It seems that most people who read about these sticks fail to continue to
read how God, through an angel, told Jacob about how he really got all
those speckled, streaked and spotted goats:
"The angel of God said to me in the dream, 'Jacob.' I answered, 'Here I
am.' And he said, 'Look up and see that all the male goats mating with
the flock are streaked, speckled or spotted...'" Genesis 31:32
There was no miracle here. God explained simple breeding genetics to
Jacob. God told him that it wasn't the sticks that gave him the flocks
but normal breeding.
The only way it may be a miracle is that it was primarily the speckled,
streaked and spotted male goats that bread with the flock.