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 historical accounts of Constantine's vision before the Battle of Milvian Bridge in 312 AD, which played a significant role in his decision to convert to Christianity. It highlights the connection between his military success and his newfound faith.