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.