This guide will, hopefully, clear out the question marks about effective stacking.

Mechanics

Please don't skip this, it's important to be understood:
If army A fights B, the damage a unit in B receives is army A's damage output vs. that unit's armour class, divided by the size of army B.
This meaning, if your army has 12 damage against infantry and 24 against tanks:
When the enemy army is 1 tank and 1 infantry, the infantry receives 6 damage - 12 (your army's anti-infantry damage) divided by 2 (the size of the enemy army). Similarly, the tank receives 12.
If it was 1 tank and 2 infantry, the tank would receive 24/3=8 damage, each of the infantry 12/3=4 damage.

If an army is greater than 10, its damage output against an armour class is the damage value of the top 10 best units against that armour class. This doesn't mean only 10 units can contribute to the army's damage. Only 10 units can be fighting a certain armour class, but more than 10 units may be contributing overall.
For example, if being attacked by tanks and infantry, an army of 10 anti-tank guns and 10 infantry contributes with all its units. However, instead of the damage of the 10 AT guns and 10 Inf together, only the damage of the 10 AT is used against the tanks and only the damage of the 10 Inf against the enemy infantry.

There is no reduction of damage efficiency based on army size. The "damage efficiency" in the Status info popup only means how much % of your army is contributing.

Stacking strategy

This, however, makes overstacking quite an efficient strategy. To be successful, you first think about the armour classes you'll likely fight. Then, you make an army with 10 units specialized against each of those armour classes.

10 attack bombers, 10 tactical bombers and 10 interceptors are a such ideal army - attack bombers will contribute against tanks, tactical against infantry, interceptors against other planes.

There are other factors affecting the stacking:

- Speed. Especially if you're active, better make smaller armies where all units have similar speed than large armies where the very fast units have to go with the slowest. It's good to just not focus on units with different speed, and have an overall composition with similarly fast units.

- Research. It's important to use as few units as you can without exposing your army to major danger. The fewer units you're using, the more upgrades you can afford for them, and levels are a very important factor in 1.5. So, try to counter all likely strategies your enemy may use in the most research-friendly way (not just use few unit types, but for example replacing a unit with railroad guns can be good as they only need 1 level of research).

Countering overstacking

Large stacks are a pity to get destroyed. So, it's crucial to support them with all counter units, which usually makes them slow. It's not good to have all units mechanized not to run out of oil and metal and not to be exposed to anti-armour units, so you have to use some slow infantry class units.

Also, adding the counters makes you unable to upgrade everything to the max level. If you want to still be effective, you keep the levels (the day of availability, resp., as some units have way more, less significant and expensive levels) equal. This means all units are equally behind in upgrades. You can attack this weakness by focusing on few unit types and upgrading them to the max level. To be effective, choose them in such a way that you spend all your resources, instead of draining some and leaving an abundance of others.

If your army's enough and you want to destroy the enemy quickly, split it into stacks of 10. Splitting into X stacks to attack makes each stack receive defensive damage from the target, so your units receive X times more damage. However, as you split into 10-stacks, each of them now also uses 10 units to damage the enemy, so your damage increases roughly X times.
Roughly, as if there are different armour classes in the enemy army, the best 10 units against each class fight, so splitting actually averages it and decreases your efficiency in the fight. It does so more if the specialization of your units against a class is more significant.
This meaning, splitting into 10-stacks is used to break through quickly and be able to surprise your enemy or kill his artillery backup faster. However, if your enemy is active anyway and there is no threat to be dealt with urgently, it's better to stay stacked.

Artillery&Ranged unit tips

When using artillery, you should keep them behind and separated into stacks of 10, as artillery don't receive defensive damage, so splitting doesn't make them less effective in the ranged fights. However, it does in close combat, and planes may attack the artillery. If you're exposed to air attacks, even if you have AA, consider merging all artillery with your main army. If you encounter an enemy land army, you can split out a group of 10 artillery, fire with it, and split out another. After you split all or destroyed the enemy, you multi-select all the artillery and the main army, press Move and the position of the main army. This way, all the artillery should merge back within minutes, if not instantly. It's quite possible to do this without getting exposed to planes - if they're patrolling, just don't let their timer run out while the artillery are spread out.

If the land army is too big and you didn't destroy it, you can order the main army to move forward, then select all artillery and move to the one furthest behind. This way, you merge all the artillery and AA into a single stack, which still makes it a lot less vulnerable to planes. Everytime you fire, you split into armies of 10 and then re-merge after firing. Remember not to fire with the whole stack if not all useable ranged units would contribute - this applies to ship fights, for example. All units in the army have to reload after firing, even if some didn't contribute (army size limit or didn't have enough range).

If you want a fight to get longer, you place your army in the way of the enemy and wait for his army to ram into yours, and then do nothing with it the whole fight. This is more advantageous when artillery and bombers contribute to your overall damage more. If you wish to calculate this exactly, instead of just estimating:
- Add your offensive and defensive damage values together. This is what you deal to your enemy every 30 minutes if you're both attacking and defending. Transfer this into a rate (X damage per minute, hour etc).
- Do the same for the combined damage of your artillery and planes. Planes are usually patrolling, but if they're attacking, you have to take that into account and convert it into a rate of the same format (if the first was per hour, this should also be per hour).
- Calculate, based on this, how much the damage of the enemy army will decrease over time.
- Now, do the same for your army, calculate how quickly its damage goes down.
Then, calculate how many times slower it goes down if you're defending only and call the outcome of that x.
- And again, for the enemy, calculate how many times slower his damage goes down if your land army is defending only. Call the outcome y.
If x/y is over 1, it's likely better to only defend. It slows down the fight though, and time may get more important than strength at times, so keep that in mind.
However, this is extremely complicated to calculate accurately, as even without RNG changing things, there are hidden factors. For example, if side A has high damage and low hp units, those will die quickly and A's damage jumps down significantly. That causes the snowball effect to increase and side A to be less effective than the prediction.