My informant recalled a chant from her time playing softball between 2nd and 5th grade. It was a tradition for the team to cheer and chant for their teammates as they came up to bat; she says this particular chant used to be a handgame as well and then crossed into cheering. Everyone knew the chants, but she says that most people dont even remember learning them–heard them once and then just knew it.
Down by the banks of the hanky panky
Where the bullfrogs jump from bank to bank-y
With the eeps, ops
Hey Mister lily paddy,
I’ve heard this rhyme as well, but in a different context. When I was in Girl Scouts from 1st to 4th grade, we would play a game called “Down By the Banks,” which involved hand slapping while singing this song. The last person to get their hand slapped was “out,” and the game was repeated over and over again until only two players were left. These two players would then clasp hands, sing the song, and pull their hands back and forth, and the person whose hand was extended when the song was over was the loser. I really like this song, and have a lot of fond memories; I remember learning it from another Girl Scout leader when I was really young. Also, I’ve heard many iterations of this song, mostly with the last line: instead of “Hey Mister Lily Paddy,” I’ve also heard “He missed a lily paddy,” which I personally think makes more sense.