When the Yankees started playing “New York, New York” during the 1980 season, it resonated with New Yorkers even more than when Sinatra sang it at Radio City Music Hall two years earlier. New York was seeing its first glimmers of hope. In April, the city’s transit workers went on strike. New York’s feisty mayor, Ed Koch, would go to the Brooklyn Bridge and urge on the thousands of people who were walking into Manhattan to get to work. “He would say, ‘Go to work everybody,’ ” said Neil Barsky, the chairman of The Marshall Project, who directed the documentary “Koch.” “ ‘We’re not going to let those bums bring us to our knees.’ He rallied the city.”

Then there were the Yankees themselves, one of the few bright spots during those dark days. Steinbrenner was brash and volatile, outspoken and irascible; if Sinatra was the Chairman of the Board, Steinbrenner was the Boss. He had more than his share of detractors. But he was also willing to spend money like no owner before him, using free agency to build a great team. In 1977 and 1978, the Yankees, led by Reggie Jackson, Ron Guidry and Thurman Munson, won the World Series. They had another good year in 1980, going 103-59, only to lose to the Kansas City Royals in the American League Championship Series. “The Yankees provided great theater for New Yorkers in those days,” Barsky said. When the fans walked out of Yankee Stadium after another win, those lyrics ringing in their ears, they could finally feel optimistic about their city. All of New York was starting to feel it.

Another Voice Banished

At some point — nobody knows when — the Yankees’ music programmer started another tradition. The team would play the Sinatra recording when the team won, but the Minnelli version after a loss. Jonathan Schwartz realized this, and so did Paul McKibbins, Kander and Ebb’s musical administrator. (Ebb died in 2004.) One day, during a casual lunch, he happened to mention what he had noticed to a Yankees team lawyer. “The man turned white,” McKibbins said. Very quickly, the Minnelli version was banished, and the team played only Sinatra’s “New York, New York,” win or lose.

(Aside No. 3: McKibbins declined to tell me how much the songwriters make in royalties from the Yankees. He did say, however, that the tune “makes significant money for the guys.” The main competition for “New York, New York,” he added, is the Billy Joel song “New York State of Mind,” which the Mets used to play after every home game but stopped in 2008.)

In 1996, after the Yankees beat the Atlanta Braves to win the World Series for the first time in 18 years — it was Derek Jeter’s rookie season — the fans celebrated by singing “New York, New York” over and over again. Although Liza Minnelli sang the song at Shea Stadium after 9/11, and the New York City Marathon began playing it before the start of the race in Staten Island — also after 9/11 — the song’s association with the Yankees has never diminished. Appel recalled that on Sept. 21, 2008, after the last game at the old Stadium, “they must have played it 30 times; people didn’t want to leave.”

The tradition is unlikely to change anytime soon. “The song is an anthem to the city, and the hardworking people who live in it,” said Randy Levine, the president of the Yankees.

But let’s let Steinbrenner have the last word. In 2005, five years before his death, he was interviewed by Michael Kay for the YES Network. At one point, Kay asked him to name his favorite song.

“Anything Sinatra does,” Steinbrenner said. King of the hill. Top of the heap.