Team Logo. The Binghamton Rumble Ponies are a team in the Eastern League. They are the AA affiliate of the New York Mets. Their name is a reference to the city's nickname of "carousel capital of the world." Retrieved from "https://prosportsteams.fandom.com/wiki/Binghamton_Rumble_Ponies?oldid=15365" Categories: Eastern League teams Teams in New York Add category Cancel Save Community content is available under CC-BY-SA unless otherwise noted.