The 13 steps, and the 13 loops in the noose are both from superstition,
but there is a good reason for the step number:
13 steps at a nominal 8" each give a height of 8'6".
This gives an acceptable, average drop distance for a cleanly broken neck and humane death.
It also leaves the body handing off the ground, but close enough to be easily removed,
allowing a low cart to be moved under the body and the corpse to be dropped into it.