Yeah, it does depend on many factors, as Drewski observantly noted. For instance, fighting as the Romani in the Mesopotamia, Pahlava and Hai territories, I found that my numerous contingents of Pedites Extraordianrii were the most effective troops versus those dreaded cataphracts. Their AP swords, even with low lethality, chopped those Hai cataphracts as if they were Pantadapoi. I am not even exaggerating. Those catas lasted no longer than Pantadapoi. That is because their defence is almost solely based on armour, with only 8 defence skill I believe, and no shield. They are also mounted units, and mounted units always die faster for some reason than equivalent foot units.
But anyway, my Triarii would take either 40-70% casualties gainsay those cataphracts or even lose. Pedites Extraordianrii usually lost less than ten (large unit scale) and no more than fifteen. ALWAYS use AP infantry against heavily armoured units. AP is the single most powerful bonus in RTW. However, using PEs against low armour units is a waste, especially given the low lethality of their kopis (.11 - lower than the worst spears)
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