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.

Last Stand at Fornovo

The group of five players from Game #4 (see Still Fornovocating) returned to the table in Game #6 for a rematch.  Doug and Stephen switched sides while Mark, Brian, and Alan switched commands. 

Battle lines drawn.

The commands for Game #6 are illustrated in the photo below.

Army deployments and player commands 

While the French skirmishers and cavalry deploy,
its infantry marches on. 

French King Charles VIII prepares for the attack
he expects to fall upon his army.

The Italian League's Right awaits
orders to cross the Taro River.

The battle opens with Gonzaga sending one of his two bodies of Men-at-Arms (MAA) straight away across the Taro River and into the center of the French battleline.  Almost without effort, a French gun is overrun and the MAA carry on into de Gie's Gendarmes.  Fighting is fierce as the two bodies of heavily armored horsemen clash.  The first melee of the battle sees de Gie gaining an upper hand.  The Italians are forced back with de Gie in hot pursuit.  The Italian nobles are caught from behind and scattered.  From the opposite bank of the Taro, Gonzaga looks on as his initial attack is repulsed and his MAA destroyed.  The battle is not opening in the manner in which he envisioned.

Italian MAA charge into the guns...

overrun them and crash into de Gie's Gendarmes.

De Gie drives the enemy back... 

and then scatters the Italians in pursuit. 

On the Italian Left, de Monotone's MAA emerge from the ford and charge into the King's Gendarmes.  The clash is decided quickly as the Italians, still disordered from crossing the ford, are cut down quickly as the King leads his Gendarmes into battle.  The survivors of de Montone's MAA are driven back across the river.  They are done for the day.   

With his cavalry streaming back across the river, de Montone orders his infantry to cross the Taro.  Before the infantry can climb up the opposite bank, they are struck by a second body of Gendarmes and driven back across the Taro.  In the early going, two Italian cavalry charges end with two Italian bodies of horsemen destroyed.  This may be an uphill fight! 

De Montone attacks and his MAA are
 destroyed by the King's Gendarmes.

De Montone's infantry are stalled
 in their attempt to cross the Taro.

Gonzaga remains undaunted.

Sending mounted crossbow across the river, the Italian light cavalry overrun a second French gun.  With Caiazzo's light cavalry on the Italian Right harassing de Gie's French Wing, Caiazzo brings his German pikemen across the Taro to support Gonzaga's light cavalry in the center.

A second French gun is overrun...

while German pikemen advance into the French Center.

Overview of battle situation.

As the Germans plod forward in their dense formation, de Gie leads his Gendarmes into a frontal attack against this formidable foe.  Despite the heavy fighting and scoring four hits (blue die) against the French, de Gie overcomes the odds and drives the Germans back with very heavy losses.  The Germans retreat with only about half of the infantry they maintained moments before.

More despair for the Italians.

de Gie attacks the German pike block...

driving them off in great disorder and with great loss.

Still the Italians come on!  Gonzaga brings his infantry across the Taro as the river continues to rise.  After witnessing his Germans manhandled by de Gie's Gendarmes, Caiazzo leads his MAA through the river and into the now wavering Gendarmes.  In a flash, de Gie's Gendarmes are scattered and de Gie lays dead on the field.  In pursuit of de Gie's fleeing cavalry, Caiazzo cuts a wide swath through the French battle line.  French skirmishers are cut down and the French Army is split in two! 

Gonzaga brings his infantry across.

Caiazzo leads his MAA against de Gie.

With his army now split, the King brings up his infantry in an attempt to reclaim the center.  Heavy fighting ensues as the two armies batter each other.  Both armies are beginning to waver but neither will yield.  Gonzaga chooses this moment to decide the battle.  Leading his MAA into the rapidly rising waters of the Taro, he fails to gain the opposite bank.  The infantry clash continues.  Again, Gonzaga attempts to emerge from the raging river.  Again, he is stymied.

Brutal fighting in the center.

On his third attempt, Gonzaga finally emerges from the river to engage the King.  The hand-to-hand clash lasts many rounds as each body is slowly ground down.  Who will blink first?  The French King! 

King Charles breaks off combat and heads for the rear.  Exhausted, Gonzaga cannot pursue.  With both armies teetering on collapse, here the battle ends.  We call it a draw.

Mano-a-Mano

King Charles in retreat!

What a great game on which to end the series of Fornovo battles! 

While many of the five previous contests were close seeing many coming down to the wire, none saw such an even erosion of army morale like this one.  Like two heavyweight prize fighters in the ring, both armies kept battering each other with neither wanting to yield.  Ending in a draw seemed a reasonable conclusion to such a hard fight.  The Italians got off to a very Rocky start (see what I did there?), but they valiantly fought themselves back into the game.

The battle ebbed and flowed throughout and fate of the Dice Gods reared its ugly head more than once.  Fortune smiled upon the players as well.

Thanks to the five players for another very entertaining and action-packed game.  Great fun!  Hopefully all enjoyed fighting this action a second time as much as I enjoyed watching the battle unfold.  With six games' worth of trials and lots of data upon which to ponder, I plan to return with final thoughts on the scenario and play when time permits.

Now it is time to retire Fornovo and consider something new.

Endless Fornovocating

For those keeping score at home, four Battles of Fornovo are in the books with the French and Italians knotted at two wins apiece.  Game #5 took place last Tuesday with a full complement of five players.  Chris and Tony commanded the French Army.  Mark, Dave, and Stephen took the reins of the Italian League.

Armies arrayed for battle

Initial army dispositions and commands.

With the ground and situation likely familiar to regular readers, I dive straight into the battle chronicle. 

Gonzaga's Italian League begins the battle by occupying the three fords.  Caiazzo pushes his skirmishers into the Taro River with plans to establish a bridgehead while Gonzaga orders a body of Men-at-Arms (MAA) forward into the river.  De Montone sends his mixed infantry retinue splashing into the ford.

Having the initiative as the battle begins, Gonzaga orders Caiazzo to engage the enemy.  Caiazzo's light cavalry harass the enemy while the Italian Right Wing works to bring Caiazzo's command across the river.  While Caiazzo is bringing his wing to the French side of the Taro, de Gie comes forward leading his Gendarmes toward the river.  De Gie's skirmishers try to counter Caiazzo's demonstrations against his left.  Both French artillery and archers harass Gonzaga's MAA as they negotiate the ford.  

King Charles strikes!

Seeing the Italian MAA struggling to cross the Taro, the French King Charles, leading his Gendarmes, strikes.  Crashing into the Taro, the King hits the Italians midstream.  Unfortunately, both bodies of horsemen are hampered by the river and the slippery rocks on the river bottom.  After a protracted melee, the King is forced back to dry ground to regroup alongside de Gie's MAA.  Both bodies of horse have suffered from the exertion but the Italians gain the upper hand and emerge from the river somewhat worse for the wear.

To expand the limited bridgehead so that more of Gonzaga's command can cross, the Italian MAA debouch from the river and jump from the frying pan and into the fire.  As the Italians move toward the French battle line, they are stopped by the seemingly immovable object of de Gie's Gendarmes.  In the ensuing clash, the already wavering Italians are driven off and plunge back into the river with de Gie in hot pursuit.  These Italians are done for the day.  To replace his lead body of now dispersed MAA, Gonzaga moves up to the Taro at the head of his Famila Ducale.

Italian MAA emerge from the Taro...

only to find themselves face to face with the enemy.

Already wavering, the Italians are quickly dispatched.

Now, time for de Montone to attempt to force the Taro.  His mixed infantry cross without incident followed up quickly by his MAA.  With both horse and foot on the French bank of the Taro, de Gie orders a body of crossbowmen into the river.   

de Montone begins the crossing...

to establish a bridgehead across the Taro River.

Despite the difficulties of fighting his way across the Taro, Gonzaga repulses de Gie's MAA.  With heavy losses, de Gie retreats back through his own artillery line.  Skirmishing continues to dominate the French Left as the Stradiots swarm among the enemy. 

Gonzaga attacks from the river!

de Gie and his Gendarmes are driven off.

With de Montone forming a bridgehead on the French held side of the Taro, the King sends de Foix' Gendarmes (the second body of Gendarmes in the King’s command) in against the enemy while he buys time to bring up his infantry.  Initially, de Foix' Gendarmes see success as de Montone's MAA are pushed back into the river.  Undaunted by this setback, de Montone's MAA fight on as the melee seems to turn against the French Gendarmes.  Finally, the elastic snaps and the Gendarmes race for the rear.  De Montone and his MAA pick up the chase.  Caught from behind, the French Gendarmes are scattered.  We hear Chris decrying, Oh, the humanity! as his Gendarmes are lost.  The Italians now have a strong foothold on the French side of the river.

Chris' Gendarmes (de Foix) crashes into enemy MAA. 

de Foix wins the initial clash...

driving de Montone and his MAA back into the river.

With tenacious spirit, de Montone fights on...

and the French are eventually forced back. 

De Montone pursues and
 de Foix' Gendarmes are cut down.

De Montone gains a foothold
upon the French side of the Taro.

The Italian foothold gained under de Montone's leadership is short-lived.  

Bringing up his infantry, the King orders his crossbow and spearmen forward.  Assailed by volleys of crossbow bolts, the Italian MAA waver before dissolving back toward the ford.  Unfortunately, the river has risen even more and the horsemen drown in their attempt to escape. 

De Montone's MAA destroyed!

Even with a French advance on his right, the King is not happy with his situation in the center.  Not wanting to get caught out, he leads his Gendarmes to the rear.  Now, both de Gie and the King, himself, are falling back behind the safety of the guns.  Caiazzo brings his German pikemen across the Taro as the waters rise. 

The King retires!

Situation for the King is dicey. 

Watching the French Center fall back, Gonzaga seizes the moment.  At the head of his Famila Ducale, he charges the guns.  The French guns are overrun.  Gonzaga's pursuit carries him into the rear of de Gie's Gendarmes.  Not surprisingly, the French cavalry are scattered.  With a gaping hole cut through the French Center, Gonzaga charges on.  His luck has run its course, however.  Stymied by light cavalry to his front, he is attacked from the rear.  His Famila Ducale are destroyed.  Gonzaga narrowly escapes capture.      

Gonzaga overruns French guns...

scatters de Gie's Gendarmes...

but is finally stopped before
he could deliver the coup de grace.

Having sent off de Montone's MAA, the King's infantry advances to finish off the Italian infantry who now find themselves isolated on the wrong side of the rapidly rising river.  With preparatory volleys from crossbow, the French close with the enemy.  In a hard clash, the Italians suffer greatly.  Reduced to half strength, the Italians are compelled to retreat.  The Taro, however, has risen too high and the Italians either drown in vain attempts to cross or lay down their arms to the enemy.  

Italians fight with their backs to the Taro.

The Italians will not be crossing here!

With his army now split by the rising Taro and his remaining infantry trapped on the wrong side of the river, Gonzaga is lucky to make his way back across the swollen river.  Facing a massive Swiss pike block and French infantry marching toward the center, the remaining Italian infantry's prospects are dim.  For the Italian League, the battle is over.  

Italian infantry trapped on the wrong side of the Taro River.

Fornovo delivered, once again, another exciting battle.  The battle witnessed its share of ebb and flow as the two armies clashed, retired, pursued, and clashed again.  Watching this battle unfold with every twist and turn of fate and fortune was a pleasure.  The battle saw hard-fought action throughout with a decision up for grabs until the end.  The outcome really could have tipped the other way although weighing heavily on the Italian loss was the destruction of three or their four MAA.  Game completed in under three hours.

Congratulations to Tony and Chris for coming away with victory, no matter how narrow.  In post-game discussion the French noted that they figured all was lost more than once.  They persevered!

My condolences to the Italian commanders of Mark, Stephen, and Dave.  They also fought hard and we even were treated by some good dice throwing by Dave!  

In the end, a rising river does not float all boats but takes heavily armored men to the bottom.

Great fun, fellas, thank you!

Fornovo Game #6 is on deck for a final Tuesday performance.  After that, I clear the table and consider what to bring to the table next.