This is a set of wall brackets for a mini baseball bat. The kind you get as promos or buy at the ball park. The one in the photo is Pill Box brand but they all seem the same size to me. I used an anchor on the wall behind the screw but it probably overkill since mini bats are so lightweight.

Screws I used were just random one's I had lying around but the head measures a little less than 7mm and the body a little less than 4mm.