R. Eliezer says: It is written here "And it was in the middle of the night," and elsewhere (Genesis 14:15) "And they 'divided' against them at night." Just as here the plague did not begin until the middle of the night, there, too, (their attack) occurred in the middle of the night.
When Abraham Pursued the Kings Who Had Captured His Nephew Lot
Mekhilta Tractate Pischa 13:3