Since when do Moshe's hands make or break war?
Rashi (citing the Mishnah in Rosh ha'Shanah (29a): It was when Moshe raised his hands that the people raised their eyes heavenwards and rendered their hearts subservient to Hashem. That was when they were victorious in battle, and when he dropped his hands ... .
Rashbam: Moshe hand refers to the staff that he was holding; and it is human nature that when the army see their emblem raised, they fight harder and enter into a winning streak.
Targum Yonasan: When Moshe raised his hands in prayer, Yisrael were winning, and when he lowered them and stopped praying, then Amalek were winning.