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 statement refers to the well-documented event where Constantine reportedly had a vision of a cross before the Battle of Milvian Bridge in 312 AD, which he interpreted as a divine sign and a reason to support Christianity in his rule.