# Quantitative Division Design

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#### unmerged(157014)

##### Corporal
If you would take a look at defines.lua, you will find:

BASE_CHANCE_TO_AVOID_HIT = 0.8,
-- Base chance to avoid hit if defences left.
CHANCE_TO_AVOID_HIT_AT_NO_DEF = 0.6,
-- chance to avoid hit if no defences left.

In other words, anyone could still get hit with defense points, and that anyone could still avoid hits without defense points.

Concluding from this, the only benefit for having more divisions is to allow the inclusion of more support brigades to end a fight quicker before random factors average out.
Ok, I haven't had time to look through the lua files, so that's yet another case of the manual being wrong: L4.1 Firing Phase: "So if a defending Division’s modified Defensiveness is 6.3, it may avoid being hit by the first six shots aimed at it, while any additional shots would hit." However, it's worth noting that it still gives double the chance to hit and therefore any divisions that receive shots in excess of their def/tough will receive (on average) double damage from those shots.

There are plenty of instances where there's combat with big stacks of divisions, e.g. naval invasions (especially from the USA). The bulk of an army is generally plain infantry divisions, so if there's any advantages or disadvantages based on division size it's worth knowing about. That is the general point of this thread anyhow. So if you're playing GER, for example, and you've got stacks of small INF or GAR divisions in ports to defend against USA naval invasions then it's worth knowing if there's an advantage to be gained from merging those divisions!

Stats derived from dhelmet's, but for 2xinf & 5xinf (rounded down):
2xINF: SA:4, DEF:10, TOUGH:6
5xINF: SA:10, DEF:26, TOUGH:15

2 5xINF vs 5 2xINF:
Probability of 5xINF attacking separate 2xINF: 80%
SA 10 vs DEF 10: 10 shots at normal chance to hit of 20%, average 2 hits.
On average, total of 4 hits from both 5xINF.
Probability of both 5xINF attacking just one 2xINF: 20%
SA 20 vs DEF 10: 10 shots at normal chance 20%, 10 at double chance 40%.
On average, total of 6 hits from both 5xINF.
So 20% chance of doing 150% damage.
On average the 5xINF divisions get 0.8 * 4 + 0.2 * 6 = 4.4 hits.

5 2xINF vs 2 5xINF:
Even if all 5 2xINF divisions attack just one 5xINF division (0.2^4 = 0.16% chance!), their combined SA of 20 doesn't exceed the 5xINF's DEF of 26, so there's no possibility of increased damage, all shots get 20% chance to hit. On average the 2xINF divisons get 20 * 0.2 = 4 hits.

So the stack of 5xINF divisions get 4.4 / 4.0 = 110% the number of hits that the stack of 2xINF divisions do. I'd say that 10% extra damage just from a bit of division reorganisation is worth it, especially for your static port garrisons. Obviously for situations where you haven't got a high density of divisions, this isn't applicable. But there are cases where this could be useful to know. Note that this 10% extra damage is only for the case of attacking, for defending the bonus will be greater, but I'll leave you to work through the maths to prove that to yourself

For example, the hypothetical 2 X 5 Inf combat versus 5 X 2 Inf. While it is true that on each round the 5 brigade division will overwhelm whatever division it targets, it is equally true that the 5 divisions will overwhelm one of the 5 brigade divisions. The luck of the draw may favor one of these over the other for any given combat round, but it will eventually even out (or at least come close). I will remain unconvinced until someone sets up a rough numerical simulation to definitively prove otherwise.
So, point proven? Or do you see some nasty flaw in my calculations?

Cheers, Jason.

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#### Jorgen_CAB

##### Field Marshal
In general (mathematical probability) it is always preferable to have your divisions as large as possible. Though, smaller divisions are more flexible, so you need to have a balance.
As you point out... if you have two garrison divisions with two brigades each it would do you good to merge them into one division becasue it will make it stronger.

When you create a whole army you need to keep a balance between flexibility and firepower. The standard three brigade infantry division are a very good mix of defensiveness and attack power. Another very good division makeup are two infantry brigade and an artillery. This give you a divisions that have basically the same offensive and defensive capabilities. Add a SpArt instead and you have a really good infantry division with some reduced softness as well as increased attacking power. Though, such divisions will be more expensive in IC and supplies, but you get more of them since they cost less manpower, which some countries have an ample shortage of.

The good thing about the game are that you have so many options of constructing your army and a good balance of divisions and brigades seem to be a smart move most of the time.

Even if you have the manpower and industry to pull of an all five brigade division army with armored divisions, those will not be suitable for all location and will get beaten by both cheaper and lower grade divisions given time.

#### dhelmet99

##### First Lieutenant
So, point proven? Or do you see some nasty flaw in my calculations?

Cheers, Jason.
Sorry I haven't been following as closely as I was recovering from the swine flu this weekend and therefore in no shape to crunch the numbers. Anyway, assuming the combat model works this way (I didn't follow the HOI2 analysis close enough to confirm), then I will consider it proven. An average of 10% more damage is not huge, but since it doesn't cost anything that makes it pretty darn cost effective!

#### Scryder

##### Lt. General
This is really good work. I was wondering if making an Artillery only Corps (with 1 Inf or Arm for width) is useful and this helped a lot.

I remember seeing this thread when I first got the game, but didn't understand it at the time. Now it's handy!

#### Oberst Steiner

##### Sergeant
Divisions guarding beaches

I am preparing for an LAN party with 8 human players. I will be playing Germany and I was wondering what type of divisions would you recomend for guarding the beaches against US and UK (both human players). Since USSR will be played by human as well I'll need large part of my army on the eastern front. Probably more then 100-120 divisions for three Heeresgruppen and most of schnellen (Pz., Pz.Gr. and mot.) divisions. USA, IC whore that it is, is going to field Army Group of 5 Armies with 5 Corps of 5 divisions plus UK forces. Since Italy will also be a human player I am counting on them to provide some forces for the Eastern Front and for the Festung Europa. American invasion on Festung Europa will be, not on ports, but on territories next to ports. So my question is what kind of division type you recomend for those territories? I plan on building land fort in port (because attack will come from land provinces) and coastal fort in provinces next to ports. every lvl of forts is -9% for the attacker. So 3 divisions of 3xinf 1xart in port and on the beaches divisions of 2xgar 2xart. Maybe some militia on smaller ports. What do you think.

#### Jorgen_CAB

##### Field Marshal
I am preparing for an LAN party with 8 human players. I will be playing Germany and I was wondering what type of divisions would you recomend for guarding the beaches against US and UK (both human players). Since USSR will be played by human as well I'll need large part of my army on the eastern front. Probably more then 100-120 divisions for three Heeresgruppen and most of schnellen (Pz., Pz.Gr. and mot.) divisions. USA, IC whore that it is, is going to field Army Group of 5 Armies with 5 Corps of 5 divisions plus UK forces. Since Italy will also be a human player I am counting on them to provide some forces for the Eastern Front and for the Festung Europa. American invasion on Festung Europa will be, not on ports, but on territories next to ports. So my question is what kind of division type you recomend for those territories? I plan on building land fort in port (because attack will come from land provinces) and coastal fort in provinces next to ports. every lvl of forts is -9% for the attacker. So 3 divisions of 3xinf 1xart in port and on the beaches divisions of 2xgar 2xart. Maybe some militia on smaller ports. What do you think.
As Germany you should IC horde yourself early in the game as well. If you have a nice IC stockpile I would produce lots of (4xGar) in non port provinces with 2-3 coastal fort levels, basically to hold the enemy of the beaches long enough for support to arrive. My ports would be garrisoned with one full corps of three to five (depending on size of port) with (3xGar,1xArt). Port provinces need at least level five coastal/land forts.
Garrison are cheap and have a high defense value, this will ensure they will be able to hold against superiority odds long enough for any reinforcement to arrive and throw out the enemy.

If you also have the industry then turning your infantry into 72-74% Soft divisions and giving them (2xInf,1xSP.Art,1xTD) will be effective (also saves manpower), especially when the enemy do not expect it. Create some attack or breakthrough corps with a number of (2xInf,2-3xArt). You could keep some Eng with the HQ to swap into the divisions as necessary.

Keep your armored divisions at (3xArm,1xAC), this is in my opinion the best armoured division you can find. Use Light divisions for exploitative moves (2xL.Arm,1xAC).
I go with the same make up for mech and mot as regular infantry. Though in my opinion you should not need to construct mech infantry at all. Just Arm, Mot and Inf will be needed.

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#### bbasgen

##### Field Marshal
If you would take a look at defines.lua, you will find:

BASE_CHANCE_TO_AVOID_HIT = 0.8,
-- Base chance to avoid hit if defences left.
CHANCE_TO_AVOID_HIT_AT_NO_DEF = 0.6,
-- chance to avoid hit if no defences left.

In other words, anyone could still get hit with defense points, and that anyone could still avoid hits without defense points.
The big question that remains is exactly how damage is determined for each shot that does in fact hit. The defines.lua numbers for damage just don't seem to make sense -- or at least don't tell the full story.

#### Romeo13

##### Sergeant
So, point proven? Or do you see some nasty flaw in my calculations?

Cheers, Jason.
Good math, but you leave out the primary reason for not using 5 x Inf Brigade divisions... you can't add Art or AntiTank Brigades...

For a single attack... Divisions of 2x Inf, 2x Art, 1x Antitank (latewar), with 5 divisions being able to attack in a single stack? (Width of 10), hitting a defensive stack of 2 divisions of 5 Inf brigades? (10 front) The S/A firepower of those 5 divisions will overwhelm those 2 Division...

Granted, we are no longer using equivalent manpower, or supplies... but those Support brigades and the Firepower they bring become (IMO) more important on the Attack...

IMO its all about how you like to organize... and play... as neither force structure really gives any major advantage...

#### lpremus

##### First Lieutenant
I see no one has talked in this thread for a while but is there a newer division design excel file somewhere? I have division design 3 8_24 but the AC part seems to be broken in the if statements on 2nd worksheet. it isn't reporting softness in main worksheet of the main workbook.

#### Dalwin

##### Field Marshal
The problem I have with statsitical analysis of unit composition as usually done is that it ignores a key and poorly documented feature of the combat system. Not all combat factors are equal.

By that I mean if a hit is scored on an infantry unit by a tank unit a different amount of strength and org loss is assessed than if that hit had been scored by an infantry unit.

There is a complex grid listing how much damage is done when a hit is scored based upon attacking and defending unit types.

Therefor a strict breakdown of getting so many hard or soft attack factors for so many IC days of production does not show a true picture.

#### bbasgen

##### Field Marshal
There is a complex grid listing how much damage is done when a hit is scored based upon attacking and defending unit types.
Can you tell a little bit more about where you are getting this information? It is true that the lua defines some different probabilities for tanks, but I've never seen any data showing damage inflicted is dependent upon the unit inflicting the damage.

Here is damage data correct for version 1.4. The release notes for Semper Fi say some values have changed, so I don't yet know what exactly is different:

#### Dalwin

##### Field Marshal
Can you tell a little bit more about where you are getting this information? It is true that the lua defines some different probabilities for tanks, but I've never seen any data showing damage inflicted is dependent upon the unit inflicting the damage.

Here is damage data correct for version 1.4. The release notes for Semper Fi say some values have changed, so I don't yet know what exactly is different:
I have heard it referred to several times in the past in threads breaking down how the combat system actually works. All I have is second hand.

Things like defensiveness and toughness and how the calculation is done to determine whether a hit is scored or not is all pretty clear and well documented. The actual damage assignment is less transparent.

It is possbile that I am wrong and that this stopped being true after HOI1 and HOI2 but the basic building blocks of the combat system have not changed, so I believe this aspect is still present as well.

Someone like Blue Emu or Lothos could probably shed more light.

#### unmerged(232155)

##### Sergeant
Just downloaded the xls spreadsheet. I see at least one other person has mentioned it, but it was a while ago...

The AC softness value is absent or broken.

If it makes a differance, I downloaded it from the HOI wiki.

Cheers

PS. The flaw is either...

in the cells "Division_database" AQ149 to AQ153, with the "0" in =IF(\$C149<=\$A\$2,S149,0) needing to be changed to "". The result is called on by AQ154 to provide the minimum number =MIN(AQ149:AQ153) and the given to a higher year (eg 1946 if you are researching 1938) 0 over-rides everything else.

or

AQ154 is wrong in calling for the minimum number and should be =MAX(AQ719:AQ723).

And it looks like four locations need fixing AQ149-154, AQ434-429, AQ719-724, AQ1004-1009, one for each brigade calc.

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#### unmerged(181758)

##### Colonel
The problem I have with statsitical analysis of unit composition as usually done is that it ignores a key and poorly documented feature of the combat system. Not all combat factors are equal.

By that I mean if a hit is scored on an infantry unit by a tank unit a different amount of strength and org loss is assessed than if that hit had been scored by an infantry unit.

There is a complex grid listing how much damage is done when a hit is scored based upon attacking and defending unit types.

Therefor a strict breakdown of getting so many hard or soft attack factors for so many IC days of production does not show a true picture.
Can you tell a little bit more about where you are getting this information? It is true that the lua defines some different probabilities for tanks, but I've never seen any data showing damage inflicted is dependent upon the unit inflicting the damage.
I don't know the grid Dalwin is talking about but there definitely is a difference between hits from Infantry and hits from Armour, as he says.

There is something like this "Armor_On_Soft" modifier increases damage inflicted by mutliplying between 2 to 5 or 6 points or somethink.

It is definitely there and working in game, myself and a couple of others checked it out and proved to ourselves on a thred that it works somehow, it multiplies the damage results, not the probabilities.

I found it to work from when the unit is 50% Soft or less, even below 33% and too hard for CA bonus but is not invoked between 50% and 66% just because there is the CA bonus.

I suspect its not working as intended and meant to be for Brigade Softness/Hardness, but it is definately working when 50% Soft or less Divisions are hitting Soft targets. It really helps to melt through them like butter.

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#### Chromos

##### AHOI-Mod Series Developer
Demi Moderator
I suspect its not working as intended and meant to be for Brigade Softness/Hardness, but it is definately working when 50% Soft or less Divisions are hitting Soft targets. It really helps to melt through them like butter.
I think it represents the ability of tanks(hard targets) against soft targets, and this is a different thing as sa combined bonus. So different prerequisites are coming into play..

Kind regards,
Chromos

#### unmerged(181758)

##### Colonel
@ Chromos; it is on top of the CA bonus when both are into effect, it is an extra Hard firer on Soft target thing, so yeah different prerequisites which is why it still comes into play when the CA bonus doesn't at below 33%.

#### unmerged(181758)

##### Colonel
Ah, found a couple of links to what I was recalling:

The multiplier is x2 for Strength and x5 for Organisation, so it means that for each hit it multiples the damage result in the two areas by those amounts, doubles MP losses inflicted but increases by 5 times the disorganisation suffered to the Soft target of the calculated damage from the hits it receives from the Hard firer AFAIUI.

#### Forster

##### Field Marshal
The width is one of the columns in virtually all my tables. I am looking at the unit statistics and the stacking penalty only right now. I find it difficult to believe that units shatter when the support brigades still have org. If you have some source for this I would love to see it.

Also, note that my analysis of stacks assumes that the full width is being utilized, and therefore even if your theory is correct I have accounted for width in those tables.
When this happens, the support units, usually artillery, end up lowering their guns and firing directly at the enemy until they too are overrun. It occurred in WW II, Korea, and Vietnam. Since Vietnam, artillery has also had the bee-hive anti-round for direct fire against infantry. (REALLY nasty results with this baby.)