Domains At War Using Mismatched Scale Units

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TL;DR - If I have some super powerful units that would operate in smaller groups than the scale of the battle, this just means taking 1/4 of the regular BR in Campaigns, for say companies against battalions. Do people think it’s still balanced in Battles, where a company has 1/2 health and 1/2 damage of a battalion, so 4 combined would have 2x a battalion’s combined strength?

So in D@W Campaigns and Battles, there are rules for scaling up unit sizes - and in the case of Campaigns, how to handle splitting a larger unit into smaller sections. But by my reading, do they not have significantly different outcomes?

In Campaigns, if you have a battalion sized group of troops in a company scale battle, you can either multiply the BR by 4, or split it into 4 companies of the standard BR. Or in the inverse, a company at battalion scale has 1/4 the BR. This makes neat, logical sense with the 4x scaling.

In Battles, if you did the same thing, a company would have 1/2 the UHP and 1/2 the damage of its battalion equivalent, not 1/4. Or alternatively, a battalion has 2x the UHP and damage of a company. I can sort of understand the reasoning - a battalion has 2x damage because it has 2x the frontage, and - I believe - 2x the UHP because, in melee at least, only unit depth matters for health as front ranks fight front ranks, and a battalion is only 2x the depth of a company. This does make logical sense.

But it means splitting a battalion into 4 companies in Battles the same way as Campaigns, actually results in a set of units that - combined - have 2x the UHP and 2x the damage of their combined self. You can see this with the Under-Wizards in the Battles Artashumara army - they’re a company scale unit that deals 1/2 the damage of the battalions in the same army… So having 4 of them instead would result in something 2x as powerful as the company scale BR in the Campaigns version would indicate.

Is this just a natural consequence of the system that exists as a presumably somewhat uncommon edge case that doesn’t really need balancing? The only balance I suppose it has, is that doing this would need 4x the AP, for units that will individually start making shock rolls quite quickly.

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So there are actually two ways you can do this, as distinct in-world options.

First, you can field a thinned formation with full frontage. This retains the normal unit stats, but starts the unit at proportionately less uhp. A half-strength unit of human light infantry would start at 3/6 uhp (and make 2 attacks as normal), so any damage it suffers is going to force shock rolls and it will take penalties to morale from being at half uhp or fewer, but because it retains the full frontage of a unit, it deals full normal damage with its attacks.

The second option is to pull the troops in tighter, to have full depth but a narrower frontage. This means fewer soldiers at the front in contact with the enemy, and so proportionately fewer attacks, but it starts at full uhp (that is, a half-strength unit of human light infantry would start at 3/3 uhp and only make one attack). Because its max uhp are only 3, if it gets reduced to 2/3 uhp it won’t have to make a shock roll, and it won’t suffer penalties to morale from being at half uhp or fewer.

Either way, half as many troops means half as many uhp. It’s just a question of whether you field them in a wide but shallow formation (full attacks but vulnerable to shock), or a narrow but deep formation (reduced attacks but resilient to shock).

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Thanks for the considered response - I like the idea of half health but full damage units, but I’m not sure it quite gets to the heart of what I’m describing. I’m simply trying to reconcile the maths between Campaigns and Battles versions of the scaling rules.

See, a single company of a battalion is 1/4 the size however you slice it. That’s why it comes out as 1/4 the BR in Campaigns, nice and neat. Get 4 of them, and you’re in business back at the original BR.

But in Battles, things only double upon scaling from company to battalion. A light infantry company - of which there are 4 in a battalion - has 6UHP, and 2 attacks of 1dmg each as you describe. But a battalion of 4 companies doesn’t have 24UHP and 8 attacks. It has 12UHP, and still 2 attacks but dealing 2dmg each for a total of 4. The result is that 4 companies added together have twice the UHP and damage of a battalion with the same troop count, and in the inverse, a battalion reduced to 1/4 of its health (and thus, a single company of remaining troops) has half the health of an identical but independent company.

I’m fairly sure it’s a quirk of the system - a company has half the frontage of a battalion, which explains the half damage as you describe, but it also having half the depth alongside that is calculated as being half health, not quarter health, because UHP doesn’t care about frontage.

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A light infantry company, deployed at the battalion scale as a company, would either have 1/4 of the uhp of a battalion, 3uhp, if deployed wide or would need to have the math re-done on how they look as a unit if deployed deep.

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Ah, thank you, I do see the issue you’re encountering. The scaling is very clear when you compare hero attacks - a hero makes the same number of attacks vs a unit at company or battalion scale, but at battalion scale his attacks do half as much damage and the unit has twice as many hp. One uhp doesn’t represent the same thing across different scales, but is instead a function of the scale as well.

I think the cleanest answer here is to prevent companies from deploying as such, and to instead make them form up as partial strength battalions. So long as they are all no more than a quarter strength, they could still have company scale commanders and lieutenants, though I would also rule that commanders of company divisions in a battalion scale battle halve their ZOC (round down), because the distance across a hex is doubled.

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Apologies, bit of a long one this time but I get to a pretty solid conclusion I think.

If I understand right, your suggestion for companies is to make them battalions with 3 of their 12UHP, right? At the underlying ‘damage is width, health is depth’ level, that is I suppose how it would look if the company stood in one big battalion line, similar to your description of the half strength company in your first reply. Whereas the default rules assumption of 6UHP but deal 1 damage instead of the 2 of battalions is like your full depth narrow frontage example. Both make a sort of sense if you imagine them like that; one is all attack but fragile, the other is defensive but a weak attacker.

But ah! Now here’s a thought that might see if the maths works - If it turns out the total damage a single company can deal before dying is 1/4 of the equivalent full battalion, then there’s no real mathematical advantage (but maybe a tactical one) to splitting a battalion into 4 companies, and labeling them as 1/4 battalion BR is correct.

How might we calculate this? Well - all else being equal - survivability is purely a function of UHP. A unit with 12 - like a full battalion - should survive 4x longer than a 1/2 strength ‘battalion company’ of 3UHP, and 2x as long as a default rules company of 6UHP. And damage - again, all else equal - same for each scale; 1 at company, 2 at battalion, for each attack.

Our formula then is simply (UHP*damage)

So for our Standard Battalion, we have (12*2) = 24

For our 1/4 health battalion style company we have (3*2) = 6

And for our default-rules company, we have (6*1) = 6

24/6 = 4

Would you look at that! The ratio works perfectly - both types of company have 1/4 the expected output damage of a full battalion.

For sure 4 1/4 health battalion style companies could band together to deal 4x the damage of a battalion in one turn while having a combined equal UHP… But each individual one would die 4x faster than a single battalion would. A 12UHP, 2 attack battalion might give and take 3 damage per turn, thus dealing 12 damage over 4 turns before dying (routes notwithstanding). 4 companies that each give and take 3 damage will be killed in one turn, but still deal 12 damage total. Thus, the overall ‘action economy’ if you will, is the same - the same AP spent for the same overall damage dealt.

The case of the default-rules company is a little different; 4 of them combined will only deal 2x the damage of the battalion in a turn… But they have 2x the UHP! How does this balance out? Well, in our scenario above, they spend 4AP the first turn, dealing 6 combined damage, and taking 12. Then they do it again the next turn, deal 6, take 12, die. Now they’ve dealt 12 damage, same as the battalion would over a lifetime - but it took twice the AP. because it took twice as long. And thus the 2x UHP is countered by 2x lifetime AP requirements.

You can see this if you see that ‘damage’ in our formula can be expanded out as (total damage / total AP spend). Using the numbers from our scenario above to calculate a battalion against 4 companies we have:

Standard Battalion: (12*12)/4 = 36

Set of 4 1/4 health battalion-companies: (3*12)/1 = 36

Set of 4 default rules companies: (6*12)/8 = 36

The default rules companies have identical overall damage output to the other options, and their doubled health is countered by a doubled AP cost.

Anyway, I’ve rambled for long enough - I’m happy to say that I think the maths actually works out nicely here, even if it looks counterintuitive at first. I will, I think, continue on without further tinkering, having satisfied myself that the numbers won’t break things.

Thank you for your assistance in pointing out thinned formations, and for continuing to reply while I worked my way through it!

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The issue I see with this is that survivability is not purely a function of uhp - it is also strongly a function of morale, and fielding understrength units is awful for morale, whereas fielding “full strength” companies in a battalion scale engagement would let you unreasonably avoid the crippling constant shock rolls. There should be no difference between fielding “companies” and fielding “quarter strength battalions”, they’re the same thing.

Likewise, four companies take up four hexes on the map - much greater control of territory than a single battalion would grant. If they’re FF, they can mutually support one another for a morale bonus. This on its own is sufficient to offset the greater AP cost of fielding such units.

If we treat companies at battalion scale as quarter-strength battalions, then they’ll have 3 uhp regardless of how you deploy them (assuming normal human troops). It’s just a question of whether they deploy narrow but deep (putting them at reduced attacks but 3/3 uhp), or wide but shallow (putting them at full attacks but 3/12 uhp).

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Another longer one so tl;dr - you’re absolutely right. I calculated from first principles, and it does work out that no matter how they form up, a company in a battalion scale fight will have 3uhp, because 1uhp represents twice as much actual health at battalion scale. In essence, using a unit in a higher scale battle should divide its uhp by the scale factor.

Yeah, I get you - my calculations deliberately didn’t include morale, partly for simplicity of the base maths, and partly because these companies will likely die or shock roll on the first turn anyway when they take the double damage that battalions deal.

But I went back and had a look at the UHP calculations to see if I could find them, and I think I was looking at this old playtesting comment. And now that I’ve run the numbers on it again, I think I see my issue that leads to our ‘3uhp vs 6uhp’ conundrum - and resolves it, best I can tell, in your favour. You’re absolutely right.

Going back to first principles, our standard company (at company scale) has a frontage of 20, depth 6, has 1d8-1 health per guy, and deals 1d8 damage per guy. Our base case is that 1uhp is both the amount of health one row of these standard guys has, and how much damage one row of these standard guys deals. Shakes out as:

(0.75 x 20 x 6 x 4.5) / (20 x 4.5) = 4.5, where the numerator is the total health of the troops, and the denominator the damage dealt by a one full front line of single standard attacks from an opposing unit. Multiply the denominator by the 0.75 scaling factor calculated in play from some attacks not killing a troop, gives our 6uhp.

And then as autarch says, this simplifies to

(0.75 x 120) / (15) = 6uhp

But something interesting happens when you scale this, which I think might have resulted in me not seeing this quirk when scaling in the final rules. First our full battalion is now:

(0.75 x 480) / (30) = 12uhp

Or written out in full:

(0.75 x 40 x 12 x 4.5) / (40 x 4.5 x 0.75) = 12uhp

Which shows that health has quadrupled, but damage taken from equally sized units has doubled, so overall UHP has only doubled but each represents twice as much health. Call it battalion-UHP, or BUHP. This reflects what you said about UHP being related to scaling. Although, this should also mean that battalions deal 1 of our BUHP of damage, and thus battalions should still be twice as tanky… It isn’t discussed in that thread but I believe the disparity is resolved by the doubling of time as well at battalion scale, from 10 to 20 seconds? A battalion does deal 1 BUHP per attack per unit time, but doubling time means this shakes out to 2 BUHP per attack.

And this taken together is my critical missing link. Because in a battalion scale fight, our little company now has:

(0.75 x 120) / 30 = 3BUHP where it would’ve had 6UHP. No matter how you do it, it’ll shake out this way.

Your full width partial strength battalion way:

(0.75 x 40 x 3 x 4.5) / (40 x 4.5 x 0.75) = 3BUHP

The otherwise unchanged standard company:

(0.75 x 20 x 6 x 4.5) / (40 x 4.5 x 0.75) = 3BUHP

Put simply, their original UHP has been divided by the scaling factor, just like hero damage is.

And for damage, partial strength battalions deal 1BUHP, multiplied by 2 for time, so it’s 2BUHP per attack, same as battalions. Standard companies deal 1 company UHP, which doubled by time means 1BUHP, representing its damage capability being halved by it’s narrowed width. The same scaling factor of course applies to brigades as well, with the same maths.

So in the end, yes, you’re absolutely right. If I use independent companies in a battalion scale fight (because say, they’re ridiculously powerful to the degree you’d never get 480 in one place), they should have their total UHP divided by the battalion scale factor of 2, and their damage and morale shocks will depend on their internal formation; standard formation turns 6UHP into 3/3UHP but half damage, and partial battalion gives 3/12UHP but full damage. (Interesting quirk that doubling frontage like that makes the denominator 4 times larger but, that’s just how it is!)

Thank you again for your patience and responses - I really have reached a conclusion this time!

PS: Just don’t think too hard about how ranged units also have their damage calculated as if only the front rank can deal damage. I have some thoughts on resolving that, but it’s mostly handwaving - saying all archers can fire, but the increase in range drops accuracy to cancel out the quadrupling of the number of troops who can fire, and companies at arranged as partial battalions can spread out and aim better, improving their hit rate back up to match the battalion damage.

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Aha, good catch on round length doubling. I was trying to work through those numbers but that was throwing me off by a factor.

For archery, the default abstraction is that rear ranks can fire but have obstructed line of sight so they’re volleying overhead at -4 (and potentially the rear ranks of their target can Defend for +2 to +4 AC as well), so on net it just doesn’t amount to much.

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Just circling round to this briefly to say - the only issue with using 3/3 Vs 3/12uhp to determine if a company in a battalion scale battle can resist a bit of shock… is that a battalion deals 2 damage per hit.

This means that even our 3/3uhp company, if attacked a single time by a battalion, will immediately make a shock roll. The point about territory control still makes sense, but from a morale and shock roll perspective, any 3uhp company is equally boned as soon as it gets hit once.