I have 1000 sword fighters and the enemy has 1000 sword fighters. If they form a 20 * 50 rectangle, only the 136 people on the sides can actually fight. When I encircle them with a longer, thinner formation, I should be able to do more “damage per second”. For example in the games Age of Empires and Starcraft, you would want as many melee units in contact to enemies as possible.
Why does the “oblique order” work in real life? What advantage does a solder have from having someone stand *behind* him instead of fight *beside* him? Assuming they have spears instead of swords, they could fight from the second or third rank, but they did historically form more than three ranks.
Do they maybe *push* the enemies over with their shields and having a comrade push themselves in the back makes them better pushers? Maybe you would get *holes* in your line and having holes is worse than being flanked? But isn’t the point of diminishing returns earlier than fifty ranks? Is it a *psychological* advantage?
As a concrete example, you could consider the [Battle of Leuctra, 371 BC](https://www.youtube.com/shorts/N8vDnVJU1Lk).
Edit: I read that historians are not quite sure how phalanxes worked exactly. So maybe it makes sense to also consider more modern armies, before the use of gunpowder. They also had formations with multiple ranks.
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One mistake you do is to assume that people had sward as primary weapons.
Swords are what we often see about ancient time because they look nice and was common alongside axes for weapon carrier if you need to be armed but not in battle. They are also quite efficient weapons to use if it combats a few individuals. But when you talk about pitched battles with the close-order formation of large numbers of soldiers polar arms and shields is the common armament.
It movies you often see meant just running forward toward the enemy. That is a very bad way to fight. In reality, the efficient way is to keep troops in a formation so they can help each other. You then just have the enemy in one direction. If two groups of people just run towards each other you can have enemies all around you.
It is weapons with a high rate of fire initially machine guns and ranged explosive weapons that resulted in combat as we see it today. Even in the US civil war, the fire rate of the rifles was not enough to stop close-order formation to be efficient. The last attempt to use something like that was WWI it was clear then that it no longer works.
Officers and other leaders often had diffrent weapons because moving around and commanding was their primary task so fewer shields and polearms more swards. That practice continued in the battle to a very recent time when officers had revolvers and swords while the men they command had rifles. That is what is commonly used in WWI. Even today higher rank military commanders typically have a pistol as a side arm but soldiers have automatic rifles
The linked example the Battle of Leuctra is between ancient Greeks, their main formation was [Hoplite](https://en.wikipedia.org/wiki/Hoplite) which use spears and shields as primary weapons, not swards
With pole arms, multiple rows can point them out the front of the formation at the same time. A lot more recent pike formation is the same thing, they get replaced with bayonet-equipped muskets and later one where you get a range attack method too, Pikes existed for a long time alongside muskets.
Romans did use swords a lot more in the legion but they also had their Pilum, a 2 mere long javelin line you could use as a spear to for example defend against cavalry. Because it is a range weapon too and the was often thrown before you reach an enemy infantry line more lines resulted in more weapons being thrown.
Even if everyone had swords you do not what a too-thin line. It is a lot easier to break through it and if you do the thinner the line the fewer is there so try to stop the. The extreme example is just a 1 man thick line where a breakthrough of an enemy with a thicker line can result in you men needing to fight an enemy in front and behind them, which quite certainly results in death.
Another factor is in a compact rectangle it is quite hard to flee for someone on the front. Inexperienced troops might do that in contact with the enemy, so the enemy can get through the line because of that. When a unit starts to flee it is no longer organized and people get far apart. If the enemy has cavalry this is the perfect opportunity to use them and kill everyone that just run away. Keeping unit cohesion is more important than that some formations might be a bit more efficient.
Keeping the formation even in combat when people get afraid, and their friends die around is hard, especially with inexperienced soldiers. So a formation taht is more efficient with experienced and well-disciplined troops might be terrible if used inexperienced men. Humans soldiers are not like soldiers in computer games that can follow orders all the time. You need to take human behavior into consideration and a compact rectangle has the advantage is simple to command and keeping the troops fighting, Troops just running away is the work that can happen
Add to that maneuvering, you can have a line that goes on forever so you need the ability to proter from enemy infantry on the side of your unit or even cavalry that got around the line completely. The corners of a formation are countable o you need some depth on the sides.
The development of a compact rectangular formation is a hollow square where you get more from an area with fewer men. The drawback is maneuvering is a lot harder and if they break apart they are vulnerable to cavalry. The famous usage of this formation is in the Napoleonic wars. Hollow Square requires more training and troops that do not run away.
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