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 reflects a widely reported event known as the "Vision of the Cross," where Constantine purportedly had a vision or dream of a cross with the words "In this sign, conquer" before the Battle of Milvian Bridge in 312 AD, which significantly influenced his decision to adopt Christianity and support the religion within the empire.