Collocations for decisive - adj.

be, prove

potentially
He had one potentially decisive factor in his favour/favor: the element of surprise.

ultimately (esp. BrE)
It is the chief executive's opinion which is ultimately decisive.

Decisive is used with these nouns:
action, advantage, battle, blow, defeat, edge, effect, element, evidence, factor, goal, impact, influence, intervention, majority, manner, moment, move, role, shift, step, try, turn, turning point, victory, vote, win