History is FULL of examples of a numerically smaller force encircling a numerically larger one.
Encirclement is one of the most effective ways to achieve a battlefield victory.
Encirclement puts the encircled at a tremendous disadvantage.
- restricts the movement of the encircled
- cuts the encircled from their lines of communication (and supplies)
- causes great psychological distress among the encircled troops
- distressed and panicked troops often did irrational things
In fact the whole concept of Blitzkrieg was based on fast breakthrough, deep penetration, and envelopment.
What the Germans didn't know was the Mongols actually did one better. The only thing better than total encirclement was, an INCOMPLETE total encirclement. In this case the encircling forces have the means to fully encircle the victims, but choose not to. This entices the encircled forces to panic and make a break for it from a corridor deliberately left open by the enveloping forces. Trying to escape from a collapsing pocket with a disintegrated command and control is quite possibly the most dangerous situation for an army.
Let's look at a few super famous examples.
The battle of Teutoburg Forest In this battle, numerically inferior Germanic forces encircled and annihilated 3 roman legions. The Romans were lured into Teutoburg Forest where they were cut off and then whittled down by a series of ambushes.
Battle of Tannenberg The German Empire won a major victory against a numerically superior Russian army. In this battle, the Germans learned of the russian plan via unencrypted wireless communications. They let the russian push forward into a trap where upon german reinforcements fell on their rear an encircled them.
The battle of Ulm was a beautiful battle of the War of the Third Coalition. Technically, Napoleon had overwhelming local numeric superiority. But he achieved it by striking before his massively larger foes could gather their forces.
But to me, the absolutely weirdest encirclement battle was the Battle of Alesia where Julius Caesar built the famous double wall encirclement. He encircled his Gallic foes at Alesia. But his enemies had strong walls. So he built another set of walls around Alesia. Then the Gallic forces rallied to relief Alesia. Caesar built another set of walls outside his first wall to fend off the reinforcement. So the Romans had numeric superiority against the forces defending Alesia. But the Gallic relief force had numeric superiority on the Romans, who were themselves encircled. Spoiler alert, the Romans won.
Except for Ulm, mobility didn't even come into play. Teutoburg was won by the clever use of terrain. Tannenberg was won by the clever use of information, and letting the enemy encircle themselves. Alesia was a fine example superior siege engineering.