When a crossbow bolt pierces a scotum and breaks the left arm of a legionaire, that legion has lost some of its combat power. Multiply that by thousands and you have a problem. I don't need to kill you to make less effective.
The only enemy that Rome ever faced that knew how to use a combined arms army was Hannibal. He only lost at Zama because Scipio manage to convince the Numidian Cavalry to change sides.
The Gauls, Macedonians, Greeks, and Germans were mainly infantry types.
Mark Anthony invaded Parthia with 100K troops and lost 1/3 that number without ever fighting the Parthians in a pitch battle. The main problem I have with the Roman army is they use a 1 size fits all approach to war, the heavy infantry. Don't get me wrong, the legion was very good. However, it took the Romans 400 years to figure out that what works against barbarian infantry does not work against cavalry base army of the Parthians and Sassanids.
Terrain is what did in the Persians against the Greeks.
Alexander was a special case. He was a genius and he commanded the Persian army, he would still have won.
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