To try and put a date on the introduction of Harpastum is hard but we can consider that the Romans conquered Greece in 146 BCE so it is fair to estimate that the Romans discovered the Greek versions of the games shortly after that date.

Harpastum was still a rugby style game (you could use your hands and feet) and was used by Julius Caesar and his generals as a form of military training to improve the physical fitness of the Roman Army.
Harpastum was known as the Small Ball Game. This is due to the fact that the other ball games played by Romans had much larger balls. The Harpastum ball was made from a stitched leather skin and stuffed with chopped sponges or animal fur. The ball was approximately 8 inches in diameter.

Little is known of the exact rules of the game but we do know that the pitch was rectangular and just a little smaller than an average sized football pitch today. The number of players varied from game to game - some reports suggest games with hundreds of players on each side.