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matball

n. A sport resembling kickball, but with larger bases (often gym mats) that can be occupied by more than one player.

Wikipedia
Matball

Matball, known in some areas as Big Base, is a sport, usually played indoors but also sometimes outdoors, played in schools throughout the United States. Matball is a safe haven game (sometimes termed a bat-and-ball game, despite the lack of a bat) similar to kickball, but with the key difference that bases are larger, often gym mats (giving the names "matball" and "big base"), and multiple runners can be on each base.