When those little white balls got old we would cut them in half, and use them to play a type of half-ball stick ball sometimes. (It was easy to pitch a "curve ball" with those half balls!)
Hose ball used small (maybe 4-inch or 5-inch sections) of those old, hard, rubber hoses, and an old broomstick (as in stick ball). Some guys could pitch with the hose flipping in end-over-end, and it was usually difficult to hit them that way very good, but if you hit a line drive, and a person caught it in their face, rather than in their hands, it would really hurt!
I grew up in Kensington. What was your neighborhood. And...Yes, I remember the pimple ball games.
This is my ‘era’, but they didn’t play this game in my neighborhood. I was curious, and found this: