”The legionaries circle can't hold 120 men, or even 100, it's likely closer to 90”For that to happen, the radius of the circle of Romans has to be ¾ of that of the circle of barbarians. With 2 meters distance between their heads, that would make a radius of 6 meters vs 8 meters, and circumferences of 36 and 48 meters, or about half a meter per man. Tight, but yes, at that scale, the outside army has the benefit.
These armies were larger, though. At 900 defenders and the same distance between the lines, there would be 930 attackers. At 9,000 defenders, there would be 9,030.
”barbarians rush around them causing panic”.
Panic is what I put in as an option, and what surprises me. I would hope the Roman army, knowingly marching into enemy lines in a fairly shallow column would be prepared to see enemies appear in their flanks.
What you describe must have happened, but I don’t see how an army that large with such superior numbers would get there, unless its soldiers weren’t as good as those of the enemy in some way by quite some margin. Lack of leadership decreasing soldier resilience? Lack of experience?