Googling for Sockball, I clicked my way to
this illustration, subtitled "sockball of death." Apparently, this was one of the games played at a church-sponsored "mini-olympics."

No details about actual gameplay were included. Suggestions and speculations are most welcome. I'm thinking maybe you have to hit other players with your sockball. Probably if you get hit, you're frozen or out. I'm also thinking that this is not a game for the stiff-necked many. My informant cautioned me that this can take a lot longer than you'd think.
Turns out that the object of the game is to try to tangle your Sockball of Death with someone else's so as, with appropriate head snap, to remove your opponent's Sockball clear off his head.
Needless to say, this game could prove to be one giant step forward for used pantyhose.