You don't break a Mongol formation as it was under Genghis Khan. There is a reason why Mongol armies consistently suffered mild or heavy defeats against the Chinese and the Kharwezm, and all of a sudden, once Genghis Khan came into place and reformed the Mongol army, those same armies that had experience in dealing with Mongol armies were suddenly overrun and dealt consecutive defeats.
The Roman army, no matter who is at the head of it, plays into the strengths of the Mongol army. Mostly composed of Infantry, it had little mobility, and required a Cavalry escort to maintain any strategic mobility against cavalry armies. The cavalry itself was trained on providing additional shock force to the army. Only that with the Mongols, the shock part would never come until the Mongols were absolutely sure that they had real chances of crushing the opposing army. While Roman tactics might shield them temporarily from the Mongol pelts for some time, the cavalry wasn't as fortunate. And the problem is that no Roman cavalry either had the mobility to pursue and catch the Mongols (And the only moment they would engage with the Mongols would be if the cavalry would pursue too far, and consequently be cut off by a sudden Mongol turn-around and counter-attack.), or having the necessary speed to escape the Mongol rain (In case the Roman commander wanted to retire the cavalry to entice the Mongols to commit to moving in for the Close combat and only once the armies were engaged would the cavalry speed back to the army and charge the engaged Mongols.)
Further, Mongols had an extremely decentralized army structure (And thus a Mongol army could cover dozens of kilometers apart), meanwhile the Roman army usually required most of the army concentrated over a diminute distance. Fighting formations were also extremely concentrated, which was the biggest benefit for a Mongol army.
Almost everything plays into a Mongol victory. The only chance of a Roman victory would be if Julius Caesar could find suitable terrain where his army could block Mongol advance, avoid being encircled, being sheltered from ranged fired and propitiuous for Infantry and not for Cavalry.
Otherwise, Genghis Khan & his Mongol army vs Julius Caesar & his Roman army, in a pitched battle would result in a massacre of the Roman forces. First the Roman cavalry (Roman and Gallic cavalry can't really compare with Mongol ones) would be destroyed from a distance, then the encirclement of the Roman infantry would take place, consequent arrow shower, formation breaking in the Roman army and then the Mongol lancers move in for the final kill.
No cavalry Julius Caesar had or knew could do anything to the Mongol cavalry. The only cavalry which gets close to the Mongol army in terms of mobility is the Numidian cavalry, and even they have nowhere the range to hit the Mongol cavalry (They used javelins and not composite bows) if the Mongols are in retreat and still firing, nor do they have the ammunition for it. And since they lack the armor (They were less armored then Mongols), which means a pursuit while getting showered with arrows means having to spread out a lot to avoid quickly dieing. If you spread out too much and pursue too far, the Mongols turn-around and counter charge, which means that the Numidians in turn need to begin running away. This would be a nice exercise (As it would tire the Mongols) if the range between them was comparable (In this whole role reversal, only Numidians die) or if each Mongol didn't have several horses to switch to (Can even out the fatigue if they see the horse they are riding is getting tired). All other cavalry are either shock-based light or heavy armored, and frequently dealt with by Genghis Khan or his generals, as is documented.
So you believe that a Mongol army living 1 month off of blood and milk while accomplishing military objectives makes for poor work ethic?
And how does 23 miles of wall defend you against an highly decentralized army that covers hundreds of miles in a day?
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