SARATOGA SPRINGS, N.Y. — At Christmas, horses in this historic racing city take a back seat to another celebrated creature, its legs designed to be somewhat fragile and far stubbier.

And pink.

The Peppermint Pig, a local hard-candy confection about the size of a pig’s foot, has become an unusual holiday tradition around the world — its popularity rooted in peppermint and a nickel-plated hammer. As the candy pig is passed around the dinner table, each person uses the hammer to break a piece off, and then shares a bit of good fortune from the year just passed, with hopes of good luck and prosperity for the new year ahead.

The pig dates to the 1880s, when Saratoga Springs was a thriving resort town with two of the world’s largest hotels and lively casinos. It is believed that chefs from Europe who came to work at the hotels influenced Jim Mangay, the originator of the pigs, to make something that approximated marzipan candy. But marzipan was not readily available, so Mr. Mangay adapted, using peppermint oil from his father’s apothecary.