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 account of Constantine's vision before the Battle of Milvian Bridge in 312 AD, where he reportedly saw a cross in the sky with the words "In this sign, conquer." This event is often cited as a pivotal moment that influenced his conversion to Christianity and his subsequent support for the faith.