if the period ranking would remain the same across two distinct groups. I conducted an informal survey on the Society of Ancients (SoA) Forum to address this curiosity. The question asked was as follows:
Although the sample size is small at 26 responses, the ranking seen above from the SoA survey maintains the same order as in Figure 1. That is, Ancients then Medievals then Dark Ages.
What happens to the clustering solution as we move from the three to four-cluster solution? Moving to the left and cutting the dendrogram one more time to reach a four-cluster solution, shows that the Modern Historical cluster is split once again.
In a four-cluster solution (below), Non-Historicals and Ancients Historicals clusters remain unchanged. Rather, with this cut, Modern Historicals splits into two groupings. This bifurcation seems to carve out Musket & Rifle periods from more Modern periods. We could similarly group these into Pre and Post-20th Century groupings too.
What about grouping of Old West and Age of Sail/Pirates into the Modern camp? This is an odd grouping, isn't it? Well, given that counts for both Old West and Age of Sail/Pirates groups were low as seen in Figure 1, variability and fuzziness in grouping is possible. In Figure 7, I label this cluster as Hollywood Historical. The grouping with Historicals suggests that Hollywood gaming tends to come from Historical wargamers and not non-Historical gamers.
I could continue crawling out on the branches of the dendrogram tree, pruning along the way, but for now, I stop at the four-cluster solution with the Hollywood split. Did I manage to answer some of the questions originally set out at the beginning of this analysis? To recap...
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Using only gaming period choice, do distinctions between historical and non-historical gamers emerge?
- Indeed! The two-cluster solution identifies this bifurcation early on.
- Do some game periods tend to cluster together? Which ones?
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If distinct groups emerge from clustering, are these distinct groups intuitive?
- The two, three, and four-cluster groupings identified were given (what I consider) intuitive names. Now, other labels are possible but cluster labels identified here seem to capture the component periods.
This exercise in cluster analysis produces some interesting and hopefully logical tendencies as responses are grouped by wargaming period preference. Keep in mind that these groupings, wherever pruned, are brought to light by simply examining respondent choices in game period and using the tools of machine learning. Notice, once again, the clear and early distinction between non-historical and historical game periods using no more input than a survey respondent's period preference.
I hope you find these results of interest as well.