@fluffy The conversion of the people within the Roman Empire is a combination of factors.

1. Hellenism, and the further attempts at cosmopolitanism, had the same effect on people as modern globalism. People's social ties and place within society was shattered, leaving them isolated and without meaning.
2. Paganism, or more specifically piety, was already on the decline. Numerous pagans lament that their people are simply going through the motions rather than actually believing in their gods. It became a superstition. Before they became Christians the stopped being pagan first.
3. Christianity is true.
4. Christians wanted it more. The zeal of Christians simply overpowered the Roman Empires ability to destroy it
5. Christianity appealed to all the deficiencies with paganism: lack of purpose, lack of truth, lack of coherent paradigm, lack of kin group, lack of real encounters with the divine