In battles, the weapons, training, tactics, and discipline are all factors. Discipline and morale may be the most important factor.

At Gaugamela, the largest number of troops in the Persian army was peltasts. These men carried wicker shields, hardly any personal body armor, and javelins to serve as missiles and then a light axe for melee combat. Compare that to the men in the Macedonian phalanx: every man is wearing armor, a shield, and carrying a very long pike. These layered pikes meant attacking soldiers would have to go through 5 pikes before reaching the first line of troops. So simply charging wouldn't work. Phalanxes are weakest at their flanks, but Alexander knew this and maneuvered his forces to keep the Persians from doing what they wanted to do.

Morale and discipline also play one of the most important roles in a battle. In ancient battles, one routing unit could turn into an army as soldiers see friendlies fleeing and think the battle's lost, so they need to run as well. For example, let's compare Napoleon's Grand Armee against the Imperial Russian Army in the early 1800s. French officers advanced by merit, the soldiers had campaigned together for years through dozens of battles, and their weapons and supplies were top-notch. The Russians, on the other hand, levied mass conscriptions, the lower-level officers were poorly trained and aristocratic, and had generally worse equipment (except artillery). In battle, the French soldiers trusted their commanders, relied on the man next to them to watch their back, and had been in combat before. Many Russian soldiers did not trust their officers, barely knew their comrades, and their weapon they had fired a few times did not give them confidence. While the Russians outnumbered the French, Russian soldiers seeing people dying for the first time and seeing and hearing combat drove many to rout.

A more current example is the Battle of Mogadishu in 1993 between 160 American Rangers/Delta Force against ~5,000 Somali militiamen. The exceptional training, weaponry, and discipline of the Americans allowed them to inflict hundreds, possibly over a thousand casualties against the militias while only losing 18 men (although 73 were wounded).

Numbers alone is not a good indicator of army strength.

Edit: typos

This is not a developed answer to your question, but rather a suggested way to think about these battles that might help you understand battles and warfare in general.

One important thing to keep in mind when visualizing and thinking about battles is that soldiers did not charge at each other and fight for hours on end killing a majority of the other force before leaving (as you would see in most media/games like the total war series). Obviously if this was the case, it would be ludicrous that 40k could defeat 200k. It would never happen.

Before a battle happens, you must assume that there is a strategic reason for each side fighting at that specific spot in that specific time (with exceptions of course, but this can generally be assumed as if it were untrue they would not be fighting afterall). So what kind of things are battles fought over? Land mainly. And more tactically within a battles strategic placement you'll have specific landmarks or formations that prove to be vital to the battle, and the taking of these positions can win or lose battles depending on the situatuon.

For example, army a is 80 thousand strong and army b is 40 thousand strong. This battle will be overlysimplified to make a point. Say you have a piece of land that has a vital resource cache that army a currently holds and army b wants to take it. This would be the strategic reason the battle is fought. Within this battle, there is a ridge that had a high point on its right flank that dominates the landscape. This is the objective for the army b to take. Now all tactics of specific battles and other things aside, assume that army b attacks that hill on the ridge and takes it. For this specific instance of the battle the 2:1 ratio of forces doesn't matter because only a few thousand men can fit on the hill. Army b loses 1000 taking it and army a loses 500 losing it, and another 500 withdrawing from the hill. you will withdraw before you lose a majority of forces in a spot in almost all cases, they won't just keep killing eachother until out of men.

Now the situation we have now is army 8, still will roughly a 2:1 ratio of men to army b positioned on this ridge, but not holding a hill which overlooks the entire ridge and battlefield and provides the single greatest tactical asset of this specific battlefield. They obviously want to tske it back.

Say thy counterattack and take the hill back. Army a loses 2000 retaking the hill and army b loses 1500 losing the hill. Army a has won, without use of much of its force as without repeated more counterattack from the smaller army, which needs it's men more than army a and can't afford to throw away men like that (ignoring factors that could influence this). They will withdraw in an organized fashion but likelu be given chase by the victorious army and lose say 5000 to capture/being killing in the until retreat (retreat is where a huge amount of casualties occur). This is one scenario where the large army wins.

I'm on my phone at work now so sorry about being unorganized on my writing,and not providing some sort of sketch as well.

But what if they don't tske the hill back as their number advantage is relatively meaningless on this single hill. Army b repels 2 or 3 counterattacks losing 2000 and killing 4000 and in the meantime has set up an ansrtilley battery on this hill overlooking the entire ridge. What is left for Amy a to do? They have lost. Again, ignoring specific strategic influences to this thinking there is no long a reason to continue this battle for army a. So army b wins with only a small portion of its army used, and army a loses with an even smaller portion of its army used due to tactics and strategy. Sure army a could probably have just fought and fought and eventually won due to attrition but that's a high risk low reward scenario and not worth doing. After losing that key fight over the hill retreating makes the most sense. This is why you also see battles between huge amounts of forces have relatively low amounts of casualties.

I know there are typos, I'll fix and reorganize when I'm at a computer I