Division width

[Kethevin]

If two divisions are fighting 1v1. Would a 40 width one typically beat a 20 width one assuming they are equally matched?

I'm having trouble understand how wide to make my divisions.

[Ваня]

division width is how much physical space a division takes up. A typical fight will have a combat width of 80 and +40 from each additionl province you are attacking/being attacked from.

It's not as simple as larger width division beats smaller width division, but it almost is. An infantry battalion adds +2 width to the division and artillery adds +3 and I don't remember all the others. So a division with a larger width basically means it has more battalions in it.

What you want to do optimization-wise when building a division is give it a width that is a factor of 80. The standard way to do this is a 20 width division or a 40 width division. this way you can fit 4x20 width divisions optimally into an 80 width fight instead of 3x21 for example (leaving 17 worth of wasted space) unoptimally.

[Ryan]

A 40-width division would beat a 20-width one because it has more battalions in it. However, they are more expensive to build. Most people build 20-width divisions, so they can have more of them. Smaller divisions give you some extra flexibility to mix different types rather than one big one. In the grand scheme of things, if you got resources to burn, nothing wrong with 40-width divisions.

[bunny32794]

I don't understand what you mean by "equally matched". I don't see how, in a 1 on 1 match, a division with twice as many battalions could be equally matched.

In any case, a single 40-widther vs. a single 20-widther goes in favor of the former.

Either way, I go with 20-width divisions because of greater flexibility. For example, two 20-width divisions and 1 40-division can theoretically do the same amount of work, but two 20-divisions means I can have one in one place and one in another. Of course, the first part is theoretical; I would only have to assume that 20 divisions could take on 1 if you had an equal number of battalions on each side.

More practically speaking, I actually did some math for you on whether a 40-div and a 20-div are truly equal in combat.

Firstly, we have to understand the HOI4 combat system:
1. Divisions have different attack and defense stats as determined by battalion number and type as well as technollogy and doctrine.
2. In each round of combat, units "fire" at each other with their attack stats and do damage based on "hits".

Seems simple, right? Yes, but in order to truly understand damage output I went on the wiki and discovered that each defense point is a "shield" and that each attack point (a "shot") has a 10% chance to hit when its target still has shields left and a 40% chance to hit when its target has no shields left. Each hit removes one point of shield.

This means that a division with 100 for its defense stat (whether that be Defense or Breakthrough) being shot at 100 times will take 10 hits on average (all hits will be when there are shields left), but taking 1000 shots means that all it's shields will be down (1000 shots at 10% needed to hit 100 times) and that each point over 1000 will have a 4x chance of hitting.

Obviously because of the ludicrous amount of shots needed to reduce the shields given the abysmal low base hit chance, this is not a concern in 1 on 1 division fights. It is important to remember that in huge battles that it seems damage is not spread evenly across divisions (I suspect each division randomly targets another each combat hour and its possible to have multiple divisions ganging up on 1) and thus units may lose a lot of Org this way.

Here is the math for a balanced, 2 on 1 fight between 2 20-divs and 1 40-div of equal composition. Each division is comprised entirely of infantry battalsions that have 3 soft attack, 20 defense and 2 breakthrough each. Each side has the same amount of stats.

1 20-div: 10 INF battalions
30 soft attack
200 defense
20 breakthrough

1 40-div: 20 INF battlaions
60 soft attack
400 defense
40 breakthrough

The 40-div's 60 soft attack is not enough to break a single 20-divs's 200 or even 20 shields (this would reqire 2000 and 200 on average respectively), so each shot has a 10% chance to hit for 6 hits. Similarly, both 20-divs with 60 attack total can't break through 400 or 40 shields, so each division fires 30 shots each at 10% chance for 3 hits each for 6 total.

As seen in this small example, there is no meaningful combat difference between a 40-width and 20-width division for the same composition and wdith (i.e. 2 20-divs are equivalent to a single 40 div).

In larger fights,note the doubling of stats is negated by double the amount of divisions firing on the larger divisions at any given time. Twice as large divisions are twice as powerful but you can only bring half of them to bear.

Your choice is essentially an operational question. If you want greater flexiblity, go for 20-width divisions, but if you want a smaller number of divivisions to manage, go with 40-width ones.

[ancienthighway]

One thing that hasn't been mentioned is support troops. If all are equipped with the same support units, e.g. engineer and artillery, 2 20-width units will bring twice as many to the battle as 1 40-width unit. Four 10-width would bring 4 times as many support troops.

Smaller units deploy faster because they will get the equipment needed sooner. If you were building all the equipment needed, you could have 1 20 width division on the ground and in action while the larger division is still waiting for equipment.

[Kethevin]

Wow, thanks for the information. I'm going to need to read it a few times but I totally appreciate it!

Sorry for the confusion when I said "equally matched," I just meant like infantry vs infantry with similar technology, not something like 1936 infantry vs. 1945 elite forces.

[billy]

you would have to compare two 20 width divisions Versus one 40 width division.

Unless you are doing some silly min/max super unit for multiplayer there's no reason to go 40 width other than having less units to manage mid to late game when you can have huge amounts of units to manage.

Having all you units as 40 width would never be sensible as often you only need one 20 width unit defending places. Or when launching naval invasion 20 width is better for similiar reasons.

Also at the start 40 width isnt sensible , which means you then later on have to turn your 20 width into 40 , which takes a ludicrous amount of supplies saved up . Or create new 40 width divisions.

Also having more units is better than fewer larger ones in various scenarios , as you often dont need the extra men.

I see no reason to go 40 width other than to have less units , which is a perfectly viable reason later on but not one i can be bothered dealing with usually

[glythe]

I seem to recall 40 width divisions having issues with reinforcements.

One problem with 40 vs 20 division size is that you have fewer troops to hold a line. This is a big issue if you are pushing into Russia.

Originally posted by bunny32794:

As seen in this small example, there is no meaningful combat difference between a 40-width and 20-width division for the same composition and wdith (i.e. 2 20-divs are equivalent to a single 40 div).

In larger fights,note the doubling of stats is negated by double the amount of divisions firing on the larger divisions at any given time. Twice as large divisions are twice as powerful but you can only bring half of them to bear.

Most of the time you won't have the same army composition; if for no other reason due to production differences. The Soviets can have problems giving every man a gun to fight the Germans (just likein : Enemy at the Gates).

It's kind of stupid but if you have one really high prodcution 40 width division they will stomp all over 4x 10 width division on defense. If you make some strategic decsions at the start of the game it is very possible with Germany to have about 8 generals with 20x infantry (20 width - 2 arty rest infantry) and 4x tank (3 medium tanks, 1 heavy tank, 2 heavy spg +3 motorized) per general by the time you fight the Soviets. Play around with doubling that width and you will have insane stats on that division.


Something to bear in mind is that everything you add to a template changes its stats. So that means if you have a 26 width army vs a 20 width army.... all things being equal the larger group has the advantage. The problem is that width becomes an issue for large numbers. Note: A better tech 20 width army can have better stats than a 40 width army.

The reason you attack in even numbers of 20 is because if you flank an enemy you increase the width (by either 20 or 40... dont remember). So if you start with 80 width and attack from 3 directions you increase the width three times. If you massively outnumber the enemy this is good. But if he is entrenched with the great battle plan doctrine it can actually make the battle worse. Some tactics chosen by generals will aslo affect the width but that is rare and you can basically skip that.

[Ваня]

I was just perusing some things in game and noticed a couple that would support the idea of either the 20 or 40 width division.

The first is Foreign volunteers. I know this doesn't usually happen much beyond the Spanish Civil War and Sino-Japanese War. But, in any case, you're limited to a certain number of divisions you can bring. Let's say it's mid-late game and for whatever reason you don't want to go to war but want to have an impact. Would you rather bring 10 20 widths or 10 40 widths?

The second is tactics. I noticed a fair number of tactics that reduce the combat width by 25%. Out of a standard 80 that brings it to 60. Now assuming a 4x20 vs 2x40 situation, that former would be forced down to 3x20 (75%) but the latter would be forced down to 1x40 (50%)

Unless I misunderstand the effect of combat width modifications from tactics. If I do, and no divisions are kicked out of combat, but instead a combat penalty is slapped on for the duration of the tactic, that still leaves the 2x40 at a disadvantage.

[HugsAndSnuggles]

Originally posted by Ваня:

Unless I misunderstand the effect of combat width modifications from tactics. If I do, and no divisions are kicked out of combat, but instead a combat penalty is slapped on for the duration of the tactic, that still leaves the 2x40 at a disadvantage.

Depends on the situation. If penelty is not large enough to offset extra firepower, division is kept in the fight (can often see it during the war China, if it's controlled by AI with some strange ideas about division composition). Thing is: if you have, say, 79/80 space taken, it's only possible to put 1 more division in there, regardless of its size.

Edit:

Originally posted by Ваня:

The second is tactics. I noticed a fair number of tactics that reduce the combat width by 25%. Out of a standard 80 that brings it to 60. Now assuming a 4x20 vs 2x40 situation, that former would be forced down to 3x20 (75%) but the latter would be forced down to 1x40 (50%)

Just wanted to point out that those tactics usually come in pairs: if defender uses one that reduces combat width, so does attacker. Thus, you rarely see combat width of 60, it usually goes all the way down to 40.