To comment on the Mongol drive west...
I have a question: How far can the Mongol way of war be compared to the Polish-Lithuanian way of war in the fifteenth and sixteenth centuries? If some comparrison can be found, it might be interresting to look at the different situation in eastern and western Europe.
In this, I don't mean the terrain. If I would, I would be contesting my own theory of: "The experienced Mongol leader can trick the enemy into fighting him on a terrain of his [Mongol] choosing".
What I do mean, is the urbanization difference between eastern Europe en western Europe. The Mongol threat came in the thirteenth century. In this century, the people in western Europe were even more settled then those of eastern Europe. Warfare in an urbanized land differs a lot from war on the steppes.
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To explain my question: The Polish-Lithuanian troops mainly used cavalry in their army, they used raiding tactics and harrasing tactics but also charge tactics. They manouvered on the battlefield to win a battle on the flanks. They used feigned retreats and rode to meet the enemy to stop different enemy groups from rendevouz.
We would all agree this looks an awful lot like the Mongol way.(Poland-Lithuania tried to use western style armies, based on the tactics used my Maurice of Orange in the Dutch 80 years war against the Spanish Habsburgs, on several occations. This all failed.)
The Swedish adopted the Polish-Lithuanian way of fighting and used it to devastating effect during the rule of Gustav Adolf. During the series of wars in Germany, Gustav Adolf and his successor (Charles X) won all major battles and took large portions of North Germany. Charles X found it impossible to fund its defence. And more so, the swedish didn't have enough manpower to garrison their defences. Only one fifth of the soldiers in Charles X armies where Swedish, and that's only for north Germany. (source - Robert I. Frost, "The Northern Wars")
It is understandable that he could not hold his possesions, since the northern Italian way of war and the Dutch way of war (siege warfare) which was adopted in the whole of western Europe was based on the principle of avoiding the enemy's army and constantly take back the cities he just took, making the enemy capturing the same town over and over. This explains why the Dutch independence war is called the 80 years war.
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Back to the mongols... The tactics that the Mongols used so succesfully in eastern Europe might not work in western Europe, since the Mongols might be riding around Europe, taking all they can and losing it a few weeks later, because they can't defend what they took.
If you are ruler of a land with 5 settled communities and you don't meet your enemy, you will be defeated in no-time.
If you are ruler of a land with 30 settled communities, it's a whole different story (and that is the kind of comparrison that we can make between settled west en east Europe at that time).
Now give me all the differences between my example and the mongol horde (like, how will the Mongols react to a population they conquered for the second or third time, will they murder them like the Romans did with the Dacians?) and we will analyze them.
I think this is an interresting discussion, worth the space it takes in this thread.