My informant played a game similar to what is now known today as Wallball. His version of the game was called Ledgeball due to the ledge against which it was played. Ledgeball does not have the same free-for-all nature that Wallball does, and is played for points instead of for staying power. However, it still involves throwing a ball against a flat surface and catching it.
According to my informant, the game was played by a group of throwers and one or two defenders. Throwers would take turns throwing the ball against the ledge and trying to get it to land inside a marked area. The defenders would attempt to catch the ball before it hit the ground. If it hit the ground the throwers got a point. If the defenders caught it or if it landed outside the marked area, then the defenders got a point. One of the strategies that throwers could use was aiming very low on the ledge, so that the ball would only go a little bit before hitting the ground. Another strategy was to throw it so that it would bounce over the heads of the defenders. People who frequently defended would get really fast and develop good reflexes. Ledgeball was played with either a tennis ball or a rubber playground ball, with tennis balls being preferred.
While this is markedly different from the Wallball that I played in my youth, this has many of the same traits. Players throw a ball against a wall, other players attempt to catch it. And most importantly it is played with either a tennis ball or a playground ball, both of which are still used in Wallball today. Granted, this version of Wallball was played back in the 30’s so it will understandably be very different from what we know today, although it could be an ancestor or cousin of modern Wallball.