Apopudobalia is a fictional sport, which was the subject of a famous fictitious entry (a mild or humorous hoax in a reference work). Although no such sport actually existed, the German-language Der neue Pauly Enzyklopaedie der Antike, edited by H. Cancik and H. Schneider, vol. 1 (Stuttgart, 1986, ISBN 3-476-01470-3) gives a description of it as an ancient Greco-Roman sport that anticipates modern soccer. The article goes on to cite suitably sparse documentation for the non-existent sport (this includes a Festschrift to one M. Sammer), and to assert that a Roman form of the game enjoyed a certain popularity amongst the Roman legions, and consequently spread throughout the Empire as far afield as Britain, "where the game enjoyed a revival in the 19th century." (It also notes that the game was frowned upon by some early Christian writers, such as Tertullian.)
In reality, the ancient Romans did play a game resembling rugby called harpastum.