This wear pattern is formed by spinning while some rough object touches the disk. Are you spinning them a lot in the cases with your fingers - absentmindedly? If not, it's for sure the player.
In the book "Off To See The Wizard" by Scott Meyer, the wizards are time travelling hackers. One of them has a glowing blue orb in his study that turns out to be the display of his Commodore 64 computer.