The first pic made me think that it was what they called a lawn marble which was used in a game (not regular marbles) but seeing that it is just half there leads me to believe that it is definately for decoration of some sort.
I'd lean towards the carpet ball. I've seen examples made just like china marbles with lines and flowers on them but none in spongeware. Very interesting
I would lean towards the carpet ball that broke. It'd be hard for someone to accidentaly throw something like that away, but would make sense for them to throw it away if it were supposed to be a sphere but broke