Alexander faced armies from about equal to his in numbers to about twice his numbers.
The number of the Macedonian army in the battle of Gaugamela is around 47.000 (9000 horseman) troops facing around 250.000 persian troops, its around 1:5.
But here there is a big problem with Persian forces, namely that outside the Immortals and mercenary Greek hoplites their forces were essentially junk. And even the Immortals were not as well trained or equipped as the Macedonian forces, who were trained for war as a permanent standing force, with the best armour and arms, and new innovative tactics developed for their increased training and better equipment.
Yes I agree with you, and that is why I said battle experiences, training and discipline also factor that can increase the troops quality, and number not the main factor of quality, but only one of many factor of quality, include troops faith, moral, leadership, and many others factor, but you also must note that technology also can't cover all of these factor, it again only one of many factor that reflect the troops quality. And in civ 5 this are reflect with promotion (experiences, combat specialty, etc) while leadership reflect on leader or GG that give combat bonus. I really not againts you in this I build my argument base on the very same idea with you. Am I right?
The other two, not being that familiar with Muslim history, I cannot talk about. But my two examples do show that when you've either equivalent or broadly similar equipment training and leadership, numbers will nearly always show through. And frankly numbers are most often the most decisive condition on the battlefield.
Well, now my activity have something to do with history I work to help a university one of my subject is Islamic history in the future it will be Balkan which I don't know much about and Ottoman, that will be interesting.
About Khalid Ibn Walid is a muslim general that confront byzantium army in the time of Heraclius one of the world super power at that time, the muslim also open got a front from Persia or the Sassanid which is another world super power, that days was tough.
Khalid Ibn Walid lead an army of 40.000 to fight with 150.000 Byzantium army, and he lost 4000 men and the Byzantium lost around more then 50.000 (around 70.000 almost half) men, in 6 days battle, base on the primary source by Tabari. In equipment the muslim were poorer comparing with the byzantium army at that time, but their discipline and solidarity also great tactic is one of the factor of their victory.
In christian sources it said Heraclius devastated and enraged because of the result of the battle, he retreated to the cathedral of Antioch and summon a meeting of his advisers at the cathedral and scrutinized the situation. He was told almost unanimously and accepted the fact the defeat was God's decision and a result of the sins of the people of the land including him (Regan, 2003). But it correlated with muslim source, it said before the battle Heraclius send his men to monitoring muslim troops, and they make a report :
"They are people who monks during the night (it mean they are praying like monk in monasteries), and fast during the day, and if the son of their leader would steal, they would cut their hand, and if anyone of them, high or low, would commit a crime, they would be punished."
and after the battle, he summon his close adviser and peoples, and anger because the lost his brother Theodore in that Battle he say :
Heraclius said: "Woe to you! Aren't these men like you?"
They said: "Yes"
Heraclius said: "Are you more, or are they more?"
They said: "We are more."
Heraclius said: "How come you are losing, and how come they are winning?"
One of the elders said:
"The reason why they are winning and we are losing is because they pray at night, and they fast during the day, and they fulfill their covenants, and they enjoin good and they prevent evil, and they are just among themselves, and because we drink alcohol, and we commit adultery and fornication, and we commit every sin, and we betray our promise, and we oppress, and we commit wrong and transgression, and because we encourage evil, and we prevent people from doing what pleases God, and because we corrupt in the land"
Heraclius said: "You are telling the truth"
after this he say his famous quote which is :
"Farewell, a long farewell to Syria" (Runciman, 1987)
So it is a discipline, good general, a leader that can give example, a great tactician, are some of many factor that results on winning or losing the battle. Civilization society policy, GG, unit promotion, can be a bit like a miniatur of it. I want to tell you more about these men, but maybe it will bit out of topic and interest, but I hope we can get fruitful knowledge from each other