Reading this lead to a lenghty discussion between my wife and I about the very nature of Wallball because we had very different definitions.
I grew up with Wallball being a game played with a rubber ball, similar to those used in playground games like Four Square. Two people played at a time and tried to get the other person "out" by either performing a shot werf's opponent couldn't return, or causing werf's opponent to make a mistake.
Mistakes included Pockets (ball hit exactly where the wall and the sidewalk meet), Rainbows (ball didn't bounce between when it was hit and when it reaches the wall), and Carries (similar to volleyball: you can't carry the ball, it has to be a solid hit).
My wife's version involved a tennis ball and a large group of people playing simultaneously. I don't remember the rest of what she said because 1. it's hard to describe some games if you aren't watching someone play them and 2. the details are always a bit foggy 20 years later.
At this point I must boast a bit and let you all know that in second grade I went through the entire line of kids waiting before I got out. That was probably the greatest day of my life.