Question about stacking capacity and penalty

[NPC A]

I never really compared the stats of divisions during battles in the game. Recently, I started comparing and noticed something called 'Stacking penalty'.

I don't understand what 'stacking penalty' is. But when massive battles involving at least a dozen of divisions happen, the stats indicate my divisions suffer Stacking penalty: -75%. Yet when I look at the stats of the enemy's divisions, they do not seem to suffer from stacking penalty.

Can anyone explain what this 'stacking penalty' is and why AI units don't suffer from it(or at least doesn't show up from my point of view)?

[irgend1 L4rry]

The more units you have fighting on one side, the higher the stacking penalty is. I think it's in the game to represent the difficulty to manage a sizeable army properly.
The AI units are suffering from this penalty as well.
There's a thread on the official forums: https://forum.paradoxplaza.com/forum/index.php?threads/confused-by-stacking-penalty-compared-to-hoi2.464500/

What you can do to increase your odds while keeping the amount of units in your attacking army the same is that you need to attack from 3+ sides (when on land) or use navy to bomb the shores (when doing a naval assault)

[76561198814511849]

Stacking penalty means that all else equal firepower will only increase approximatly with the squareroot of your amount divisions in the respective battle. The precise formula is:

stacking penalty = 1 - (sqrt(8*units + 1) - 1) / (2*units)

{LINK REMOVED}https://forum.paradoxplaza.com/forum/index.php?threads/stacking-penalty.580760/

By this formula we get 33.33% stacking penalty for 3 divisions, 50% for 6 divisions and 77.78% for 36 divisions.

You need to maximize the quality of your divisions as only mere quantify is penalized. Also use tactics that increase your effective quality like using 3+ angles of attack. If somehow you can manage 6 angles of attack you get +100% on attack and defence which obviously is a gamechanger.

[NPC A]

Thank you all, I now understand how it works.

I always do try to encircle my enemies. Before even when I had trapped my enemy in a single province(fully encircled) and attacked from 5, 6 directions, my divisions suffered -75% of stacking penalty. So I thought I must have missed something but now I understand it's just part of the game you can't do much about.