One info I see nobody takes care - some archers had shield crushing arrows - short range, huge head. This is the reason partians executed romans at Carrahe - 1-2 of those heavy arrows will destroy even scuttum (I saw what replica of skythian bow with heavy arrow could do to replica of scuttum.)
HA's in EB are very powerful indeed and could exterminate most enemies if terrain isn't bad (forrest, enemy on 50 degrees slope) on they own, or with little help from heavy cav.
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