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 the commonly accepted historical account of Constantine's conversion, particularly his vision before the Battle of Milvian Bridge in 312 AD, where he reportedly saw a cross in the sky and interpreted it as a sign from God. This experience played a significant role in his decision to embrace Christianity and significantly influenced the future of the religion in the Roman Empire.