The statement that best evaluates why Constantine I converted to Christianity during his fight to gain control of the Roman Empire is:
Constantine thought he saw a cross in the sky the night before a big battle and believed this celestial clue helped him win the battle.
This event is often referred to as the Vision of the Cross, which allegedly occurred before the Battle of Milvian Bridge in 312 AD. It was a significant moment that influenced his conversion to Christianity and his subsequent support for the faith within the empire.