Cavalry archers did not dominate battlefields as chariots had in a similar role previously. Iron Age battlefields were dominated by infantries. The initial battlefield role for cavalry was to defeat the opposing cavalry and drive them away. This protected friendly infantry from harassment and freed the friendly cavalry to help destroy the enemy infantry by encircling them, shooting into their unprotected rear and flanks, and generally lowering their morale prior to the moment of infantry combat. If the enemy infantry panicked and fled, cavalry could pursue and run them down.
Assyrian reliefs show cavalry dispatching fleeing foot troops with lances.
The people of this region were noted horsemen and developed a tradition for using a lance from horseback. This was a difficult skill to master because the stirrup did not yet exist. The lance had to be released just prior to impact to prevent the horsemen from being pulled off his mount. The Macedonian army built by Philip and Alexander was unique for the last millennia of antiquity because its decisive arm was its cavalry. The Macedonians had not adopted the phalanx of their southern neighbors for their entire army because the terrain of their homeland was very broken and enemies to the north were mainly horsemen.