Why did Christianity spread so fast in the Roman world?

it spread so fast because when the started to kill martyrs, or people willing to die for their beliefs, in the collesseum it just made more people belive in the life after death, chritianity.
then in 313 A.D just before a war the emporor, condenstine saw the roman words "chi" and "rho" and under that it said "by this sign you will conquer" he had all his men write it on their sheilds and they won the war!