From what I recall, "Stickball" was played in the back alleys of cities such as Chicago and New York due to the unavailability of baseball playgrounds.......
As a side note, while I was raised in northern Michigan, I spent the summers of the 1950's with my grand parents in Detroit.
At that time, my grandfather was a Detroit police officer and on his bedroom cabinet he had a baseball signed by all the Detroit Tigers in a plastic case. Well, me and my buddies needed a baseball so I took that baseball out to the park and we played with it. My grandfather never said a word but in retrospect, he should have whipped my butt.......
Usually it involved just two guys, a hitter and a pitcher. If a ball got past the pitcher, it was a single. Against the school fence, a double or a triple. Over the fence, homer. No running involved.