Step 2: Explanation, If You Care

Picture of Explanation, If You Care
This method works because over time the duct tape will slide around due to friction of your foot (on the top side) and the ground (bottom side). This is good.

On the bottom side, the excess stickiness of the duct tape around the edges will collect small pebbles and dirt making a tarlike gook. This tape/dirt amalgum is very good at filling in the hole and keeping it filled. Even after most of the tape has been eroded away, this amalgum stays and keeps the hole filled, it seems to be surprisingly resistant to erosion.

If you wrap the duct tape laterally around the flipflop (as I told you not to do), this shifting of the duct tape wil not happen as well and the amalgum will not form well. Also, because the duct tape cannot shift, it will not collect dirt on the sticky parts as easily and it will keep sticking to the back of your foot, which can get very annoying.

The sticking to the back of the foot doesn't really happen with my method (I've tried both).