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corkball

n. A game resembling baseball but with a smaller ball and without baserunning.

Wikipedia
Corkball

Corkball is a "mini- baseball" game featuring a ball, which is stitched and resembles a miniature baseball. The bat has a barrel that measures in diameter. Originally played on the streets and alleys of St. Louis, Missouri as early as 1890, today the game has leagues formed around the country as a result of St. Louis servicemen introducing the game to their buddies during World War II and the Korean War. It has many of the features of baseball, yet can be played in a very small area because there is no base-running.