Small Figures and Large Collections?

The recent GWS post examining four wargaming traits and their relationships (see Tinker, Tailor...) prompted some discussion on social media.  While I am not present on Bluesky, I was asked a follow-up question based upon a discussion on that platform.

From my secondhand understanding, conversations centered around the hypothesis that gamers using smaller figures tend to have larger collection sizes.  I reckon the insinuation was that the analysis was being distorted by a missing Figure Scale variable.  The question posed to me was, it this true that there is a negative correlation between figure size and collection size?  That is, as the size of the figure decreases, collection size tends to increase.  Can the survey actually test this hypothesis?

The short answer is No, not directly.

While Figure Size (Scale) is included as a variable in the survey, the variable is a ranked choice field where a respondent can rank up to the Top 3 choices.  If many of the respondents are like me, they will have figures in more than one scale.  Perhaps even many scales.  I certainly do!

To answer this question definitively, a separate question would be needed to ask each respondent the distribution of their figure collection by number of figures in each scale.  Not something many would be able to provide without a lengthy (or even impossible) counting exercise.  If those data were captured, then, yes, a correlation analysis could be produced.  Could the existing survey offer any clues or provide a proxy to help answer the question on a possible inverse relationship between figure size and collection size indirectly?

Perhaps.

For the sake of exercise, let's claim that a respondent's top choice of figure size directly reflects the largest holding in a collection.  If so, top figure size might be utilized as a reasonable proxy to compute a correlation between figure size and collection size.  We could do something similar by aggregating across all Top 3 choices too.  Will this result be meaningful to answering the question posed? Perhaps not directly but possibly a useful insight or two will emerge.

Let's begin with respondent's first ranked figure size.  Graphically, the distribution of figure size stratified by collection size is illustrated in Figure 1.

Figure 1

First off, notice that Figure 1 demonstrates 25/28mm dominates all smaller figures sizes across all collection sizes.  When 28-32mm "Heroic" size is added into the 25-28mm mix, especially at the smaller collection sizes, this market concentration is impressive.  While 28-32mm "Heroic" makes up a sizable first choice in the smaller collection sizes, 25-28mm garners nearly 40% of the first choice in collections at least 501 figures in size.  

28-32mm "Heroic" first choice percentages of total fall markedly as collection size increases.  Conversely, 15-18mm figures sizes see an increase in first choice as collection size increases.  So far, this may support the original hypothesis if all else is equal but how to account for the large and fairly stable position of the 25-28mm category?  The near monotonic tendencies seen in 28-32mm "Heroics" and 15-18mm figures sizes are not seen in the smaller figure sizes as collection size increases.  06mm, 10-12mm "Epic", and 20mm show no first-choice pattern of either increasing or decreasing as collection size increases.  From the results in Figure 1, these three figure sizes cannot reinforce the original hypothesis that smaller figures necessarily lead to larger collections.  However, it is worth noting that these figures sizes make up a smaller representation of totals in comparison to other, larger figure sizes.

What if we tackle this hypothesis from a different angle?  Past analyses have demonstrated that a gamer's primary interest drives a number of decisions and tendencies.  Primarily Fantasy/Sci-Fi gamers (values of '5' and '6' in the survey) are typically younger, spend less, have fewer years of accumulation, prefer skirmish-type games, and require fewer figures to game.  Primarily Historical gamers (values of '0' and '1' in the survey) tend to be older, have more disposable income, have many years of accumulation, tend to fight entire battles, and often field larger armies.  

Turning to a gamer's primary interest and collection size, Figure 2 shows that the percentage of those respondents having a primary interest in Fantasy/Sci-Fi decreases monotonically as collection size increases.  Again, conversely, as collection size increases, the percentage of gamers having a primary interest in Historicals tends to increase.     

Figure 2

In this case, do results suggest figure size or primary interest drives collection size?  Of course, correlation does not mean causation.

What about examining these data by bringing figure size, collection size, and primary interest together into one analysis?  To accomplish this task, multiple correspondence analysis (MCA) is called up for action to plot the relative relationships between these three variables.  Figure 3 details the initial plot.

Figure 3

As seen in other analyses using MCA, the four quadrants are marked out to see if any meaningful inferences and labeling can be made for the underlying associations.  Figure 4 shows Figure 3 with quadrants delineated to help in visualizing the results.

Figure 4

See the clustering that falls out from MCA?  Figure 5 colors codes the quadrants to ease explanation.

Figure 5

Once color coded, three clusters emerge from the quadrants.  Each labeled cluster corresponds to one of the primary interests of Fantasy/Sci-Fi, Historical, and Mixed.  The Mixed cluster spans two quadrants.  With only three primary interests defined, having three clusters emerge makes sense.  Given that figure size was based only upon a respondent's first choice, these are interesting results.  The three clusters are:

• Fantasy/Sci-Fi (blue) grouping tends to favor collection sizes of 0-100 figures and prefers 28-32mm "Heroic" figures more than the other groupings.
• Historical (yellow) grouping tends to prefer figure sizes of 20mm and under and collection sizes greater than 5,000 figures.  That is, compared to Fantasy/Sci-Fi and Mixed. 
• Mixed (green) grouping tends to hold collections from 501 to 5,000 figures and prefers 25-28mm figures when compared against the other two clusters. 

Collections of between 101-500 tend to be seen in Fantasy/Sci-Fi and Mixed more so than in Historical gamers.

Once again, the survey results produce some interesting and (I think) remarkable results.  Based upon this study, can we reject the hypothesis that smaller figures lead to larger collections?  Even using a proxy for precise allocation of the number of painted figures stratified by figure size, data and results suggest, this answer is "no" to the hypothesis question.  There is a caveat, though.  A gamer's primary interest may have a hand in driving both figure size chosen and collection size amassed.

  

Where do I fit into these clusters?  Well, I do track painting output so the question can be answered authoritatively with no need for any proxy.  I am solidly in the Historical camp and my painted collection size is in the top category at 25,001+.  Only a small percentage are 6mm.  A larger (but still small percentage) is 10mm.  The mass of 15/18mm figures makes up the majority of my collection coming in at 56%.  25-28mm takes the second spot at 23% of total painted figures.  Perhaps my entry point into the hobby helped define my preference too.  15/18mm figures were my entry point into tabletop wargaming.  25/28mm figures came relatively later. 

Figure 6

As a wargamer, do you find yourself situated within one of the corresponding quadrants present in the MCA graph?  Does the hypothesis that smaller figures lead to larger collections hold with you?

If you have yet to do so, please take the time to complete the 2025 survey.  Survey closes on 31 August.

A Week of Gaming

On the gaming front, this week was a busy one.  Four games passed into the Gaming Log, two of which I hosted.  Until I have time to chronicle the two I hosted, following is a brief summary of the gaming action seen this week.

Monday: Continuation of the Battle of Quistello with the Rejects.  We concluded the two part battle with a clear victor but as often is said, "it was a near run thing."  Battle report to follow.

Tuesday: ECW Siege hosted by Peter.  I tried my hand at assaulting fortifications in a siege game as Peter ran the programmed defenders.  I took the town but only just.  Peter's account of the battle can be found at ECW Siege.

Friday: Battle of Quistello.  A second playing of this scenario with a quartet of new players.  We managed to complete this game in one, four-hour session which is a faster decision than with the Rejects' game earlier in the week.  Not as close as the Rejects' game but a good contest, nonetheless.  A rematch may be in the offing.  Battle report to follow on this one too.

Saturday: Battle of Arzobispo.  A Peninsular War battle pitting the French vs the Spanish.  Had not played Napoleonics or Shako II in a very long time.  Battle outcome came down to the very last die roll, literally.  The Spanish just managed to sneak out a victory despite their army in shambles and the French driving hard to annihilate them.

Whew!  That was a lot of gaming!  Sunday may require a day of rest.

The latest GWS analysis (see Tinker, Tailor...) generated several follow up questions from a variety of sources.  These data will provide some answers; others may be unanswerable.  I will attempt to tackle some of these questions in upcoming analyses.

Dog Days of Summer

Yes, the Dog Days of Summer are upon us here in the Pacific Northwest and temperatures have been hot.  Even the dog seeks refuge from the heat.

The latest addition to the household, Milo, tends to hang out with me when I am downstairs in the game room whether painting, reading, or studying the game laid out on the table.  Now, I tend to think he likes the company but it could simply be that he enjoys the coolness of basement.

Anyway, I stood up from the painting desk one afternoon and looked all over for the dog.  He had been on the couch earlier.  Well, he was there last time I noticed, anyway.  He was nowhere to be found.  Then, I heard a faint rustle coming from under the game table.  I walked around to the end of the table and looked between the boxes lining both sides of the table.  I see two eyes and a white curly head peeping up over one of the boxes from under the table's dark underbelly.  In the few seconds it took to grab the camera, he jumped up onto one of the boxes and walked over to me.  Clearly climbing over my boxes of figures was no concern to him.  The box he is padding across is the one containing my 1/72 WWI aircraft collection.  Funny dog.

Given that we are in the throes of the heat of summer, my attention turned to a little retail therapy from the comfort of the couch in the game room.  Besides a small order to Lancashire Games for FPW Prussians and Bavarians, Pat Smith's Volume 3 of Setting the Scene arrived in my post box.  Looking forward to diving into this work with thoughts of returning to Norway for an early WWII game.  That game may wait until winter when the snow flies.

Also in the mail was an order from Jerry's Artarama for a fistful of Rhapsody Kolinsky Sable brushes that were on deep discount.  Rhapsody brushes are a regular staple in the brush arsenal along with Winsor & Newton Series 7 Kolinsky Sables.  Why not stock up?  Exactly!

On the gaming front, this week is a busy one with games on Monday (in a conclusion to the Quistello battle with the Rejects) and Tuesday with Peter (see ECW Siege Battle Report).  On the schedule are two more games on Friday, and Saturday.  Four games in a week is a lot!  Hopefully, I can carve out some time to chronicle many of these games.  For now, though, it is time to walk the dog.

Tinker, Tailor, Soldier, Poor Man

While we wait for the 2025 survey to run its course, still more to discuss from the 2024 survey.  If you have yet to complete the 2025 survey, you can do so at WSS 2025 Great Wargaming Survey.

Today's analysis examines four wargaming traits in the hope of reducing these data in order to produce a few identifiable and meaningful wargaming profiles based upon survey responses.  The statistical technique used to explore relationships and correlations between these four variables is Multiple Correspondence Analysis (MCA).  MCA extends Correspondence Analysis (CA), which is typically used for two categorical variables, to more than two variables.  MCA is a powerful exploratory tool for summarizing and visualizing relationships in datasets with several categorical variables, helping to uncover patterns and associations that might otherwise be hidden.  MCA has been utilized in a number of past analyses.

Very briefly, the key points of MCA are:

• Purpose: MCA helps to detect and represent underlying structures in complex categorical data, making it easier to interpret relationships between variables and categories.
• How it works: It transforms categorical data into a numerical format (indicator matrix), then applies dimensionality reduction (similar to Principal Component Analysis for quantitative data) to project the data into a lower-dimensional space.
• Output: The results are often visualized as maps or plots, where similar categories and individuals are positioned close together, revealing associations and clusters.
• Applications: Widely used in social sciences, marketing, and survey analysis to explore patterns in responses, profiles, or preferences.

The questions pulled from the survey and used in this study are:

1. Do you consider yourself mostly a historical, or more a fantasy/sci-fi wargamer on a scale of '0' (pure historical gamer to '6' (purely fantasy/sci-fi gamer)? 
2. How do you rate yourself as a craftsman on a scale of '1' (terrible) to '5' (great)?  Variable name = CRAFTSMAN with values 1-5.
3. On a scale of '1' (not interested) to '5' (deeply interested), how much do you research the (fictional or not) background to your game?  Variable name = RESEARCH with values 1-5.
4. How many painted figures do you have in your collection?
5. How often do you currently game?

The variables under consideration are Craftsman, Research, Collection Size (Collection_Size), and Gaming Frequency (Game_Freq).  Will any identifiable patterns emerge from these data manipulations?  Well, let's see.

To begin, only survey respondents whose primary interest is historical wargaming ('0' or '1' in question 1) are included.  Total number of respondents in the sample is 1,652.  With that criterion set, the frequency counts of each variable and its values are illustrated in the following four bar graphs:

Craftsman

Research

Collection Size

Game Frequency

While pairwise comparisons between any two variables can be useful, all four of the variables need to be considered simultaneously to extract any meaningful patterns and relationships between wargamers and their tendencies.  To produce enough separation between values, outlier removal can be a useful technique used in an iterative process.  Upon first inspection (see MCA: Initial), many of the data points are compressed into the lower left of the graph.  This is a good candidate to test select outlier removal techinques.

MCA: Initial

In the first iteration of outlier removal, two outliers are removed.  They are Research1 and Collection Size of 20,001-25,000.

Outlier Removal: Research1 and Collection Size 20,001-25,000

After Iteration 1, values are still compacted into the lower left quadrant of the graph without much separation.  In Iteration 2, three variables are removed as outliers.  These are Research2, Craft1, and Collection Size 0-100.  Now, these three could have been removed in Iteration 1 but I kept them in to illustrate the process.

Outlier Removal: Research2, Craft1, Collection Size 0-100

After Iteration 2 of outlier removal, the spread between values is improving but Craft5 emerges as an outlier.  Iteration 3 removes Craft5.

Outlier Removal: Craft5

Having completed three outlier removal iterations, the spread between values is improved with enough separation and distinction to stop and assess the results.  Next step is to move onto the analysis and interpretation of the resulting graph.

MCA: Final 

Using the origins in both dimensions (1 and 2) four quadrants are delineated.  By studying each of the four quadrants, is there any underlying inference that emerges to help classify each of these spaces into any meaningful grouping label?

Overlaying wargaming terminology of troop experience to each of these four quadrants seems to fit the model inference in a reasonable fashion.  I use the terms of Crack, Veteran, Regular, and Green to distinguish the attributes within each quadrant.

MCA: Interpretation

The loadings of variables and values into each quadrant present themselves counterclockwise as shown by the green arrow as follows:

Crack: Identified by high research values (5) and craftsmanship (4) values, gaming more than once a week and having massive painted armies (Poor Man!).

Veteran: Identified by large armies with weekly gaming.  Little distinction with Regulars with respect to research values (3).  No loading on craftsmanship. 

Regular: Identified by high research values (4) and medium craftsman values (2,3).  Gaming tends toward bi-monthly with painted armies 100-500 figures.

Green: Identified by good sized painted armies (501-2,500) and infrequent gaming but with less interest in either research or craftsmanship than the other three groups.

Interesting results and equally interesting groupings between the loadings within each quadrant.  Always a surprise when data reveal their hidden, underlying tendencies.  Where do I fit into this analysis?  Well, I fit into the Crack classification quite closely with the exception that my craftsmanship rank is not likely up to '4' standards.  I need to step up my game!

Where would you fit into this scheme or do you?

I wonder if adding in rules source would add anything worthwhile into this analysis?

Quistello, Act I

Monday saw the first outing of the Quistello scenario mentioned in an earlier post.  With six players, fighting the battle remotely, four, action-packed turns were completed in a little under three-and-a-half hours.  With the hour getting late in the UK, we called a halt to the fighting.  The question on the table is whether to call a truce or pick up the game another day.

When the battle began, army dispositions were as illustrated in the game photos below:

The Allies (Franco-Piedmontese) control the west bank of the Secchia River while the Austrians control the east bank.

The victory conditions on this day are:

• Sudden Death: Army Breakpoint Reached.
• Major Allies: Hold Quistello and the western line of the Secchia River.
• Minor Allies: Hold the line north of the canal.
• Major Austrians: Hold Quistello and either Mirasole or San Benedetto or exit five units off western table edge north of canal.
• Minor Austrian: Hold Quistello and Gaidellina with no Allied units south of the canal.
• Otherwise: Draw

When the battlefield smoke cleared once the fighting stopped, army dispositions and front line are shown as,

with Quistello in Austrian hands and the Allied Center breached.  After hard fighting and a traffic jam crossing the Secchia, the Allied Army has been split and the Austrians are threatening to cross the canal.  Still, both armies have plenty of cavalry available to fight and possibly affect the outcome.  The Allies have one brigade broken while the Austrians have two brigades broken.  To achieve Sudden Death victory, both armies must break two more enemy brigades. 

After four turns of play, the Butcher's Bill shows the casualties as,

Allied Losses

Austrian Losses

With not all players available for continuation and the battle leaning in the direction of a possible draw, the decision to fight on or withdraw from battle remains.  Good game, so far, but is the writing on the wall?

What will be the choice?

That Time of Year, Again

Yep!  If it is August, then it is once again time to complete WSS's The Great Wargaming Survey.

A few new questions have been introduced into this edition and a few of the old questions have seen some amendments.

You can take the survey at Great Wargaming Survey.  Completing the survey takes about ten minutes or less depending upon your familiarity with the questions and your verbosity on the open-ended questions at the end.

As a test, in the "Final Observations" open-ended question at survey's end, if you put in PWJ2025 along with your final observations, I will be able to capture results from readers of this blog.  With enough responses, I may tailor some of the analyses to this subset of survey respondents to see how readers collectively view some of the questions.

Go ahead, fill out the survey and try to remember your answers when some of these topics are discussed in analyses throughout the upcoming twelve months.  Survey closes on 31 August.

Piedmontese Reinforcements and a Game

With an expected return to 18th Century battlefields after a series of WotR games (Solden Hill and Mortimer's Cross) seeing action on the table, the brushes saw work adding to the 18mm SYW/WAS/(and now) WPS collection.  Yes, a third conflict is being studied.  That study focuses on the War of Polish Succession (WPS) of 1733-1738.  Many of the same antagonists seen in the later War of Austrian Succession are seen here and some of the same Northern Italian ground is fought over again. 

Since the Piedmontese/Sardinians fought in both conflicts, two more regiments were pushed into the painting queue.  This time I field two of the many provincial infantry regiments.  Marching out today are IRs Aosta and Asti.  Foot figures are Old Glory led by Eureka mounted colonels.  Flags are David's handiworks from Not By Appointment.  These two 23-figure regiments will be added into the regulars already on the muster rolls.

What WPS battle is on deck first?  Well, I will present my interpretation of the 1734 Battle of Quistello first introduced to me by André in his PBEM game several years ago.  André's inspirational work on this scenario can be found on his blog at Quistello.

Research turned up the following contemporary map,

and an account by Ben Franklin.  Yes, the Ben Franklin!  Franklin's 1734 account of the battle can be found at Variant Accounts of Battle.

Using André's map and Google Earth as guides, my interpretation of the battlefield topography and troop dispositions are illustrated in the photo of my game table below:

First game is on deck for Monday with six of Postie's Rejects in a remote game.  Looking forward to it!

Still have work to accomplish before Monday with writing a Battle Briefing, updating the QRS, affixing labels to all of the units, and positioning units onto the table.