Working on Mass Combat System

[Username17]

At this point, I'm putting tables here so I don't lose them and can easily check up on them when I'm writing and mathhammering things. Most of the text hasn't been committed to computer, and the numbers haven't been finalized at all.

Soldiers	Bombard	Flank	Hold	Shock	Siege	Patrol	Morale	Toughness	Special
Ashigaru	0	10	10	10	10	10	10	10
Guard	0	10	15	10	15	20	20	10
Miner	0	10	10	10	30	10	10	10
Slinger	2	15	3	5	10	10	8	10
Archer	5	10	5	5	10	10	8	10
Warrior	0	15	10	20	10	10	10	10
Light Infantry	0	20	10	10	10	10	20	10
Pikeneer	0	10	20	10	10	10	20	10
Heavy Infantry	0	5	30	15	20	10	30	20
Elite Infantry	0	20	30	20	20	20	40	25
Berserker	0	20	10	50	20	10	50	25
Defender	0	15	50	15	40	20	50	25
Ranger	10	20	10	10	20	50	30	20
Light Cavalry	0	50	5	30	10	30	20	10
Heavy Cavalry	0	60	20	60	15	25	40	30
Elite Cavalry	0	80	30	80	20	30	50	40
Archer Cavalry	5	50	5	25	10	30	20	10
Special Cavalry	10	150	30	150	50	30	60	60
Ogre Soldier	0	20	200	200	100	5	40	50
Giant Soldier	30	100	500	500	250	20	50	200
Demon Soldier	0	250	200	300	100	80	100	100	Dark Power, Unstoppable/Silver
Dragon Rider	50	500	300	500	750	200	250	500	Flying
Champion	10	100	300	300	50	100	200	80
War Mage	100	60	20	100	150	50	50	40	Unstoppable/-
Officer	5	40	50	50	50	120	150	60
Engineer	5	20	30	20	500	50	50	30
Cannon	50	0	0	50	150	0	X	30	Unstoppable/-
Ghoul	0	10	10	50	10	10	30	20
Risen Soldier	0	5	20	10	10	10	X	20
Lycanthrope Soldier	0	25	20	50	10	25	30	30	Unstoppable/Silver
Vampire Soldier	0	25	40	30	25	20	50	30	Dark Power, Unstoppable/Silver
Darter	2	2	0	1	5	30	2	2	Flying
War Dog	0	12	4	10	2	15	5	5	Undisciplined
Great Beast	0	200	200	300	250	10	5	150	Undisciplined
Winged Beast	0	15	5	12	10	25	5	5	Flying, Undisciplined
Great Bird	0	40	20	30	40	30	20	30	Flying

Tactic	Action	Target	Type
Harass	Flank	Flank	Adaptive
Feint	Flank	Patrol	Defensive
Screen	Flank	Flank	Adaptive
Raid	Flank	Hold	Aggressive
Race to Feature	Flank	Flank	Adaptive
Shieldwall	Hold	Flank	Defensive
Regroup	Hold	Shock or Flank	Adaptive
Steady Advance	Hold	Hold	Adaptive
Press	Hold	Shock or Hold	Aggressive
Ambush	Hold	Patrol	Defensive
Hold Line	Hold	Shock	Defensive
Storm	Shock	Shock or HoldHold	Aggressive
Seize Feature	Shock	Flank	Adaptive
Pursue	Shock	–	Aggressive
Take Ground	Shock	Hold	Aggressive
Slaughter	Shock	Shock or Hold	Aggressive

(In case you were wondering: Aggressive > Adaptive > Defensive > Aggressive)

Army Totals	Combat Value
Less than 19	0
19-22	1
23-28	2
29-35	3
36-44	4
45-55	5
56-69	6
70-86	7
87-108	8
109-135	9
136-169	10
170-211	11
212-264	12
265-330	13
331-413	14
414-516	15
517-646	16
647-807	17
808-1009	18
1010-1262	19
1263-1577	20
1578-1972	21
1973-2465	22
2466-3081	23
3082-3851	24
3852-4814	25
4815-6018	26
6019-7523	27
7524-9403	28
9404-11754	29
11755-14693	30
14694-18367	31
18368-22958	32
22959-28698	33
28699-35873	34
35874-44841	35
44842-56051	36
56052-70064	37
70065-87581	38
87582-109476	39
109477-136845	40
136846-171056	41
171057-213821	42
213822-267276	43
267277-334095	44
334096-417619	45
417620-522024	46
522025-652530	47
652531-815663	48
815664-1019578	49
1019579+	50

Primary Settlement Race	Development Level 1	Development Level 2	Development Level 3
Dwarf	Miner Guard Warrior Heavy Infantry	Archer Elite Infantry Defender	Special Cavalry Cannon Great Beast
Halfling	Ashigaru Slinger Light Infantry Light Cavalry	Guard Ranger Archer Cavalry War Dog	Darter Great Bird Special Cavalry
Human	Ashigaru Archer Pikeneer Light Infantry Light Cavalry	Heavy Infantry Guard Elite Infantry Heavy Cavalry	Elite Cavalry Special Cavalry Cannon
Elf	Archer Light Infantry Light Cavalry Guard	Darter Ranger Archer Cavalry Elite Infantry	Special Cavalry Great Bird Elite Cavalry
Goblin	Pikeneer Light Infantry Warrior Ashigaru Slinger	Light Cavalry Heavy Cavalry Archer Cavalry Miner	Ogre Soldier Elite Infantry Elite Cavalry Special Cavalry
Gnoll	Warrior Berserker Heavy Infantry	War Dog	Great Beast
Lizardfolk	Warrior Heavy Infantry Archer	Elite Infantry Defender	Ranger
Orc	Warrior Light Infantry Archer Guard	Heavy Infantry Berserker Elite Infantry Heavy Cavalry	Special Cavalry Great Beast Ogre Soldier
Necropolis	Risen Soldier Pikeneer Archer Guard	Vampire Soldier War Dog	Heavy Cavalry Demon Soldier

[Blicero]

How did you decide the size thresholds in the "Army Totals / Combat Value" column?

[Username17]

How did you decide the size thresholds in the "Army Totals / Combat Value" column?

It's a log function with an exponent of 1.25. So if your force is 25% larger than the opposing force, you get +1 to your combat value. Damage subtracts from army totals, so as the battle progresses you expect the larger force to have a larger bulge. When forces are near the breaking point, it doesn't take a lot of extra army total to be a large difference in combat value.

I haven't decided if those numbers should be rounded or left as-is. I might even decide to change the exponent. But so far I rather like the effects of a 1.25 log on battle progression.

-Username17

[RadiantPhoenix]

Can't you go with an easier-to-headmath progression like:

• ...
• 100
• 125
• 150
• 175
• 200
• 250
• 300
• 350
• 400
• 500
• 600
• 700
• 800
• 1000
• 1250
• ...

[Username17]

Can't you go with an easier-to-headmath progression like:

I could do something like that. Right now I'm just using actual powers of 1.25, which is easy to get a calculator to output. I am definitely considering adjusting the numbers so that they are "rounder." But I don't know if that's ultimately a good idea and in any case wouldn't be a thing to do until after I was sure I wasn't going to use an exponent of 1.2 or 1.3.

I'm not sure that there are a lot of people who are going to want to total up army totals and not use a calculator or a look-up table.

-Username17

[Blicero]

Do you have designer reasons for why the exponent should be 1.2, 1.25, or 1.3? Or is the plan to just choose the one that works out best with the other arrays of numbers that get chosen?

[Username17]

Do you have designer reasons for why the exponent should be 1.2, 1.25, or 1.3? Or is the plan to just choose the one that works out best with the other arrays of numbers that get chosen?

The intention is that initial differences in army size in the expected ranged should equate to small absolute differences in Combat Value. So progressions like "doubling" (exponent 2) or "Fibonacci" (exponent 1.618) grow way too fast - most armies would have the same combat values as anything it made any sense for them to fight.

What that leaves us with is an exponent somewhere south of 1.5. Which number ends up working best is one I'm not sure of. I started at 1.25 because it was in the middle of 1.0 and 1.5, and for no better reason than that. Initially it looks like it does the job I want it to, but I'm not wedded to it.

Another possibility was to not do exponents at all and just do X:1 odds like World in Flames. But I figured that a lookup table for brackets was actually easier to use than long division of 4 digit numbers by 3 digit numbers.

-Username17

[maglag]

With what system is this supposed to be used?

What kind of dice are supposed to be rolled, or are there no dice used at all? Basically how do the numbers interact with each other?

How do you convert regular soldiers into mass scale? If I get a bunch of halflings riding red wyrmlings, do they count as the same kind of dragon rider as the 20th level samurai riding a paragorn prismatic ancient legendary wyrm for mass combat purposes?

[Roog]

I often use a scale approximately based on 10^(1/10) - which falls in the range that you were looking for.

Scale	Value
0	1
1	1.2
2	1.5
3	2
4	2.5
5	3
6	4
7	5
8	6
9	8
10	10
+10	x10

It has a number of useful characteristics.
- minimizes the significance at any point
- as +10 converts to x10, they convert easily into exponential notation, with the right most digit determining the significand, and the remaining digits giving the exponent. This means that (with a little familiarity) conversions can be done without needing to refer to a table
- the scale is at least as even as any similar type of scale that is rounded to the same degree of significance
- the rounding in the scale includes rounding in both directions, calculation errors accumulate relatively slowly

[Grek]

What's the basic order of operations for all of this? Currently, I'm working on the assumption that both sides declare one tactic on one target for every unit, rolling opposed 1d20+Stat+Combat Value checks to decide if the tactic succeeds and using the Aggressive > Adaptive > Defensive > Aggressive RPS rule to decide who wins overall if both or neither tactic is successful.

[DrPraetor]

It doesn't have to be 10 points = x10, but yeah, if you are going to use an exponent base, make it something that rounds to whole numbers.

The cubed root of 2 is very close to 1.26 (1.25992105...), so if you use that, every +26% increase in army size is +1, and every doubling is +3?

For round numbers it could be:

Army Totals	Combat Value
Less than 19	0
-25	1
-32	2
-40	3 (and just double these three bases?)
-50	4
-64	5
-80	6
-100	7
-128	8
-160	9
-200	10
-256	11
-320	12
-400	13
-512	14
-640	15
-800	16
-1024	17
-1280	18

[AcidBlades]

Dr Praetor. I'd be able to split my costs through 3 400s and get a much better value than I would if I had them all in a big-ass army.

[DrPraetor]

AcidBlades - that comment is more appropriately directed to Frank (who hasn't specified any game mechanics), but I think the idea is that RNG will be small enough that if you bring 2 ~120 pt (CV 9) armies and one CV 10 army, my ~400 pt (CV 14) army will smoke them.

Ideally this would be somewhat facultative/strategic - so *sometimes* you are better off splitting up your army? Or there are clever tactics or something.

But, for example, if resolution is 1D6+CV, then the CV 14 army would be all the way off the RNG for the CV 9 armies...

[Grek]

Ideally this would be somewhat facultative/strategic - so *sometimes* you are better off splitting up your army? Or there are clever tactics or something.

This seems obviously true if you're allowed to make each division be of a different unit type. Having 100 Light Cav and 100 Pikeneer is clearly a much more flexible army than 200 of either, and that probably translates into being a better composition.

[maglag]

An Ahisguru has 10 on all stats.

A dragon rider has a 500 on multiple stats and a 750 tops.

I suspect the RNG needs to be pretty large, or perhaps there's some multiplier factor, or dragon riders just literally smoke everything else. I suspect CV multiplies your unit's stats. So 1000 000+ ashiguru (CV 50) can take on a 20 strong dragon rider force (CV 1), as the ashiguru army will have an effective 10x50=500 on every stat.

I predict having advantage on tactics will be perhaps a flat-out bonus to the rolls. It's not just a matter of picking the best tactic, but exploiting the enemy's weakness. Ogres for example have a miserable 5 on patrol, so you want to hit them with Feint.

Bombard seems to be like the auto-damage option representing long-range artillery. No roll, no tactics, just inflict X damage automatically to the enemy. So the dragon riders can choose to just safely breathe fire from afar, inflicting an attack with power 50 instead of using a tactic with their uber 750 top stat.

[Chamomile]

What's the difference between a harass tactic and a screen tactic? Their entries in the chart are identical except for the name.

[virgil]

There are going to be side-effects with each tactic; the chart just shows which stats get compared to to resolve success. Screen would likely be a maneuver performed by an army's flank to reduce casualties to their core detachment. Harass should do something essentially like increase damage to unit morale at the expense of reducing actual casualties.

An Ahisguru has 10 on all stats.

A dragon rider has a 500 on multiple stats and a 750 tops.

I suspect the RNG needs to be pretty large, or perhaps there's some multiplier factor, or dragon riders just literally smoke everything else. I suspect CV multiplies your unit's stats. So 1000 000+ ashiguru (CV 50) can take on a 20 strong dragon rider force (CV 1), as the ashiguru army will have an effective 10x50=500 on every stat.

It's more of a raw number. A single Dragon Rider performing Storm or Slaughter is going to have a 15 to its CV before things like terrain or Bombard are factored in; which you need 50+ Ashigaru to match. In an ideal situation like that, there should probably be a tactic that forces both sides to only be able to use their Bombard stat (requiring uncontested air space). Call it Strafe, an Aggressive maneuver.

[maglag]

But bombard is a base stat. It's zero on most units, but it's still one of the base stats, not a special. Which makes sense, no matter how many ashiguru you have, they'll never be able to perform artillery duty.

Also less than 19 units have a CV of zero, which probably means army units need to be at least 20 strong or they don't get to participate in the mass combat minigame.

As for the table, I predict it's simply a typo. There's a few more typos down the line there, like double holds or null targets.

[Username17]

Army totals are simply all the relevant strength (shock, hold, etc.) of all the units in the detachment added together minus attrition. So a single Dragon Rider would get stomped by 100 tiny men if it went head to head (and 100 tiny men are cheaper than the Dragon Rider). This is not likely to happen, because the Dragon Rider flies and is able to be deployed into a privileged flank (sky). So what actually happens is that if one army has a Dragon Rider and the other doesn't, it pretty much gets to do an attack on unprotected flank over and over again and racks up a lot of attrition on the enemy army.

Unstoppable units (such as Vampires) get to rampage and inflict full attrition every round unless the opposing army has a means to stop their unstoppability. So if you have silver weapons in your army, enemy vampires are just high quality infantry, but if you don't they are also a fast clock on your army.

Heroic actions (that is: RPG stuff) can be done in between warfare rounds, so a typical thing you might want to do would be to do strikes on enemy cannons or war mages to stop them from inflicting attrition every round.

The intention is that the RNG will be fairly small. A quite significant army bulge will only give a small raw bonus (until attrition drops both numbers such that the significant bulge is now a significant multiple). A very good command roll only needs to add a few points of CV to be a very big deal indeed.

But yeah, cube root 3 has a lot of advantages as far as explicability. Hypercube root 3 has a fair amount of advantages as well (that is: doubling the army gives you +4, and a 19% bulge is +1).

-Username17

[Username17]

So I tried out the fourth root of 2 as my exponent, and I have to say it seems to do pretty well presentation wise. Four columns that each double on the way down with each doubling giving you +4 to your combat value. That seems pretty solid.

Army Total	CV	Army Total	CV	Army Total	CV	Army Total	CV
25-29	1	30-35	2	36-42	3	43-49m	4
50-59	5	60-70	6	71-84	7	85-99	8
100-118	9	119-141	10	142-168	11	169-199	12
200-237	13	238-282	14	283-336	15	337-399	16
400-475	17	476-565	18	566-672	19	673-799	20
800-951	21	952-1131	22	1132-1345	23	1346-1599	24
1600-1902	25	1903-2262	26	2263-2690	27	2691-3199	28
3200-3805	29	3806-4525	30	4526-5281	31	5382-6399	32
6400-7610	33	7611-9050	34	9051-10763	35	10764-12799	36
12800-15221	37	15222-18101	38	18102-21526	39	21527-25599	40
25600-30443	41	30444-36203	42	36204-43053	43	43054-51199	44
51200-60887	45	60888-72407	46	72408-86107	47	86108-102399	48
102400-121774	49	121775-144815	50	144816-172215	51	172216-204799	52

Obviously I have to fiddle with attrition rates, but the fourth root of 2 seems like a pretty good conversion of raw army totals to combat value.

-Username17

[Blicero]

Do you have an expected (IRL) duration for a mass combat under this framework? Is this the sort of thing you whip out any time the party and their followers run into a mercenary warband, or is it mostly meant to be used for big climactic setpieces? Also, are there existing systems that you are looking at for mechanical inspiration, or is this mostly from designed from first principles with the intent of avoiding the issues of previous attempts at mass combat?

[Grek]

So, a 50 archer detachment would have CVs of +14 Bombard, +18 Flank, +14 Hold, +14 Shock, +18 Siege, Patrol, +18 Morale +17 and +14 Toughness?

[Username17]

Do you have an expected (IRL) duration for a mass combat under this framework? Is this the sort of thing you whip out any time the party and their followers run into a mercenary warband, or is it mostly meant to be used for big climactic setpieces? Also, are there existing systems that you are looking at for mechanical inspiration, or is this mostly from designed from first principles with the intent of avoiding the issues of previous attempts at mass combat?

Realistically, I expect this to take about an hour. No reason it has to be done that long, I think you could probably put all the inputs into a phone app in 5 minutes and crank through turns until one side broke in 30 seconds. But what's actually going to happen is people are going to spend ten minutes dividing up their army and arguing about what tactics to use at the beginning, and then it's going to take players several minutes to do the math on each turn because "math is hard" and there will be more arguments discussions about what tactics to use before each round. And players will get to take heroic actions in between rounds, so that's like 3 vignettes of RPG actions in between, which will cause things to be recalculated.

Basically, I see the following real world bottlenecks:

• Splitting armies into detachments.
• Adding up army totals.
• Comparing army totals to CV charts.
• Choosing and comparing tactic choices.
• Adding leadership, tactical, and terrain modifiers to CV and them then comparing CVs.
• Multiplying army totals by fractions and then adding rampage numbers to get attrition numbers.
• Subtracting attrition from army totals to get new army totals and repeating for next round.

All of those things could take seconds but will take minutes because math is hard and people are drunk and/or distracted. Especially the bolded part where actual attrition values are a fraction of your Bombard and Shock rather than the whole thing. Because if I didn't do that, armies would blow each other up in one turn. But by doing that, I'm requiring division, which makes peoples' balls ache.

A possibility would be to not do division and simply have morale numbers that were about twenty times the size of the other numbers, but that seems kind of terrible.

As far as design inspiration, I'm mostly looking at strategic wargames. Crusader Kings 2 is obviously a big inspiration, but so too are the old hexes and chit table breakers like Empires at Arms and World in Flames and Noun preposition Noun. I'm certainly looking at RPG systems and table top wargames like Warhammer and BATTLESYSTEM, but mostly to simply shake my head and sigh about how they don't really do what I want them to do. The key insight is that any X:1 unit conversion merely allows you to play out battles that are X times the size of the battles that the regular RPG system handles. So if you make a Warhammer Fantasy Battle character six times simpler, you can handle fights that are six times the size. If you make one BATTLESYSTEM "stand" be 20 D&D characters, then you can handle fights that are 20 times the size. But if you want to have different battles to have orders of magnitude different numbers of soldiers (which given even a cursory reading of any epic fantasy book at all, you do), that's not really an option.

So, a 50 archer detachment would have CVs of +14 Bombard, +18 Flank, +14 Hold, +14 Shock, +18 Siege, Patrol, +18 Morale +17 and +14 Toughness?

You don't actually make CVs out of Bombard, Morale, or Toughness, but yes. Bombard is just a number that adds attrition to the other side regardless of what you happen to be fighting with. Morale and Toughness are just numbers that are compared to attrition totals to see when your army breaks and how many casualties it suffers.

-Username17

[DrPraetor]

Been thinking about this, reading the 40K comment thread, the discussion of Primarchs gave me some thoughts.

Before you work out the mass-combat system proper any further, figure out (if you haven't?) how exactly our heroes are going to exert their command traits.

As a related question - not answered well in 40K - what paradigm(s) is this game meant to include (Aggressive > Adaptive > Defensive > Aggressive = 3 Paradigms??)? If I'm Leonidas, then troops under my command have the discipline to hold a pike square (which is the Greek paradigm) - and this beats the Persians because their paradigm (more undisciplined tribal levies than you) is aggressive? If I'm Genghis Khan, I've got horse archers who don't retreat (this is Adaptive?)

[erik]

Before you work out the mass-combat system proper any further, figure out (if you haven't?) how exactly our heroes are going to exert their command traits.

That seems ass-backwards. You can't figure out exactly how heroes fit in until you have the basics down. You have to know what the moving parts are before you decide how heroes can meddle with them.

Heroes affecting it is an add-on.