During the roman peak in group size was a mix of large and small. Roman citizenship created a lrage in group though it was weaker than clan ties which is what enabled the civil wars. During this period most people were most loyal to families. But you didn't have to bear the name, you could be a client of a family and as such Rome was more a collection of Mafia style families trying to work together rather than one large group.

When Christianity came to Rome it provided an alternative in group for people to attach themselves too. Instead of thinking of themselves as a client of the Julie as being their most important attribute they might instead say they are a Christian. But unlike a Mafia family which only has so much benefit to spread throughout its clients and therefore a scaling issue. The Christians get their reward after death and as such it can scale infinity. Each new member benefits the group because the value they extract from the group is zero. Meanwhile a Mafia style family has a give and take relationship with all its members and as such each new member might be seen as a burden to the group and actually rejected by the group itself.