Corkball is a "mini-baseball" or "bat-and-ball" game featuring a 1.6 oz. ball and bat with a barrel that measures just 1.5". Corkball is St. Louis' classic baseball game. Originally played on the streets and alleys of St. Louis in the early 1900s, 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.
It's important to note that corkball is not "stickball," as played up East and on the streets of many cities throughout the country. In the game of stickball you ran bases and it was similar to baseball with the exception it was played in and on the streets between curbs and sidewalks.
You will not find corkball in the dictionary, or encyclopedia, you won't find it under types of balls, either. It was a St. Louis creation and how it was established here and nowhere else is a puzzle to me. But it was a favorite among ball players in Dogtown. And I would like to add so was "bottle caps." A game played using the rules of cork ball but using bottle caps from soda and beer instead of a cork ball.