Back in Biblical times it was considered an act of God on casting lots - I think they picked the new apostle/desciple or whatever that way that replaced Judas. (Not having anything to do with the non-Biblical books of Mary or Nephi, just a comment.)
Another thing I have learned is that back in those times, healings and other miracles were much more common than today. It was not only Jesus that could heal people. (Of course he DID one-up the others with many of His miracles, like the casting out of demons and that Lazarus thing!)
I'd like to see the data that supports this.