I didn't know what this curious ball was when I found it, but have learned that sometimes when the leather skin came off a softball, people would wrap the center in black cloth tape like this. To me it's like a more visceral version of a rag ball, wounded and wound, looking almost as if coated in tar and with the salvaged core peeking out here and there. Quite an evocative thing I think.
Approx 3" in diameter and tightly wrapped.