Whether it is a good or bad thing is ultimately in the eye of the beholder, but the relationship is intentional. If all the die roll results are average, then the two smaller Formations will Fatigue out prior to the larger Formation. The presumption of Cohesion is a characteristic of a given body of troops not "whatever troops are present". Thus, two brigade-sized Formations each have weaker Cohesion than a larger division-sized Formation equal to their combined size.

The chance of the two smaller Formations successfully tripling the larger Formation is approximately equal to the chance of the larger Formation tripling one of the two smaller Formations. The chance of the larger Formation tripling both is substantially lower.

The chance of the two smaller Formations successfully doubling the larger Formation is approximately equal to the chance of the larger Formation doubling one of the two smaller Formations. The chance of the larger Formation doubling both is substantially lower.

Lastly, the chance of the two smaller Formations failing to double the larger Formation slightly greater than the chance of the larger Formation failing to double one of the smaller Formations.

But, as you correctly realize, equal outcomes here are not equal. The impact of each point of Fatigue on either of the two smaller Formations is materially greater than the impact of each Fatigue on the larger Formation – that's the core benefit of the larger Formation, it has more staying power.

For the two smaller Formations to succeed against the larger Formation, they need some of those odds to break their way – or they need the context and circumstances of the battlefield to influence the results. The benefit of more Formations (regardless of their size) is flexibility. I would generally not encourage taking multiple smaller Formations head-on into a larger Formation of nominally equal size. But, I would encourage utilizing one smaller Formation to pin a larger Formation in place while using a second in an advantageous way – whether that be by flanking, Threatening while avoiding the enemy's arc, etc… Similarly, a larger Formation desires a larger frontage and footprint than a smaller Formation and this can potentially be used against it.

Again, all of this comes down to the design philosophy behind Cohesion and a Formation. The basic presumption is that a Formation is not just a jumble of Units present in the same place but those under a unified command structure functioning together in a coordinated fashion. Two different Formations are necessarily two different command structures – they'll likely join somewhere up the chain whether it be at the Force-level or the Army-level, but they are still separate elements.

Posted by: @lloydeaker

We did wonder if Wellington could just add several brigades together to make a divisional sized formation

Whether or not this is a good choice will vary, but can a Force Commander do this? Yes, by using the Create/Absorb a Formation Leader Action (3.4)

Hi David, To start with I really love these rules. But I am having trouble with players in our group because of this issue. We have the same problem, in reverse, with "Fire & Fury". With smaller units having such an advantage as to almost break the game.

David said: "Again, all of this comes down to the design philosophy behind Cohesion and a Formation. The basic presumption is that a Formation is not just a jumble of Units present in the same place but those under a unified command structure functioning together in a coordinated fashion. Two different Formations are necessarily two different command structures – they'll likely join somewhere up the chain whether it be at the Force-level or the Army-level, but they are still separate elements."

I understand your point on the design philosophy. Which is why I asked Feature or Bug. If armies with better command & control values handling larger formations, where other nations could not, it would be a Feature! But it is not so in the rules or other paraphernalia currently, as I read them.

However, I do disagree about your points above that, about the relative affects on the various formations. Skip the following math to the bold below if you wish. The math is to show I took your points into consideration.

Again, if a formation is 12 battalions in 2 lines of 6 facing 2 formations of 6 battalions in 2 lines of 3 each (a starting point only for math purposes). Then the larger formation will generate about the same threat against each of the smaller formations as the smaller formations each do against the larger formation.

l, r, L, R= threat value against each formation. (These numbers are in the case above 3(3)+1+2d6=12-22 with the peak at 17.)

L & R for the larger threat against the left and right smaller. l & r for the left and right smaller against the larger.

On the average roll the values of l,r,L&R are the same calling it t. Averages lie but it is a good starting point.

c= cohesion of each Smaller formation.   (This number is in the case above 6(1)+1 =  7.)

C= cohesion of Larger formation. (This number is in the case above 12(1)+1 =  13.)

l+r/C=Damage to larger. L/c & R/c=damage to each smaller.

Using the numbers above:  smaller formations= (12 to 22)/7 which yields 1 to 3 with 2 being really the most likely.

The larger formation= 2(12 to 22) or (24-44)/13 which yields 1 to 3 with 2 being really, really, the most likely.

This averages of 34/13 = 17/7+17/7  -or-   2.62 vs 4.86. or .54/1, pretty close to 1/2.

The comparisons of the 2 formulas is 2t/13 Vs 2t/7. This is not anywhere near balanced.

Yes, at this point due to the d6 per 9 variablity the smaller formations will have a larger chance of doing 3 fatigues than the larger of doing 6 fatigues total. (The smaller have to roll 4d6 obtaining a total of 17 (almost 1 in 4), while the larger must roll 2d6 obtaining an 11, on 2 different attempts (1 in 6), to do 3 on 1 of the smaller formations.

If the larger does take more than either smaller formation it will roll for those loses first (this is about 1 in 5). But this is very unlikely to break contact with the smaller pair, who will also have to roll and take about the same damage EACH!

However, that is a red herring. The mostly likely outcome will be the smaller formations taking 2 each (1 in 3 of 1 smaller taking 1 hit) and the larger taking 2 as well. I can run all of the probabilities of this fight, but the different possible sizes of formations will materially affect the outcomes because of the variable number of the d6s involved due to the +1d6/9 initial threat valuations.

Conclusion: This means the larger formation is really almost twice as strong as the 2 smaller formations combined. Not twice as strong as 1 of the smaller formations, but almost twice as strong as both together. This is initially. With 1 or 2 combats the scales will tilt, precipitously, in favor of the larger formation, assuming even a modicum of normal luck (which can bite the smaller formations as well). 

Lloyd

Lloyd,

I'm not really sure what your question is. Are you asking for confirmation of your conclusion, or contextual input as to how the Threat/Cohesion system works, a justification, or something else?

@david Thank you for the detailed explanation.