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Saturday, May 11, 2024

Grouping Wargame Periods

In one of the many analyses from WSS' 2022 Great Wargaming Survey (GWS), I explored aggregated survey respondent tendencies based upon wargaming period choice.  Do particular periods tend to group together was the question I asked.  This analysis utilized cluster analysis (see Game Period Choice: A Cluster Analysis). 

Why revisit this topic two years in a row?

Well, two motivations came to mind.

  • Unranked vs Ranked and Top 5 vs Top 3.  The 2022 GWS asked respondents to choose their top five wargaming periods in an unranked manner. The 2023 GWS asked the same question but responses were limited to the top three in rank order.  What effect will these changes have upon the results?
  • Reliability of Data.  While questions often surface about the data collection methods and data reliability, I regularly offer analyses in an attempt to mitigate these reservations.  Do groupings remain reasonably consistent across these two years of survey responses?

Today as in last year's analysis, we switch from descriptive analytics to predictive analytics.


Cluster analysis is again the tool of choice.  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" denotes that the results do not rely on any predefined labels or categories. Rather, the machine learning technique discovers patterns and structures present within the data itself.  Cluster analysis can provide a powerful exploratory data analysis tool that can reveal hidden structures and patterns even within complex datasets.

What questions can be answered from this analysis?  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? 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.  There are 9,282 respondents having 26,741 data points (each respondent could have up to three period choices) used in this analysis.  Using only respondent wargaming period preference from the survey, these data are aggregated and classified using cluster analysis.  Only respondents and their choices are utilized in building this model.  Figure 1 illustrates the initial dendrogram showing how each of the twenty wargaming periods groups.

Figure 1
Starting from the position of hierarchical clustering, we begin on the righthand side of Figure 1 and identify the two-cluster solution by drawing a vertical line through the dendrogram bisecting the graph at the two-cluster solution.  

Figure 2
The two-cluster solution clearly and cleaning bifurcates the twenty wargaming periods into two, distinct groups. The two groups identified, with no ambiguity, are Historical periods and Non-Historical periods.  Well, perhaps a bit of ambiguity.  Pulp groups into the non-historical grouping but perhaps that makes sense since Pulp identifies with a wide genre of adventure/RPG gaming. 

The results demonstrate that historical wargamers generally tend toward historical gaming while non-historical gamers tend to remain in the non-historical genres.  Notice within Non-Historicals that Warhammer periods show distinct separation from the Fantasy/Sci-Fi/Pulp periods.  What emerges if the clustering is taken down to the three-cluster solution?

Moving the vertical cut to the left, the dendrogram is bisected across three branches to identify a three-cluster solution.  Note that the three-cluster solution keeps Non-Historicals separate and intact but Historicals are further split.  As we saw in the two-cluster solution, the split in the three-cluster solution is intuitive in that the Historical groupings are clearly split between Pre-1700 and Post-1700 wargaming periods.  

Figure 3

Note that while Pike & Shotte clusters with the Ancients/Dark Ages/Medieval groupings, that clustering does not occur until much earlier in the process. While Ancients/Dark Ages/Medieval periods join at the ten-cluster point, Pike & Shotte does not join until the four-cluster point.  Pike & Shotte is its own, distinct entity for a long time.

Let's cut the dendrogram one more time to examine the four-cluster solution.  What happens to the clustering solution as we move from the three to four-cluster dendrogram?

Figure 4

In a four-cluster solution (Figure 4), Non-Historicals and Pre-1700 Historicals remain unchanged. This time, the four-cluster solution splits Post-1700 Historicals into two groupings.  This bifurcation breaks out Napoleonic Wars, World War 2, and American Civil War from the rest of the Post-1700 Historical group.  I will classify this subdivision as the Big 3 Post-1700 Historicals cluster.  Naturally, my cluster naming conventions are subjective but I reckon they give a sense for the periods within each grouping.  Other naming conventions are possible.

Did I manage to answer some of the questions I originally set out at the beginning of this analysis?

Let's recap...
  • Top 5 Unranked vs Top 3 Ranked.
    • While there was slight movement in the ultimate clustering solutions, almost all results showed similar results between 2022 and 2023.  Perhaps any variation can be attributed to the addition of two more choices in the 2022 survey which may have dampened the distinctions between groups.  
  • Reliability of Data.
    • With the exception that WWII grouped with ACW and Napoleonics in the 2023 survey (perhaps due to the reduction of choices from Top 5 to Top 3), results were almost identical between the two surveys.  This suggests a level of stability and robustness present in the survey even across years.   
  • Using only gaming period choice, do distinctions between historical and non-historical gamers emerge?
    • Of course!  The two-cluster solution identifies this bifurcation early on.
  • Do some game periods tend to cluster together? Which ones?
    • In the 2023 survey as well as in the 2022 survey, wargaming period preferences tended to group within the same clusters.  See the figures above to verify.
  • 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.  Each name represents its component periods well.

Like in 2022, the results are fascinating and quite clear given that the only data inputs consist of up to three period choices for each survey respondent.  No other inputs are needed for formulating the inferences highlighted in this analysis.  

Hope you find these results of interest as well.

35 comments:

  1. That is fascinating, perhaps to be expected, but it is good to have expectations backed up by the data. Although it is surprising how often they aren't! Thank you for the analysis.
    John

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    1. Fascinating results to me too, Sev! Good to see your intuitions sometimes reinforced by data.

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  2. It is interesting, yes. So fascinated by those boundary conditions of Pike & Shot...putting Killicrankie and Sherrifmuir, and Steenkirke and Blenheim (and Narva!) in different categories...plus the power of the commercial and the vibe, with Warhammer Fantasy and SF being more closely aligned than Warhammer Fantasy than other Fantasy, not interesting generally but interesting in the context of gamers who are aware enough of other stuff that they come into contact with WSS magazine...

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    1. Pike & Shotte is an interesting period with respect to these groupings. Notice that it joins the pre-1700 grouping late. With WSS having a foot in both Pike & Shotte and 18th Century periods, one wonders where it actually falls within the survey.

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  3. Ye gods, Jonathan, this is starting to make sense to me. Interesting to see the march of interest period change to musical chairs. Fantasy/Sci Fi is bound to show up during migration of players to historic periods. Over the long term, the big battle versus skirmish games, break through rules sets, change of metal to plastic, resin, print rather than castings may be a factor in games played?

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    1. Starting to make sense? Hooray! The attributes you list could affect games played but for this exercise, I wanted to focus only on period choice to see how the wargame periods clustered, naturally.

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  4. Perhaps it makes sense that it gets overshadowed by the higher-order "fiction/history" divide, but I can't help but feel that there should be some traceable link between the Ancients/Dark Ages/Medieval cluster and the non-GW Fantasy, since figures are often able to cross over.

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    1. I agree with you Norman. We see in survey results that there is some crossover between non-historicals and historicals often through Ancients/Dark Ages/Medievals. Notice in the graphic that these periods are closest of the historical groupings to fantasy/sci-fi.

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  5. Jonathan, I am concerned that respondents to this post seem to understand all of this and despite me reading it 3 times - I can’t get enough of a grip of it to make any cogent answer that can add to the discussion ….

    Other than to observe that my boardgame collection spans from ancients through to WWII and if I had the time, money and space, my figure collection would do likewise. I don’t even think I could rank periods of gaming importance to me, so perhaps I straddle all of the above historical categories.

    I suspect that when I complete my survey each year, my answers probably just reflect my current rather than overall interests.

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    1. You are funny, Norm! If you cannot make it through the analysis, well, then that is on me.

      How did you pick your Top 3 wargaming periods in the 2023 survey? Do you throw darts or simply choose what was recently on your table? My preferences tend to evolve over time as well but my main interests remain "mostly" constant.

      By the way, you added to the discussion without even trying. Thank you!

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    2. I think my answers for the annual survey are probably based on that months gaming habits, perhaps not solely, but I’m sure there is a big element of that as I am quite fickle.

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    3. Don’t worry Norm. I had to pass three courses on stats to get my doctorate and I can’t make it through either. I just skip to the conclusion. 😀

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    4. Stew, you give up too early. You’ve yet to reach the point of “statistical maturity” as a professor once announced.

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    5. I do give up early. It’s one of my defining traits.
      The intro and the conclusions do make sense to me. 😀

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  6. As Sev noted in the first comment Jon, nothing particularly surprising...except perhaps, to me, the ACW is one of the Big Three....does this perhaps indicate a greater proportion of your countrymen answer the survey? Have you looked at period choice v geographical location (as I type this, I think I remember that you have!)
    I am a bit like Norm, given unlimited time, space and finances, I would have Ancient and Medieval collections too, to add to the multitudes I already have. WWI is an Era that does not greatly interest me...but even there, I do have a small collection of East African Brits!

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    1. Hi Keith, I suppose ACW is one of the Big 3 when Ancients are excluded and rolled into the pre-1700 grouping. I have looked at period choice by location! Without looking, I recall North America saw more ACW gaming while UK saw more Pike & Shot.

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  7. Our group played its first game of a 10mm fantasy ruleset last weekend, with another planned for next weekend, so I look forward to altering this analysis in the next survey. I'm not exactly sure what the game was, but there were lots of dice.

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    1. Lawrence, it is good to see some diversity of gaming. Fantasy has its place but not yet at my table.

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  8. As others have pointed out; the longer you’ve been doing this hobby the more likely it seems that your collection will include some of everything. But I still think it’s valid that you’d have some favs. These are likely the largest parts of the collection. I kinda thought the survey might one day ask the same collection that way. Like what are your 3 biggest collections? 😀

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    1. Thanks, Stew. Perhaps a question for this year’s survey?

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  9. It seems to me that the clustering is pretty much as one might predict, which isn't a bad thing, as it validates our more subjective impressions.

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    1. Indeed! Not only do results match our impressions but lend credibility to the survey, itself..

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  10. Interesting as always, as Norman points out lots of fantasy games, like Stews recent convention game are essentially dark age bashes! I think my three biggest collections would be be my three period choices, well definitely two!
    Best Iain

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    1. Thanks, Iain! I am not so sure that my three largest collections are in my Top 3 periods. My top preferences tend to change more quickly than my top collections grow.

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  11. After seeing the subject of this post I went away, made myself a cup of tea, then settled down to read it very carefully. Your analysis is interesting but, as already observed, not surprising. A pleasant tea break digesting your hard work. As always, interesting and thank you for your work on this.

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    1. A welcome response to my efforts! Much appreciated, Richard!

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  12. Rather like Norm, I'm still baffled by the charts, but then I was happy to pass my 'O' Level maths at secondary school! However the results make sense and in the 10mm Pendraken 'World', certainly WWII followed by Napoleonics are their top sellers by a country mile.

    As for increasing collections and periods with age and possible space, maybe I'm bucking the trend by actually only focusing on a few core periods with a very heavy ImagiNations bent, with the exception of WWII.

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    1. Thanks, Steve! While I cannot understand those who are able to limit their collections to a few periods, I do envy them.

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    2. I envy my friend, Keith Flint, at times, as he really just games the SYW and Poland 1939, so just two collections. He has dabbled in Ancients, but not in the any meaningful way.

      I suppose after my brush with cancer 5 years ago, my shaky arm and parent/carer duties, all of which have made me realise that I know I need to focus on core periods first, then we will see what transpires after that.

      Another reason maybe that after my working life making models and designing things, sometimes it can feel like a busman's holiday rather than a hooby!

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    3. Well, Steve, you have good reasons for limiting your collections! My problem is that I rarely find a conflict or period that does not draw me in.

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  13. ummm... apologies but I didn't understand either? For the non-statisticians here, how do you decide the order in which to list the categories down the side of the page - and what determines how they 'cluster together' at each level, and how you draw the dividing line?
    Apart from that, it's all very clear... :)

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    1. It's all magic, David...The unsupervised machine learning does the association, ranking, clustering, and confusing.

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