what agi does is it increase reaction time of the unit, or decrease the lag of motion. So the motion to pick up the gun and fire would be faster. More like a quick draw. For melee units, u can draw ur sword faster than ur enemy. Meaning u will get the first hit even though both u you press atk at the same time. Its more apparent for units that has stun beams. Both of you click stun beam at the same time, but the person with greater agility will fire first, leaving the other stunned. Works great with units with zero system and limit release, godly atk speed.
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Be awed by my prowess!
俺様の美技に酔いな!
別沉醉在本大爺絕妙的球技下!
-Keigo Atobe