Saturday, November 7, 2020

Favorite Game Period: A Cluster Analysis

The prior series of GWS2020 analyses focused primarily on descriptive analysis of a few select topics or survey questions.  Today, we dive a bit deeper and turn attention toward predictive analytics.  

For now, we take the familiar favorite gaming period analysis one step further.  While earlier analyses counted responses across various categories, this analysis attempts to infer relationships and tendencies between respondents and their top selection of game periods.  To accomplish this task, the top five game periods for each respondent are identified and added into the study. Respondent's choices (the Top 5 per respondent) are aggregated and examined using statistical modeling techniques.  The technique for this study is cluster analysis in which game period choices are grouped in such a way that game periods in the same group are more similar to each other than to game periods in another group(s).

Some possible questions to consider before diving into the analysis are:
  • Based upon gaming period choice only, do distinctions between historical and fantasy gamers emerge? 
  • Do particular game periods tend to cluster together?  Which ones?
  • If distinct groups emerge from clustering, are these distinct groups intuitive?
  • Do favorite game periods group into reasonable and explainable buckets?
  • What can be inferred from this analysis?
First, using only data from Question 12 showing a respondent’s favorite game period (Top 5 only), these data are aggregated and classified using unsupervised machine learning.  The result of this classification is illustrated in Figure 1.  Each of the 21 game periods are represented in the dendrogram.
Figure 1
Starting from the right and drawing a line across the first two branches of the dendrogram tree identifies two clusters of game periods (see Figure 2).  What does this primary division suggest?
Figure 2
This initial clustering cleanly bifurcates favorite game periods into two, distinct groups.  Based upon the periods found in each cluster, we can infer that there exists a clear distinction between Historical and Non-historical gamers with respect to favorite periods chosen.  Historical gamers tend to select other historical periods and non-historical gamers tend to stick with non-historical game periods.  Of course, there will be cross-over but in broad terms, this holds.  At a high level, this is a reasonable result.  What if more granularity is wanted?  What does the analysis suggest is the next clustering solution as focus moves farther out onto the dendrogram?

The next clustering solution as we move from right to left, crosses three branches as shown in Figure 3.  What is this three-cluster solution?
Figure 3
The three-cluster solution keeps Non-historicals intact but bifurcates historicals into two components.  I label this break-out as Pre-1700 and Post-1700.  Pike & Shotte, Medieval, Dark Ages, and Ancients are in the former and all other periods cluster into the latter.  It may seem odd that Pike & Shotte finds itself grouped into Ancients/Dark Ages/Medieval but notice that there is a distinction between Pike & Shotte and its trio of Pre-1700 compatriots.  Perhaps, this grouping is more focused on combat with hand weapons, primarily.  That is, spear, pike, sword, and bow?

There remains many game periods within the Post-1700 cluster.  Can the Post-1700 be broken into meaningful components?  For that, let's move to the five cluster solution as shown in Figure 4.
Figure 4
In a five cluster solution, Non-historicals and Pre-1700 remain unchanged.  The Post-1700 group is split into three parts.  The three new clusters form the Age of Muskets/Rifles, Hollywood, and Modern.  Of course, these are general names I give to each group for my own identification but more interesting (and precise) identifiers are possible.  Suggestions?

The analysis could continue marching down the tree, pruning branches along the way to group game periods into even smaller groups, but I stop here for now.

What this exercise suggests is that aggregating the 10,783 survey respondents' answers to top choices of game periods brings forth underlying and hidden patterns.  These seemingly natural groupings are brought about simply by examining respondent choices in game period.  Notice, once again, the clear distinction between non-historical and historical game periods that the analysis identifies using no more than personal choice.  It is fascinating that distinct period clusters emerge from within this one analysis.

If there is interest, I can continue the analysis by climbing out on a limb to investigate these ever smaller tree branches.  Hopefully, I do not prune the branch upon which I am sitting.

As always, questions and comments welcome.

36 comments:

  1. Once again, great that you are delving into the data further Jonathan. It's interesting for those who completed the questionnaire to know where we fit.
    I wonder if you did this as a principal components analysis if it would show more clearly the groupings and then were individuals lie on the axes. Likely we'd see a few who cross over many periods (near the origin), but many who fit squarely into a quadrant. What do you think?
    Regards, James

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    1. Glad to see you continue to enjoy these analyses, James! Your idea of exploring PCA is an interesting one. I typically use MCA for these categorical variables (which you will see in later analyses) but will look into applications of PCA for this study. I may generate a MCA on these game periods to see what the picture holds.

      Good question!

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  2. Well I literally have figures in each of these five sections - even the non historical, as I have a few Pulp figures. What does that say about my personality/psyche I wonder??

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    1. Keith, it says you are well-rounded and a diverse gamer! Either that, or you have trouble making commitments...

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  3. I'm trying to think or any friends who don't game/collect in all these groups but failing.

    Perhaps an artificial selection of "favourite" at the moment of doing a survey may not reflect the ebb and flow of life as well as one might hope.

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    1. Ross, I tend to agree with you. My favorites changes from survey to survey and even from day to day!

      Thanks for your response!

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  4. Personally I game from around the ECW through to WWII, with the latter, the 18thC & 19thC being my favourites. At anyone time they very as to which one is currently in vogue with me, so my response during the survery might be different now if asked to choose again.

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    1. Thanks for your feedback, Steve. Like you, I expect many of us wander from grouping to grouping. The survey suggests, that broadly, we tend to stay within functional groupings. My responses likely vary from year to year as my interests fluctuate. I wonder if I ever have filled this question in the survey the same?

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  5. I found this analysis especially interesting, Jon. The groupings and associations seem pretty logical. Like most of the commentators, I have figures and interest in Sci-Fi Naval and fantasy, but they wouldn't be in the top 5. Same for 18th century Naval and Renaissance Naval. That merely illustrates that even top 5 fails to capture the diversity of individual gaming interests. I found the relatively sparse overlap between pre 1700 and post 1700 interesting. I suppose the cluster makes some sense, as many popular rules systems can be used for much of the pre 1700 era - WRG, DBX, Impetus, Hail Caesar (etc), To the Strongest! and many others.

    Thinking of my own answers, no question 25/28mm Napoleonic is always going to be my top interest, but after that I may have put down Renaissance/Pike and Shot or Ancients.

    Other indicators of wargaming interest worth exploring by era and/or scale might be games played in the past 1-2 years, rough size of existing collection (painted only!), and purchases made in the past 1-2 years.

    I have thought about some kind of color graphic badge displaying a "pie chart" of interests, much like your painting data analyses, with the color and an icon representing the period, and of course the size of the slice indicating intensity of interest. Maybe we could program it into a sort of Apple Watch for Wargamers, counting brushstrokes and die rolls, perhaps, LOL!

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    1. Very good that you found this installment interesting, Peter!

      Yes, I constrained this analysis to top five choices of period. I have varied interests too but mine are almost exclusively historical. You make an interesting point about transportability of rulesets across periods. Your examples of Impetvs, To the Strongest, and Hail Caesar dovetail into your hypothesis very nicely. I had not considered the "closeness" of Pike & Shot to Ancients/Medievals/Dark Ages may have common rules as a contributing factor. Great observation.

      As others have noted in this and other analyses comments, top 5 changes over time. You and I are no exception to this.

      I had the figure collection size question added into the 2020 survey along with the frequency of gaming. Annual hobby spend is included into the survey but it is not broken down by either period or figure size.

      I would like to see more on your notion of badge use to better classify us. But badges? We don't need no stinking badges.

      Thanks, as always, for comments and insights!

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    2. "The Multicolored Badge of Wargames"
      The troops of the WOtR rather liked badges as well...
      OK, we can call them icons or infographics if one prefers. :-)

      Re wargames periods, I though you might enjoy Brent Oman's recent comments on how many army lists were needed for a 300 BC to 1500 AD set:

      I break it down into the following subgroups:

      1. Early - everybody wears towels and uses pointy sticks.
      2. Classical - big shields, big helmets. Longer pointy sticks and hacky swords. Cavalry with a purpose.
      3. Romans. Big bad Romans never admitting that they're beaten.
      4. Romans. Everyone finally gets to beat the Romans.
      5. Scrum. Not much tactical nuance. Foot supreme.
      6. Scrum. More tactical nuance. Horse supreme.
      7. Heavy metal. Clang. Wicked cleavers. Long pointy sticks.

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    3. Very good, Peter!
      Are you building armies for WOTR?

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  6. Is there a way to track shifts in the groups over time? I'd be interested particularly to see if there's any tendency to transition from one to another as one ages, and if overall trends can be related to shift in the demographics of the hobby as a whole.

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    1. You ask hard questions to answer, Markus! The 2020 survey was the first that asked for a game period ranking by choice. Prior years simply asked for level of interest for each period. some periods could have high interest and some medium or low with no monotonic ranking. Could something similar to the analysis here be done across time? Yes. I did something a similar graphic for the 2019 survey and could carry the same techniques back to earlier surveys. Something to put onto my "To Do" list.

      Thanks, Markus!

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  7. I wonder whether some periods / rulesets have a natural proximity to both historical and non-historical gamers, so a favourite period crosses two interests or at least fraternises with them .

    Just two off the top of my head are;

    1. 1946, WWII ends but there is non-historical scope to explore further action and a non-historical scope to make this period 'Weird War', so that the gamer has an army that is both rooted in late period WWII and new technology / Sci-Fi with things like werewolves, zombies and 'special weapons'. Whether you are historical or non-historical, if you choose this period / genre, you end up with an army that has both historical and non-historical elements. Warlord Games do this with their Conflict '47 system.

    2. Ancients seems another cross-over period, with some rule systems having a sister rule set that covers the 'other' interest, So for exampleGreat Escape Games do Sword and Spear rules for Ancients, but they also do a fantasy version of the same rules for fantasy elements.

    Mantic Games did the Kings of War system (fantasy) for Historicals.

    In each of these cases, the player ends up with duel purpose armies, historical and non-historical, but perhaps only declaring one part, that reflects their prime interest, as favourite, yet buying the other part from a trader and generating significant sales by default in what would count as a non-favourite period.

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    1. Norm, you raise some interesting questions. Where exactly would "Weird World War II" fit into the categorization scheme? I would likely classify it in the "Alt-Hist" game period but C20th or Pulp might to be fitting as well. I think of Bob Murch's fine collection of Pulp fiction figures. Where would one classify German Zeppelin Troopers and US Rocket Corps?

      For (2), Peter makes a similar point with respect to rules like Impetvs, Hail Caesar, and To the Strongest used for many cross-period games.

      If a respondent's favorite historical and non-historical game periods both made the top 5 then that cross-genre relationship ought to show up in this analysis if commonplace. Since non-historical appears as a distinct and somewhat isolated branch, then having both historical and non-historical periods in the Top 5 may not be as common. Note that Pulp and Alt-hist find there way into this non-historical branch along with fantasy and sci-fi.

      Good discussion, Norm. Thank you!

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  8. I was thinking about something similar only yesterday, in that the DBMM Ancients rulesets go right through to Italian Condottiere and Ottomans, stopping just short of the thirty years war. Although the rules work fine and actually make for a good game, it does feel a little strange to me, especially when we also play the DBR renaissance set by the same author with the same armies.

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    1. Thanks for your feedback, Lawrence. I have neve tried DBMM or DBR but I may have a copy of DBR on my bookshelf. What are your thoughts on DBR with respect to pros and cons?

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    2. It's quite a fun game, although like DBMM it feels very geometric at times, with bases lining up. There is also a strange result that occurs on a die roll when you throw and even as opposed to an odd which feels a little gamey, and the use of a D6 can have quite a dramatic effect if someone throws a 1 and the other a 6, but they give a decent enough feel for the period and it is possible to get a game concluded withing three hours or so. I'd recommend them, but I'm also very keen to convince the group to give FK&P a go.

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    3. Thank you! I look forward to seeing your success in convincing your group to try FK&P. I will pull DBR off the shelf and put on the nightstand.

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  9. Another fun read Jonathan and nicely illustrated with the graphs. The groupings presented make perfect sense to me and I think are other ways to represent/ label our primary interests as intended.
    I’m thinking of rule sets that try to cater to these groups, not do much crossing history and fantasy lines but trying to target specific groups and would wager that the more commercially successful ones either try to cover all the genres within a group or target one specific genre really well. For example rules like Hail Caesar tries to cover all the genres in the Pre-1700 group. Or as I would call it “gonna hit you with something hard and metal” group.
    Like a lot of people I have cross over in all of the groups so I get to be a club member wherever I go. 😀
    Nice job on all these posts discussing the survey so far. 😀

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    1. Stew, you make my day with your kind comments. Thank you!

      The groupings make sense to me as well. Isn't it interesting after that processing of these responses from almost 11,000 wargamers worldwide that we can reach conclusions that make sense?

      I like your label of "Gonna hit you with something hard and metal" for the pre-1700 group. I bit long but descriptive. I wrestled with appropriate labels for each group. Some were more obvious that others.

      Glad you are enjoying these survey deconstructions. I have enough topics and explorations to carry me through until the next survey in August. Hope I can maintain your continued interest.

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  10. Hi Jonathan,
    I'm an old codger whose first thoughts as to what constitutes a 'Wargame'- I think of Napoleonics everytime. When I think of Sci-Fi (such as Laserburn 15mm) I tend to think of it as a 'Game using Miniatures' and not necessarily a 'Wargame'. Just the same as thinking about AVBCW (A very British Civil War)- I think it isn't a 'Wargame' though rather 'Alternative History'...anyway it is just me...I like your efforts on Surveying the Hobby. Regards. KEV.

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    1. Hi KEV. “Games using miniatures” works too. If battling it out on a table is involved, perhaps, “battle gaming” is more appropriate for these alt-history conflicts? Thank you for your thoughts!

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  11. Interesting analysis, and it bears out as a logical outcome. I am curious if the responses here in the comments are more a result of shared interest with your blog and thus more representitive of a more diverse interest. (I.e. you have a wide array of models in your collection, and so does your fan base)

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    1. You ask a very good question, Jake! One I think about too. If this blog focused on one particular period, for instance, would readership and especially commentary show such diversity in cross-period interest?

      Thanks!

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    2. I was actually thinking about how you could tie this into a Social Network Analysis project. Look for trends in terms of Followers, areas of interest and post frequency. Not sure if the juice would be worth the squeeze, but would make for an interesting diversion.

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    3. Interesting suggestion. I am not sure how useful "Followers" would be as a predictor. Most Followers are silent, some probably long gone, and many not active readers. How would you scrape the data from Followers to make meaningful assessments?

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    4. When you click on a follower you get both a link to any blog they have as well as a link to all the blogs they follow. From there you can start aggregating interest groups. Tie the blogs into the their focus areas. Segregate out for blogs followed, versus comments left. I would be willing to bet, for example that you and Peter would have relatively high centrality measures based on how often your comment. Also, I would be interested to see which blogs act as central nodes that link the disparate interest groups together.

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    5. This sounds like an interesting exercise. Have you tackled this for your blog? Perhaps if you had a prototype working, I could give it a try?

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    6. Not yet. I was bouncing around using it for an SNA course I was taking, but it was a little too niche for the training audience. I have some new software I am playing with, so I might give it a whirl in the near term.

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    7. I am very interested in seeing how you manage the web scraping to pull the data from the various blogs. Let me know how your experiment goes.

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  12. Another interesting post,I've got armies that cover a lot of these periods, historical and fantasy, especially when you consider that the warhammer empire is really the holy Roman empire of the 16th century! It's funny that TtS can be used with my early Imperial Romans,dark age types and also with my Italian wars figures standing in as condittore,I'm missing the 19th and 18th centuries, but I'm okay with that!
    Best Iain

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    1. Thank you, Iain! You are another well diversified gamer.

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  13. Interesting points for discussion and interesting to see people thoughts as well. I think like so many who have commented i don’t fit Into into any strict norm. My interests have gradually moved towards ‘historical’ where most of my focus in painting an developing projects. One of the most interesting questions in my view is why we are interested in the periods we game. Mine certainly go way back to my early years. I certainly don’t think I hit your initial model as the only 2 subjects on the list which don’t attract me are old west and pirates, which I don’t really think of as Genres on their own ? The challenge is can we actually game that much ! to make the most of our collections👍

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    1. Hi Matt! The discussions revolving around these analyses are my favorite part of these GWS series. I try to lay out the topic, make some inferences, and then step aside as you all weigh in with your thoughts and insights.

      My interests have always been historical. Why do we gravitate to the periods that we do? That is an interesting question too. One I need to ponder for my own wargaming development. My interests certainly go back to my youth as well. Are wargamers made or born?

      When I did a similar analysis for GWS2019, Old West and Pirates grouped into the non-historical bucket. I suspect that was more due to the manner in which this question was asked. Last year, it was a free-for-all. This year choices were ranked with only Top 5 contributing here.

      Your last question is really a good question for all of us to ask ourselves. Perhaps this should be the focus of a future blog post?

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