# Infantry Combat ability vs discipline

#### Zwirbaum

##### (Formerly known as Zwireq)
Ok, and now let's start with the meat. Mind there may be a lot of unneccesary wall of text, so be warned.

We'll try to see what will bring us the most benefit -> +20% infantry CA or +5% discipline. To delve into that, let's quickly put what each of the benefits actually mean

+X% Infantry/Cavalry/Artillery Combat Ability, means that this unit deals +X% more damage than it would normally indicate from combat equation. (1.X damage done where X is changed from X% to x/100)

Y% Discipline (note: You start with 100% discipline) means all your units deal Y% damage than it would normally indicate from combat equation (so 105% discipline means units deal 105% damage). Also it increases/decreases military tactics based on the discipline. 100% means no change in military tactics, above 100% increases military tactics in proportion, below 100% decreases military tactics. Military tactics is modifier that all damage dealt to you is divided by that value, so the higher military tactics, the less damage you suffer.

Now I will introduce what I use for my calculation - which is Real Damage modifier. (RDM in short). RDM is the current damage modifier from the tech applied against current military tactics. For example - RDM for infantry on tech 3 is 0.7 for fire phase and 1.0 for shock phase. (Because fire is 0.35 and tactics is 0.5 so 0.35/0.5=0.7 and shock is 0.5/0.5=1).

Infantry RDM for fire phase is (in approximation, I have precise values calculated, but that would take more time to write here)

Fire RDM:
0.5 (tech 0)
0.7 (tech 1-3)
0.47 (tech 4-5)
0.55 (tech 6)
0.44 (tech 7)
0.64 (tech 8)
0.53 (tech 9-11)
0.46 (tech 12-13)
0.63 (tech 14)
0.55 (tech 15-18)
0.49 (tech 19)
0.71 (tech 20)
0.64 (tech 21-22)
0.58 (tech 23)
0.53 (tech 24-26)
0.7 (tech 27-29)
0.65 (tech 30)
0.95 (tech 31)
0.89 (tech 32)

So now we see, that in terms of Fire RDM, biggest one is on tech 31, then 32, then 20, 27-29 and tech 1-3.

Shock RDM:
0.4 (tech 0)
0.6 (tech 1)
1 (tech 2-3)
0.67 (tech 4)
0.87 (tech 5)
0.95 (tech 6)
0.76 (tech 7-8)
0.63 (tech 9-10)
0.77 (tech 11)
0.66 (tech 12-14)
0.58 (tech 15-18)
0.51 (tech 19-20)
0.67 (tech 21-22)
0.6 (tech 23)
0.55 (tech 24-27)
0.72 (tech 28-29)
0.66 (tech 30-31)
0.61 (tech 32)

Biggest shock RDM is on tech 2-3, then tech 6, tech 5, tech 11 and so on.

So for example with +20% combat ability, the RDM on tech 3 would be 0.7*1.2=0.84 for fire and 1.2 for shock.

Now let's go and make simple assumption (otherwise it would take pages of further number crunching here, and theorycrafting to extreme). We will use Western Tech group infantry units. I chosen them the same way as in my unit guide (link down below), with going for most offensive choice (casualty wise) if there was tie mentioned there. Let's assume we fight against same unit (infantry of the same unit type). Let's compare the unit pips for that.

Infantry unit pips comparison:
Tech 0-11. It will be no fire pip advantage/disadvantage and +1 offensive shock pip advantage. (I will use short 0 fire +1 shock from now on)
Tech 12-14. -1 fire +1 shock
Tech 15-18. 0 fire +1 shock
Tech 19-22. +1 fire +1 shock
Tech 23-25. 0 fire 0 shock
Tech 26-29. +1 fire 0 shock
Tech 30-32. 0 fire +1 shock.

Now when we would calculate average damage done by regiment, we will assume 4.5 as die roll result (average between 0 and 9). No general advantage/disadvantage and terrain influence.

So it means we get on:
Tech 1-11, result of 4.5 for fire phase and 5.5 for shock phase.
Tech 12-14. 3.5 fire phase and 5.5 shock phase.
Tech 15-18. 4.5 fire phase 5.5 shock phase
Tech 19-22. 5.5 fire phase 5.5 shock phase
Tech 23-25. 4.5 fire phase 4.5 shock phase
Tech 26-29. 5.5 fire phase 4.5 shock phase.
Tech 30-32. 4.5 fire phase 5.5 shock phase.

Then we add +3 base (so 3.5 becomes 6.5 etc.) then we multiply it by 5 and RDM. That gives what average casualties should regiment deal, assuming 100% strength remains.

Now from tech 16 and onwards artillery brings defensive benefits to units being in front of them

So 16-24 subtracts one from fire phase result
25-28 subtracts two from fire phase
29-32 subtracts two from fire phase and one from shock phase.

So final results (adding +3 base) are infantry against infantry with artillery in backrow as supporting unit (artillery against infantry we will start counting in 'few' moments.
Tech 0-11: 7.5 Fire / 8.5 Shock
Tech 12-14: 6.5 Fire/ 8.5 Shock
Tech 15: 7.5 Fire/ 8.5 Shock
Tech 16-18: 6.5 Fire/ 8.5 Shock
Tech 19-22: 7.5 Fire/ 8.5 Shock
Tech 23-24: 6.5 Fire/ 7.5 Shock
Tech 25: 5.5 Fire/ 7.5 Shock
Tech 26-28: 6.5 Fire/ 7.5 Shock
Tech 29: 6.5 Fire/ 6.5 Shock
Tech 30-32 5.5 Fire/ 7.5 Shock

Now let's go back to RDM multiply them by 5 and this values here. We are going to have following results of average casualties done by infantry with artillery supporting from backrow (But artillery deals no damage here) (100% unit strength, no Combat ability, no discipline) Fire/Shock phase accordingly per day

Casualties:

Tech 0: 18.75 Fire / 17 Shock
Tech 1: 26.26 Fire/ 25.5 Shock
Tech 2-3: 26.26 Fire/ 42.5 Shock
Tech 4: 17.63 Fire/ 28.48 Shock
Tech 5: 17.63 Fire/ 36.98 Shock
Tech 6: 20.63 Fire/ 40.38 Shock
Tech 7: 16.5 Fire/ 32.3 Shock
Tech 8: 24 Fire/ 32.3 Shock
Tech 9-10: 19.88 Fire/ 26.78 Shock
Tech 11: 19.88 Fire/ 32.73 Shock
Tech 12-13: 14.96 Fire/ 28.05 Shock
Tech 14: 20.48 Fire/ 28.05 Shock
Tech 15: 20.63 Fire/ 24.65 Shock
Tech 16-18: 17.88 Fire/ 24.65 Shock
Tech 19: 18.38 Fire/ 21.68 Shock
Tech 20: 26.63 Fire/ 21.68 Shock
Tech 21-22: 24 Fire/ 28.48 Shock
Tech 23: 18.85 Fire/ 22.5 Shock
Tech 24: 17.23 Fire/ 20.63 Shock
Tech 25: 14.58 Fire/ 20.63 Shock
Tech 26: 17.23 Fire/ 20.63 Shock
Tech 27: 22.75 Fire/ 20.63 Shock
Tech 28: 22.75 Fire/ 27 Shock
Tech 29: 22.75 Fire/ 23.4 Shock
Tech 30: 17.88 Fire/ 24.75 Shock
Tech 31: 26.13 Fire/ 24.75 Shock
Tech 32: 24.48 Fire/ 22.88 Shock.

Ok. +20% CA means damage is 20% higher, so 18.75 fire damage would mean = 22.5 in fire phase per day for example.

But what we want to know is how the CA will be affected by enemy discipline. 20% CA against 5% discipline means 1.2/1.05 which results in approximation of 14.29% damage increase. Enemy will deal at the same time 5% more damage. So we will deal first day 9.29% more damage than he, and that will start piling on, because from smaller regiment (even though difference will be miniscule) he will deal less damage, which means, we will be in better shape for longer, which means we will have smaller penalty to damage dealt. But, that's leaving out of equation artillery or cavalry. Cavalry is actually really tricky part here, and depends on composition aspect (do you get flanked or not, or is cavalry engaging just each other, each other with artillery support, or do you engage enemy cav with infantry and so on so on. But let's just add artillery to the casualty 'track' and let's see how much artillery do damage

Quick version: RDM of artillery in terms of fire from backrow and shock.
Tech 7-8: 0.4 FRDM (Fire RDM)/ 0.04 SRDM (Shock RDM)
Tech 9-11: 0.33 FRDM/ 0.03 SRDM
Tech 12: 0.29 FRDM/ 0.03 SRDM
Tech 13-14: 0.4 FRDM/ 0.09 SRDM
Tech 15: 0.35 FRDM/ 0.08 SRDM
Tech 16-18: 0.6 FRDM/ 0.13 SRDM
Tech 19-20: 0.53 FRDM/ 0.11 SRDM
Tech 21: 0.48 FRDM/ 0.1 SRDM
Tech 22: 0.88 FRDM/ 0.14 SRDM
Tech 23: 0.8 FRDM/ 0.13 SRDM
Tech 24: 0.73 FRDM/ 0.12 SRDM
Tech 25-29: 1.07 FRDM/ 0.15 SRDM
Tech 30-31: 0.98 FRDM/ 0.14 SRDM
Tech 32: 1.2 FRDM/ 0.16 SRDM

Now, let's see at how good are the comparison of the pips of artillery attacking enemy infantry from backrow, while enemy infantry is supported by artillery as well (including +3 base to not make more senseless copypasting.

Tech 7-8: 8.5 Fire 7.5 Shock
Tech 9-11: 8.5 Fire 6.5 Shock
Tech 12: 6.5 Fire 6.5 Shock
Tech 13-15:7.5 Fire 6.5 Shock
Tech 16-17: 6.5 Fire 6.5 Shock
Tech 18 6.5 Fire 7.5 Shock
Tech 19 6.5 Fire 6.5 Shock
Tech 20-22 7.5 Fire 6.5 Shock
Tech 23-25 6.5 Fire 6.5 Shock
Tech 26-29 6.5 Fire 5.5 Shock
Tech 30-32 5.5 Fire 5.5 Shock

Casualty count:
Tech 7-8: 17 Fire/ 1.5 Shock
Tech 9-11: 14.03 Fire/ 0.98 Shock
Tech 12: 9.43 Fire/ 0.97 Shock
Tech 13-14: 15 Fire/ 2.93 Shock
Tech 15: 13.13 Fire/ 2.6 Shock
Tech 16-17: 19.5 Fire/ 4.23 Shock
Tech 18: 19.5 Fire/ 4.88 Shock
Tech 19: 17.23 Fire/ 3.58 Shock
Tech 20: 19.88 Fire/ 3.58 Shock
Tech 21: 18 Fire/ 3.25 Shock
Tech 22: 33 Fire/ 4.55 Shock
Tech 23: 26 Fire/ 4.23 Shock
Tech 24: 23.73 Fire/ 3.9 Shock
Tech 25: 34.78 Fire/ 4.88 Shock
Tech 26-29: 34.78 Fire/ 4.13 Shock
Tech 30-31: 26.95 Fire/ 3.85 Shock
Tech 32: 33 Fire/ 4.4 Shock

Pheew. Now let's see quick comparison of 20% Infantry combat ability infantry with artillery support attacking 5% discipline (So infantry has 14,29% damage dealt, while artillery will deal less damage) and compare it to 5% discipline attacking infantry/artillery without discipline.

Now, tech 0-6 Infantry Combat Ability is clear winner, and there is no dispute here. Question is what will happen on tech 7-32.

Infantry with CA, will deal 14,29% (20% modified by 5% discipline of enemy) more damage than they should, while Infantry with discipline will deal 5% more damage than they should. So Infantry with CA will deal 8,84% more damage in total than infantry with discipline.

Artillery without any benefits will deal 95,2% damage to enemy infantry while artillery with discipline will deal 105% damage to enemy infantry. (They will be 10,29% more effective than enemy artillery).

Now the biggest difference (it will be biggest when the base damage from RDM is highest etc.) in terms of casualties between infantry with CA and infantry with discipline is around 2.5 half men per regiment on average (assuming 100% strength) per day in fire phase, and 4 per day on average in shock phase. Difference may be smaller on different techs.

Let's take a look now for artillery. Biggest difference will be with 3.5 more casualties per day in fire phase, and 0.5 a men per day in shock phase. Difference may be smaller on different techs.

Now when we would compare each other, infantry advantage on paper seems better because 2,5 per fire day and 4 per day per shock day, while artillery 3,5 per fire day and 0,5 per shock day. While on some military technology levels, infantry with CA will deal much more damage to infantry with discipline, and the advantage on artillery behalf maybe smaller and may not cover the difference in matters of casualties, we need to remember that both infantry regiments will take beating, and their effectivness will start dropping fast (infantry with discipline slightly faster initially), the more battle will progress and be ongoing the +5% discipline will pull more out of their weight. Infantry combat ability like +20% is excellent though to some point due to initial big hit, and paired with some nice discipline and a lot of morale, you can find yourself doing a lot of stackwipes.

But my recommendation is 5% discipline over 20% infantry combat ability. Unless somehow we're looking exclusively at the initial stage of game (tech 0-6, or to some degree to the moment where cannons will not become more and more relevant and showing up, like tech 13-16).

(There are some calculations and extra ramblings that I decided to exclude for now; they are done somewhere)

TL;DR - Discipline

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#### atwix

##### Manager of Micro
@Zwireq you are crazy calculating all that! But its helpful

#### wingren013

##### Lt. General
Is that really so? AFAIK CA and base casualties are both increasing casualties, which both increase morale damage. AFAIK morale damage has a basic "time" component, a component based on casualties, and a component based on morale vs morale. I am not seeing how CA and higher base casualties from pips impact this differently.

The way the formula is written on the wiki is unclear but it appears that casualties is divided by 600 for the morale damage. While CA is a direct boost to the morale damage. So an extra pip inflicts more casualties but 10% infantry CA is 10% more casualties and 10% extra morale damage on top of that.

#### funguide

##### First Lieutenant
@Zwireq holy lord those are some great calculations.

Someone in the earlier posts was talking about some economic-quality idea combination and innovative-quality combination for grabbing both the 5% discipline and 20% infantry combat ability. It would seem that CA might not be worth it since the earliest you could get it from ideas would be around tech 7. But as a starting national tradition it might be amazing for a custom nation.

#### ChildeR

##### Field Marshal
The way the formula is written on the wiki is unclear but it appears that casualties is divided by 600 for the morale damage. While CA is a direct boost to the morale damage. So an extra pip inflicts more casualties but 10% infantry CA is 10% more casualties and 10% extra morale damage on top of that.
No, the wiki says base casualties, which do not have CA applied yet, are multiplied by the various things including CA. So if that's correct, CA only applies once.

#### darth254

##### Major
this is getting too complex and theorycraft-oriented....btw, quantity ftw. I like mah cheap crap monster armies.

#### telge2

##### Captain
Huh... That's weird then, why doesn't the nation who best used cannons during the period (by a mile) have cannon CA? I mean, yeah, it'd make France even more powerful, but still.

Yeah, I guess it's mostly gameplay reason.

#### Zwirbaum

##### (Formerly known as Zwireq)
this is getting too complex and theorycraft-oriented....btw, quantity ftw. I like mah cheap crap monster armies.
Question was what's better 20% CA or 5% discipline. Quantity was not the part of question

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#### Terry1824

##### Recruit

Pheew. Now let's see quick comparison of 20% Infantry combat ability infantry with artillery support attacking 5% discipline (So infantry has 14,29% damage dealt, while artillery will deal less damage) and compare it to 5% discipline attacking infantry/artillery without discipline.

Now, tech 0-6 Infantry Combat Ability is clear winner, and there is no dispute here. Question is what will happen on tech 7-32.

Infantry with CA, will deal 14,29% (20% modified by 5% discipline of enemy) more damage than they should, while Infantry with discipline will deal 5% more damage than they should. So Infantry with CA will deal 8,84% more damage in total than infantry with discipline.

Artillery without any benefits will deal 95,2% damage to enemy infantry while artillery with discipline will deal 105% damage to enemy infantry. (They will be 10,29% more effective than enemy artillery).

Now the biggest difference (it will be biggest when the base damage from RDM is highest etc.) in terms of casualties between infantry with CA and infantry with discipline is around 2.5 half men per regiment on average (assuming 100% strength) per day in fire phase, and 4 per day on average in shock phase. Difference may be smaller on different techs.

Let's take a look now for artillery. Biggest difference will be with 3.5 more casualties per day in fire phase, and 0.5 a men per day in shock phase. Difference may be smaller on different techs.

Now when we would compare each other, infantry advantage on paper seems better because 2,5 per fire day and 4 per day per shock day, while artillery 3,5 per fire day and 0,5 per shock day. While on some military technology levels, infantry with CA will deal much more damage to infantry with discipline, and the advantage on artillery behalf maybe smaller and may not cover the difference in matters of casualties, we need to remember that both infantry regiments will take beating, and their effectivness will start dropping fast (infantry with discipline slightly faster initially), the more battle will progress and be ongoing the +5% discipline will pull more out of their weight. Infantry combat ability like +20% is excellent though to some point due to initial big hit, and paired with some nice discipline and a lot of morale, you can find yourself doing a lot of stackwipes.

But my recommendation is 5% discipline over 20% infantry combat ability. Unless somehow we're looking exclusively at the initial stage of game (tech 0-6, or to some degree to the moment where cannons will not become more and more relevant and showing up, like tech 13-16).

(There are some calculations and extra ramblings that I decided to exclude for now; they are done somewhere)

TL;DR - Discipline

This is fantastic, I think a video explaining this would be really popular if you did in the way of that trade explainer that made the rounds on r/eu4 a few months ago.

#### Suzaku

##### Colonel
I smell Necromancy at work.

#### raikaria

##### Field Marshal
What is better to have 20% infantry combat ability or 5% discipline. Please explain. Some numbers would be great.

Think of Discipline like Combat Ability fused with Tactics.

Basically; for Combat Ability to equal Discipline; it's a 2:1 ratio. However; Discipline effects your whole army; Infantry CA only effects Infantry.

Still; unless you're lategame rnning full cannons and a decent amount of Cav as well; 20% Infantry CA should outperform 5% discipline.

#### seriousgigi

##### Colonel
Sounds like you're confusing Combat Ability with Morale.

Discipline and Combat Ability have effectively the same main effect: increase enemy casualties. The two crucial differences are that discipline also increases Tactics, indirectly reducing casualties on your side. And Combat Ability only applies to one unit type (infantry, cavalry, artillery) while discipline applies to all.

So while Discipline is a little more generally useful than Combat Ability on a per-point basis, I would pick 20% infantry CA over 5% discipline any time. Cavalry CA is less interesting for most nations though.

so you are saying "20% infantry combat ability ≅ 20% moral ≅ 10% discipline" right?

#### TheMeInTeam

##### Field Marshal
so you are saying "20% infantry combat ability ≅ 20% moral ≅ 10% discipline" right?

20% infantry combat isn't even close to those others after cannons are relevant.

#### seriousgigi

##### Colonel
you mean after mil tech 16 right?

#### TheMeInTeam

##### Field Marshal
Even at tech 13.

No way is having no cannons at tech 7+ "ideal". If you had enough money for them you'd run them.

#### sr999

##### Colonel
@Zwireq holy lord those are some great calculations.

Someone in the earlier posts was talking about some economic-quality idea combination and innovative-quality combination for grabbing both the 5% discipline and 20% infantry combat ability. It would seem that CA might not be worth it since the earliest you could get it from ideas would be around tech 7. But as a starting national tradition it might be amazing for a custom nation.

Funny you should say that! I have an extremely unhealthy obsession with infinitely repeating the custom nation Ideas Guy achievement - in which you must start with a 1-1-1 OPM, but get 800 custom points to spend as you will. (achievement is income of 500 ducats)

No matter what my build or starting location or blobbing/whatever strategy, I always take +20% infantry CA as a tradition.

As for discipline, certainly I always take that too at maximum +10%... but hardly ever before about the 3rd/4th national idea. Partly this is because of cost, but mainly it's because it's only at about that point discipline starts to become more important than infantry CA. Only my gut feel, of course!

Those two, along with -20% coring cost, are the only ones I always take regardless of circumstances.

OT: oddly, I hardly ever take a morale buff - must experiment with that combined with Quantity for militaristic builds, might be fun for increasing stackwipes. Sometimes you're outnumbered 4 or 5-1 and must have stackwipes or die in successive waves. Likewise, just as some people in this thread have suggested Artillery CA, I often take +20% ACA as an ambition. Unless I'm more concerned with fast sieging than just inflicting horrendous casulaties, in which case I take +20% siege as ambition.