The guide is outdated and its basis has been rendered meaningless with the partial piercing mechanics introduced with Avalanche update.

Up to date situation:

Note on updates, 5th October 2022
Please see "basic guide information".
The stuff I expected below has indeed happened and this guide is dead.

This guide is relevant for the No Step Back expansion and uses the values as of 27 May 2022 - from verision v1.11.11.2eb0 (8e75). Latest update on: 27 May 2022

Note on updates, 5th July 2022:
Some of the numbers have been outdated due to the latest patch but the description of mechanics and the idea is still the same.

I already have an update ready for these changes and quite a few improvements and visualisations for this guide.

However, these are also likely to be outdated after the latest tease of "partial piercing mechanics" on the Paradoxplaza forums today.

Therefore I am refraining from updating anymore and decided to wait for the teased update which I expect to come with the next patch or the next DLC (By Blood Alone).

To understand the effect of unpierced armour in combat, I check the wiki. Upon reading what's written there, I infer the following:

When a division has some armour but is pierced by the divisions it is facing, its armour has no effect. There is no difference between zero armour and some armour which is high, but is pierced anyway.


No Armour or Pierced Armour

Suppose there are two divisions with exactly the same stats while in combat (soft attacks are the same and the attackers breakthrough equals the defenders defense).

Let's also assume the attacks of both of the divisions are equal and defense is not a factor. Without the armour involved, they would both deal, let's say 100 to each other and this would be an equal fight with only lady luck to determine the winner.


Unpierced, Polished, Shining Armour

However, when a division with armour is facing a division which cannot pierce it, it deals 40% more damage (on average) to that division's organization and takes 50% less damage from that division. Armoured division should now deal 140 while taking 50 damage in return. This may be considered a multiplier of 2.8 to the armoured division's combat effectiveness.

It looks like the armoured side could take on one more of the other division simultaneously and still win. When it's three, I don't know.

When there are more divisions involved in either side, the situation gets a little more complicated due to the coordination mechanic (whether most of the attacks target one specific division on the other side and knocks it out of combat early) and depends on whether the attacks a division sustains in a certain combat hour exceed its defense / breakthrough value or not, etc. So the armoured division could still win 1 v 3. It's just that there are more factors determining if it does. Let's leave it at that.

Anyway, tanks are tanks man. Tanks are tanks and armour is armour. It makes a big difference when you have armour. Put armour on tanks. It's awesome. Greatest idea ever. This is enough of a conclusion for now. We now move on to see how armour / piercing works.

Since we are dealing with armour, our enemy is piercing. We need to know our enemy first.

Let's start with the numbers.

Infantry Equipment

Here we see the piercing values of infantry equipment as provided to a single battalion throughout the timeline. So a single infantry battalion with 1936 equipment (Weapons I) would have a piercing value of 4.

In 1942, there is another upgrade in addition to the Weapons III upgrade, which adds 100% piercing to infantry. The value would thereby be increased to 20 in this case. An identical research upgrade is also present in 1943 which takes it to 30.




Anti-Air and Anti-Tank



Here we have the piercing stats of Anti-Air and Anti-Tank battalions. The piercing value of anti-air battalions go unchanged whether they are added as a support company or as a line battalion. Anti-tanks on the other hand, lose some of their piercing when added as support.

Notes:

The numbers above are unchanged through doctrines, generals, officer corps spirits and so on, as far as I'm aware. So these are solid numbers to safely expect at any certain point in the game. There are also piercing stats for certain armaments mountable on tanks but I will leave those out of the scope of this guide for now.

How do these numbers add up?

These numbers are the stats of a single battalion. When the battalions come together and form a division, there are certain calculations to determine how much piercing a division gets.

The calculation for the piercing stat of a division is as follows:
The Piercing of the Division
= 40% of the Highest Piercing Value among all Battalions
+ 60% of the Average Piercing of the Entire Division

Similarly with Armour:
The Armour of the Division
= 30% of the Highest Armour Value among all Battalions
+ 70% of the Average Armour of the Entire Division

Note that the stat of the single highest battalion has a larger effect when it comes to piercing, more than it has in armour.

Also keep in mind that support companies are also counted as one battalion in calculating the average just like line battalions, so the more of them without armour/piercing gets added, the lower the average of the division.

Ok, too much information already. Next, we'll try to make sense of these info.

Now we move on to actually put these information together.

Below table shows the piercing stats of typical divisions having relevant techs researched of given year. Then, the armour required on a single tank battalion within a division of 17 battalions to be able to go unpierced against these divisions is given.

The 17 battalion division to go unpierced against these, is assumed to contain no other armoured battalion than the highest armoured battalion which is the only armoured battalion in this division (an infantry template of 12 line battalions and 5 support companies, one of them is armoured for example).




Notice that the rightmost column shows the armour required to still go unpierced despite having lost 20% of the armour stat of the armoured battalion. So this may be considered a safe number.

Why?

We take into account that our division will not be fully equipped at all times. Periods where the division will need to fight under-equipped, until reinforcements arrive after combat losses and attrition effects will be a factor. If we don't want our division to suddenly become pierced in these periods, we can go for the safe number.

More on safety: Attrition has a base value of 1.2 x Attrition, even if equipment reliability is at 100%. When the number of equipment per division is low, this effect is more of a factor. So, our division relying on its Armored Recon company (24 light tanks) for armour, enjoying life, riding over the mountains on a killing spree can lose 2 tanks during this journey and get down to 22 tanks in a matter of days. If we went for the minimum amount of armour, this loss would render our remaining tanks insufficient to provide enough armour to our division anymore. In this case, since the light tanks are "essential equipment" for the recon company, the loss in stats as a percentage would actually be higher than the losses of equipment in percentage. As it loses more and more equipment, its armour would be dramatically affected.

Going for the safe number or even a safer number could be a sensible choice especially when using a small number of equipment to achieve armour. Also go for more safety when expecting to fight in high attrition conditions and when expecting enemy close air support bombings to be a thing.

Scaling: When understanding the above table, remember that the table uses values for a 17 battalion division (a template of 12 line battalions and 5 support companies for example, only one of them being armoured) as the armoured side.

Therefore, take into account that the required armour on the single tank will be lower the smaller our division gets (less total number of battalions) and higher when it gets bigger. If we used a 5 infantry division with one tank added to it for example, we would need less armour than what the table shows. If we used a massive template of 20 infantry, we would need more.

The same is true for the enemy divisions whose piercing we are looking to challenge. We consider them to involve 5 infantry battalions in the table. The more battalions they add with very little piercing or none at all, the lower the overall piercing of their division gets. Note that pure infantry divisions can have as many battalions of infantry without a change in piercing since they are all equal. Adding support companies with no piercing to them would still lower their piercing though.

Next, we will try to draw some conclusions.

End note for this part: Numbers are always rounded in favour of our purposes. So, piercing values given might actually be an integer lower whereas "armour required" values are rounded up, for the sake of dependability & simplicity.

Armour, as well as piercing come at a cost. We wouldn't want to be putting the products of years of hard work from our military factories on the field just to see them get pierced every time. We also wouldn't want to add those Anti-Tank companies on all our divisions just to suffer from a lower organisation, watching them shoot at infantry and light vehicles which would otherwise be pierced anyway.

That being said, we are a country who has access to the most invaluable of advisors: a time-traveller who lives in 2022 and knows about all the history and research progression of WW2. This person can help us, just like it did in the previous part by listing the numbers for us.

However, the numbers won't help us by themselves if we don't know which number we are looking for. We already know how much piercing each composition provides and the required armour for that, but there's a second question: What will be the composition of the enemy divisions? This brings us to the matter of intelligence which is necessary in every step of the question "how much". By that I mean intel enough to figure out what our enemies or potential enemies are up to. What they are bringing to play with today and what they are planning to bring tomorrow.

How to Intel?

• We can see some approximate numbers hovering over the counters of other countries' divisions on the map, located adjacent to our frontline, if and when they bring them over there.
  
  Below are some examples:
  
  In this case, we can only see the existance of at least one division adjacent to our border. We can see the model, so it's an infantry but no info on the composition of this division.
  
  Here, we also have a division on our side of the border so this division helps us see more on the type and composition (what type of battalions it has) of the bordering division with some numbers. This is a big help especially for determining if they have AA or AT.
  
  
• We can send ships or submarines to their coastline and get some info on any divisions located there, even build radars to increase the quality of this information (This is usually what I do).
  
  Here we have a single submarine task force on "hold" order. This tells us if there are any divisions located in provinces adjacent to this sea tile. Here we don't even see the type of divisions, but the quality of this info may be improved with radar / army intel I think (haven't thoroughly tested). The minimal info here is especially valuable when checking the coastline for suitable targets of a naval invasion.
  
  
• We can build an intel network / use scout planes and get to a point where we see their equipment with detailed stats in their stockpile, look at their current templates, see what they are producing, what they have researched and so on.
  
  Here we see our intel ledger on the country we're looking at. A very high intelligence level (80%) is required to see stockpile and templates in full detail but 30% would also do just fine in most cases since we have an idea of how much piercing a typical division has, thanks to our reference list.
  
  We can also see in this ledger an approximate number for their total number of divisions, which may be interpret in conjunction with what we see on the map. For example: We see 7 divisions on the map near our border, by spotting with our own divisions and ships. The ledger tells us they have a maximum of 8. So we're looking for a maximum of one other division which we cannot see on the map. Time for an easy naval invasion.
  
  
• Or we can wait until the time comes and the actual combat starts. This would actually provide the most accurate information since we would get to see the exact stats as they are in effect, in combat. It's just that it could be more difficult to adapt at that point. Below screenshots show how to see armour / piercing in combat view.
  
  The combat actually started and we want to look at how our division is enjoying its armor by hovering over the shining armor icon in the combat view. The shining armor indicates that we are unpierced by any of the enemy divisions in this combat. The tooltip showing the effect of our armour says that we deal 50% more damage to the enemy. If the wiki is to be believed it's actually 40% on average, as we mentioned in Part I.
  
  Now we want to compare our armour to the enemy piercing by seeing the exact stats. By hovering over our division's rectangle, we see our division has 4.3 armour.
  
  We now hover over the enemy division rectangle to check how much piercing it has. It says 4. This is pure infantry, so as expected it has only 4 piercing in 1936, thus cannot pierce our 4.3. We should be good against these types of divisions for a while longer. This is something we already knew, thanks to our table.

Here are some contemplations on how to reliably achieve armour against certain divisions for cheap, without overkilling it.

If our end goal is to be unpierced by infantry, then light tanks should do just fine for us in early game.

A practical way of adding light tanks and their armour to our divisions is to add Armored Recon Companies. These companies only require 24 equipment in comparison to 60 equipment a regular light tank battalion would require. However, they retain 100% of the armour, as well as the piercing values of the equipment given to them, also keeping most of the breakthrough. They lose 50% of the soft attack and defences though. Still, 40% of equipment required for 50% of the stat? Bargain. In the below example, we add an armoured recon company using a good light tank and achieve over 6 armour on our division, which is a good number against infantry early game.




An honourable mention is the flame tanks. These become available after 1939 research of Engineer Support Companies. They require even less equipment, only 15 compared to 24 or 60! They lose out on all stats proportionally unlike the recons though. They use 25% of the equipment, so they get 25% of the stats with light tanks. Armour gets cut as well. However, we have other options here. Medium and heavy flame tanks are a thing. Stat retention is a bit higher with them: 30% with mediums and 37.5% with heavies.



Medium flame tanks can be an option for cheap armour if we have them researched. Even after its armour gets cut with a -70% modifier due to being a flame tank, the above design still has decent armour against early infantry. It barely has any other stats but it is a flame tank so the terrain bonuses will still apply to the division. The production cost is also very good, keep in mind that it's going to be multiplied by just 15. Could also be a choice.


Moving on to the how much table


Suppose we figured that the vast majority of enemy divisions are infantry, without any AA or AT support. We know we can easily be armoured against them.

Now we want to answer the question of "how much" when modelling our tank. We refer to our table from Part II above and see that the safe value we are looking for is 16, up until the 1939 equipment is researched & given to the divisions we're fighting against. Then, we would need 19.




We want a tank with at least 16 armour, ideally 19 so that it can keep enjoying it's title "the unpierced" against infantry for a longer time. We look at our options to see that the interwar light tank has a base armour rating of only 5. We can push this tank to its limits with cast armour + sloped armour + also clicking the plus armour icon to make it 4. This way we can achieve 10, with no other tech researched. Even if we do some research, spend all our army XP on more modules (armour skirts and some more plus icons), we would still be barely over the lowest limit. Not good.

Basic light tank (1934) has 10 base armour, while improved light tank (1936) has 15.

10 is still not quite enough for our purposes but with some tweaking it can serve us.

15 though, 15 we can work with. We can even use it as is, slightly push it to 16 for safety, or 19 for longevity but it is all we need by itself. Just spend 1 army XP to strap a gun on top of it and you're good. Spend a few more to make it better; do it cost effectively or not, you choose.

How About Enemies with Anti-Air?
That's that. Now we ask ourselves: Can we be unpierced against divisions with AA too? Well sure we can as long as we're willing to spend. The piercing of a 5 infantry battalion (10 width) division with an AA support is 14.5 so we need 43 to overpower that, 54 to do it safely (see table).

This takes us to the medium tank which has 35 base armour at 1934. We can work with that and achieve 50ish values, even without expensive modules like cast armour, probably. However, in this case we don't have the option to add medium tanks as support companies of less equipment, unlike light tanks. This will require us to actually click on a new regiment in the template & spend 25 army XP and add a medium tank there. Also spend full cost for equipment (50 medium tanks for each battalion).

How About Enemies with Anti-Tank?
Now we look at what more we can do... Can we be unpierced by anti-tank divisions? Let's check the table. Oh boy, it says we need 81 - 101 on a single tank even if they only have 1936 support AT! No worries, we have the mighty heavy TONK at our disposal, let's take a look at it's stats. Uhh, this has the same armour (35) as the medium in 1936! What a disappointment...

As expected, achieving unpierceability against Anti-Tanks involves more than a single tank on an infantry division. We would probably need expensive modules to achieve the armour we need, multiple tanks in a division, suffering from low organization as we keep adding them and so on.

Can we do it though? Sure we can. How much we need? Just use the table if a single tank battalion is involved (and see that it's impossible for large divisions), otherwise use a spreadsheet for custom divisions which I don't know if I can upload or reference mine here. We'll see.

Thank you for reading! Hope you enjoyed & found some use for this!

Credits:
Credit to @Corpse Fool for reviewing, correcting and helping with crucial elements in the guide.
Credit to Paradox employees for making this game awesome.
Credit to Feedback for his fun videos and inspiration.

Credit to BUSBY for making me actually buy this game with his enthusiasm in the Battle for the Bosporus Turkey video and getting me sucked into the abyss once again after a long time, since the times I played HOI 2 as a kid...

Against:

• Pure infantry in 1936: we need 12, ideally 16 armour on a single tank in our divisions.
  
• Pure infantry in 1939: we need 16, ideally 19. Go for light 36, work a little on it in these cases.
  
• AT sup. infantry in 1939: we need 100, ideally 125. Go for medium 36, work on it.

Don't under-design, don't over-design.
Be happy, be smart. Thank you for reading.