The Weight of Arms (WoA) score was introduced in Saga #85. The purpose of the calculation is to provide a “neutral” means of handicapping weaker armies, as defined by a standard measure. A WoA score re-calibrates the usual MW army points total (525 at Cold Wars, for example) used to generate a specific tournament list for a specific MW army list. The re-calibration emphasizes those troop types/weapons that are robust on an open table, and discounts those that are better deployed in delaying terrain, behind obstacles, in a second line, etc. The WoA formula is reproduced below. Please note, however, that the rule below adds an additional element, the “normalized” WoA calculation. As has been pointed out by several players, there are many factors outside the pale of the WoA metric that may explain differences between armies, including tabletop generalship. All of the members of the MW family are still learning good MW tactics; some are more experienced, some learn faster (or not).

The Great Cold Wars Experiment

It was proposed that some analysis of the WoA measure be performed using the results of the 2002 Cold Wars MW tournament. There were some wrinkles introduced in the CW tournament that reduced the discriminatory power of the WoA measure. First, the tournament was divided into two brackets: (i) the Dark Ages-Feudal Ages or “first” bracket; and (ii) the Age of Chivalry-Later Middle Ages, or “second” bracket. Second, the rules covering “axes” were changed, making them far more competitive in MW; specifically, 1.5 ranks were allowed to fight, and the (initial round) melee factor was increased to 3. And finally (although not a new wrinkle per se), Terry likes to match up historical opponents in the first round of a tournament, so regardless the bracket (and the WoA), the armies are likely to be well matched.

The results of the Cold Wars 25mm MW tournament have been correlated with the WoA scores of the participating armies (minimum of two games). The first observation to be made is the separation of the armies into two brackets generally worked to segregate the higher scoring WoA armies from the lower. The raw average WoA score in the first bracket was 415. If the high and low WoA scores are eliminated (what’s this, Olympic figure skating?), the average score increases to 425. In the second bracket, the average was 494, which increases slightly to 496 with the high and low scores dropped.

The second observation concerns the accuracy of the WoA score as a predictor of victory. In the Dark Ages-Feudal (a.k.a. “first”) bracket, the higher WoA scorer failed to win a single game (there were two ties) in 8 match-ups(!), whereas the high scorer won 5 out of 8, or 62.5% of the matches in the Chivalry-Later Middle Ages (a.k.a. “second”) bracket. This entire effect (4 out of 5 games) may be attributed to the Ayyubids (ahem, that would be me!) and the Anglo-Irish failing to win a game against higher scoring WoA opposition. These two armies were in fact the only armies in the second bracket whose WoA scores (386 and 314, respectively) were significantly below par (475 - 525). If the averages are weighted by the CW total points scored, the weighted average WoA score for the first bracket is 406, and 508 for the second bracket.

The weighted average was calculated by multiplying each army’s WoA score by its total victory points won in the two rounds of CW, and then summing up all of these products for each bracket; the result was divided by the total number of victory points scored in the respective brackets. It is interesting that the weighted average WoA (or WAWA) fell significantly in the first bracket, but increased in the second bracket. These results suggest the following:

(i) as observed above, the lower scorers won consistently in the first bracket, thus an average weighted by victory points had to have “gone south”; and
(ii) WoA was a meaningful indicator of expected success in the second bracket, the high scorers performing better and the WAWA shifting 12 points higher.

The author contemplated attempting a more rigorous form of analysis, and still may do so if additonal results are collected, but this is Saga, not Econometrica. As much as some of us love t-statistics and R-squares, we’ll save some tricks for another day (besides, for the reasons noted above, this data may not provide much analytical kick in a formal analysis).

Results

The results are tabulated below. Details of the WoA calculations are available in the Files section of GoreAMwar (http://groups.yahoo.com/group/GoreAMwar/), in the Weight of Arms folder. The individual game match-ups and results may be found at the end of the article.

WoA	Army List	CW Total
367	Anglo-Norman	8
417	Gaelic Alliance	8
512	Nikephorian Byzantine *	8
403	Welsh	7
136	Scots-Isles Highlanders *	6
375	PreFeudal Scots *	6
634	Normans *	4
479	Saxons	4
454	Swiss	10
565	Burgundian Ordonnance *	9
485	Free Company	8
660	Later Polish	8
467	Ottoman	7
619	Teutonic Knights *	7
386	Ayyubid Egyptian	6
314	Anglo-Irish	4

An asterisk (*) indicates a WoA score based on the author’s proxy for the actual list used. Some proxies are likely to be off the mark, but not egregiously so (he boldly claimed).

Observations

It is surprising how high the scores are for some of the armies in the first bracket. The Saxons, for example, with many stands of spear and HI, look good at 479 points; they really cannot compete on a table loaded with delaying terrain, so one ought not to be surprised at their potential in the open. Clearly, their flanks need to be anchored; I didn’t observe the army in action, so I don’t know how the games against the Gaelic Alliance and the Pre-Feudal Scots played out. Similarly, the Welch, with plenty of longbows and long spear, are not an easy mark either.

Since WoA typically (by design) over-rates cavalry and anti-cavalry armies, the relative strengths of good infantry armies may pass under the radar. It’s a “scissors-paper-stone” thing; WoA is so focused on scissors-paper and scissors-stone, that we can’t see paper-stone. That is, if scissors stood for cavalry, stone for close order infantry, and paper for loose order infantry, the paper-stone interaction is not measurable via WoA. The “paper” armies of the first bracket, including the Pre-Feudal Scots, the Scots Isles Highlanders and the high scoring Gaelic Alliance held their own against the "stones": the Welch and the Saxons. Meanwhile the “scissors” had mixed results, the Anglo-Norman and Nikephorian Byzantines rising to the top of the bracket, while the Normans faltered.

The Normans, despite the awesome shock they are capable of generating, which translates into a very high WoA score, are also a very vulnerable army (relatively poor armor, despite their aggressiveness). Shooters can mow the Normans down in droves, especially if the Norman CinC cannot control his fanatics; one would anticipate that they would have trouble against the Nikephorian Byzantines and the Welch, despite the respective WoA scores.

The numbers of long and crossbows available to players of many second bracket lists are what give them staying power, once one moves past the (mostly) FPC knights. The Burgundian Ordonnance, the Free Company, and the Teutonic Knights all feature tough knights and superior shooters. The Swiss stand out for being decidedly different, with modest numbers of knights and shooters, but masses of pikemen. The Swiss, beating the Free Company probably speaks volumes about the occasional vagaries of the shooting-dice, as one might expect longbow firepower - the Free company have lots of it -- to cripple the pike blocks before they come to grips. But sometimes it don’t always work - if the shooters go awry, they are toast, and their cavalry can’t hope to save them if they can’t get an open flank.

The Late Polish are also a different sort of army, since they are a composite of the steppes’ nomads and western steel. The championship match-up in the second bracket, featuring the Poles against the Swiss, was probably the ultimate scissors-stone fight.

The eastern entries, the Ottomans and the Ayyubids, definitely exhibit a technological deficit. The Ottomans generally have poor armor and plain old bows; their only edge is their artillery, which can deal some awesome damage. The Anglo-Irish are definitely a throwback, first bracket kind of army (like the Anglo-Normans); however, they are not to be taken lightly, as it is the author’s understanding they have defeated the Late Poles by using good tactics.

A Note on the Ayyubids

The Ayyubids’ primary shortcoming in their second bracket match-ups was relatively poor missile power and poorly armored infantry. For an army almost totally armed with bow, it is surprising that they can be outshot, but the greater ranges of long- and crossbows allow the latter to punish the lightly armed Ayyubid bowmen as they maneuver into effective range. Thus, the troops raised to screen the Ayyubid cavalry need to be screened themselves(!), a job that strains the Ayyubid budget (the cavalry is expensive and lots of it is required).

In battles against the Teutonic Knights and the Free Company, the Ayyubid cavalry pretty much held its own, but the weaknesses of its infantry proved decisive. Despite the use of woods and obstacles to shelter the largely UI footbows, they were shot-up nonetheless, crippling the Ayyubid attacks.

Conclusion

The CW analysis brings mixed results. Separating the armies into two brackets definitely limits the explanatory power of WoA. There are two facts to keep in mind: (i) in the second bracket, a WoA deficit was (apparently) significant in over 50% of the matches, all of which featured a WoA difference of (ca.) 100 points, and (ii) WAWA in the second bracket exceeded WAWA in the first by over 100 points. Regarding (i), one could infer from this that the average first bracket army would find the going (much?) tougher against second bracket opponents. It may be that the proposed WoA optional tournament rule could be reduced to the following simple formula:

If an army list scores 100 or more WoA points less than an opposing Book 2 army list, the former may pick one of the options listed under the scouting optional rule. The lower scoring list may originate in either MW army list book, but high scorer must come from Book 2.

Summary of WoA

The WoA for a MW tournament army list is computed according to the following recipe:

1. Add Full Value per stand of: All Generals
2. Add Full Value per stand of: All Mounted (wedging stands count 2x)
3. Add Full Value per stand of: Pike, Long Spear or Halberds
4. Add Full Value per stand of: Close Order Foot > LAI
5. Add Full Value per stand of: Long- or crossbows, and artillery
6. Add Half Value per stand of: Other Missiles > Javelin
7. Add Half Value per stand of: All Other Foot > LAI
8. Subtract Full Value of: UI not covered by 3, 5 or 6