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 the Milvian Bridge in 312 AD, where he reportedly saw a cross of light in the sky with the words "In this sign, you will conquer," which played a significant role in his decision to convert to Christianity and is often regarded as a pivotal moment in the establishment of Christianity within the Roman Empire.