Agonalia (January)
The first Agonalia of the year appears on 9 January in the Fasti Praenestini.
Background
The Roman religious calendar was dotted with very old festivals whose meaning had faded even for the Romans. The Agonalia was one: it appears four times a year in the calendars (9 January, 17 March, 21 May and 11 December), and the January one belonged to Janus, god of doorways and beginnings, whose month it was.
On this day the rex sacrorum, the priest who inherited the religious duties of the old kings, sacrificed a ram in the Regia. Ovid spends lines wondering what "Agonalia" even meant, offering several explanations: from the priest's question "agone?" ("shall I strike?") before killing the victim, from the word for a sheep, or from games (agones) per Ovid, who admits nobody knew for sure. Varro also derived it from "agon", the priest's cue to strike per Varro.
That a festival could survive centuries after anyone remembered its origin says much about Roman religion: correct performance mattered more than belief or explanation. For most people in the city the day passed without much notice, a reminder that state cult was run by priests on behalf of everyone.