All you Sandy Koufaxes, get out there!

Near the movie’s beginning, the Housman family is unloading its baggage from their car at the Kellerman resort. In the background, a loudspeaker is announcing the day’s activities.

Ping-Pong in the west arcade. 

Softball in the east diamond. All you Sandy Koufaxes, get out there! 

Complimentary dance lessons in the gazebo.

Sandy Koufax was a professional baseball player, a pitcher, who was Jewish. Since practically all the guests at the Kellerman resort were Jewish, the name Sandy Koufax in the announcement would resonate very positively among the guests, especially among those who would chose softball for their activity.

Sandy Koufax preparing to throw a pitch.

The Wikipedia article about Koufax describes his youth as follows:

Koufax was born in Brooklyn, New York, to a Jewish family, and raised in Borough Park. His parents, Evelyn (née Lichtenstein) and Jack Braun, divorced when he was three years old. His mother was remarried when he was nine, to Irving Koufax. ... 

Koufax attended Brooklyn's Lafayette High School, where he was better known for basketball than for baseball. At the time, school sports were not available because New York's teachers were refusing to supervise extracurricular activities without monetary compensation. As an alternative, Koufax started playing basketball for the Edith and Carl Marks Jewish Community House of Bensonhurst local community center team. 

Eventually, Lafayette had a basketball team; Koufax became team captain in his senior year, and ranked second in his division in scoring, with 165 points in 10 games.... 

Koufax attended the University of Cincinnati and was a walk-on on the freshman basketball team, a complete unknown to coach Ed Jucker. He later earned a partial scholarship. .... 

Koufax was hired by the Brooklyn Dodgers in 1955. (The team moved to Los Angeles in 1958.) He achieved little success, however, through the 1950s. The Wikipedia article:

In early 1960, Koufax asked Dodgers GM Buzzie Bavasi to trade him because he wasn't getting enough playing time. By the end of 1960, after going 8–13, Koufax was thinking about quitting baseball to devote himself to an electronics business that he'd invested in. After the last game of the season, he threw his gloves and spikes into the trash. Nobe Kawano, the clubhouse supervisor, retrieved the equipment to return to Koufax the following year (or to somebody else if Koufax did not return to play). 

Koufax tried one more year of baseball and showed up for the 1961 season in better condition than he had in previous years. .... It was the beginning of Koufax's breakout season. Posting an 18–13 record for the Dodgers in 1961, Koufax led the league with 269 strikeouts .... Koufax was selected as an All-Star for the first time and made two All-Star Game appearances ....  

On June 30 [1962] against the expansion New York Mets, Koufax threw his first no-hitter. In the first inning of that game, Koufax struck out three batters on nine pitches to become the sixth National League pitcher and the 11th pitcher in Major League history to accomplish a nine-pitch/three-strikeout half-inning. With the no-hitter, a 4-2 record, 73 strikeouts, and a 1.23 ERA for June, he was named Player of the Month ....

During the months immediately preceding the Dirty Dancing story -- the story took place from August 10 through September 2, 1963 -- Koufax was leading the Dodgers team to win the National League's pennant, which would place the team into the World Series. The Wikipedia article:

On May 11 [1963], Koufax no-hit the San Francisco Giants 8-0 ... Koufax carried a perfect game into the eighth inning against the powerful Giants lineup .... As the Dodgers won the pennant, Koufax won the pitchers' Triple Crown, leading the league in wins (25), strikeouts (306) and ERA (1.88). Koufax threw 11 shutouts, setting a new record for shutouts by a left-handed pitcher that stands to this day .... Koufax won the NL MVP [National League Most Valuable Player]  Award and the Hickok Belt, and was the first-ever unanimous selection for the Cy Young Award [for year's baseball pitcher].

The Sandy Koufax baseball card
for the 1963 season, during which
the Dirty Dancing story took place.

In early October, a month after the Dirty Dancing story, the 1963 World Series was played, and Koufax earned the Series award for Most Valuable Player. Wikipedia:

Facing the Yankees in the 1963 World Series, Koufax beat [Yankee pitcher] Whitey Ford 5–2 in Game 1 and struck out 15 batters-including the first 5, breaking Carl Erskine's decade-old record of 14. ... In Game 4, Koufax completed the Dodgers' series sweep with a 2–1 victory over Ford, clinching the Series MVP Award for his performance.

By the summer of 1963, Koufax also had appeared in several acting roles on television. Wikipedia:

Koufax appeared on television from 1959 through 1962. 

He was cast as Ben Cassidy in the 1959 episode "Too Smart to Live" of the syndicated western series Shotgun Slade, starring Scott Brady. In 1960, he played the role of "Johnny" in the episode Impasse of the ABC/Warner Brothers western series Colt .45, with Donald May as Sam Colt, Jr. He made minor appearances in two other ABC/WB productions, 77 Sunset Strip and Bourbon Street Beat. 

Koufax also appeared as himself along with several Dodger teammates in an episode of Mister Ed entitled "Leo Durocher Meets Mister Ed" in September 1963.

Koufax portrayed himself on CBS's Dennis the Menace in the 1962 episode "Dennis and the Dodger". He also appeared as himself on NBC's detective series, Michael Shayne in the 1961 episode entitled "Strike Out".

In 1965, two years after the Dirt Dancing story took place, Koufax supplemented his fame among Jews by declining to play in a World Series baseball game because it took place on the Jewish major holiday Yom Kippur. Social commentator Steve Sailer tells the story:

Koufax had been scheduled to pitch the first, fourth, and (if needed) seventh games against the Twins, allowing him the then-usual three days’ rest between starts. But he asked fellow Hall of Fame pitcher Don Drysdale to take his place in Game 1 because it fell on Yom Kippur. 

Koufax was a worldly man (he owned the Tropicana Motel in West Hollywood, the center of the rock & roll business, where Jim Morrison of the Doors lived for three years), but honoring his religion struck him as the right thing to do. Koufax, never an articulate speaker, didn’t much explain his decision, but his taciturnity was appealing in its cowboy-movie “A man’s gotta do what a man’s gotta do” fatalism. 

Drysdale, unfortunately, was shelled. He joked to manager Walt Alston, who came to take him out in the third inning, “I bet right now you wish I was Jewish, too.” Then Koufax lost the second game, putting the Dodgers in a deep hole. 

Los Angeles rallied, however, with Claude Osteen, Drysdale, and Koufax winning the next three. When Osteen lost the sixth game, however, Alston had to choose between Drysdale on three days’ rest and Koufax on two. 

He called on Koufax. Sandy found his arm too tired to throw his ferocious curveball, but managed to rely on his famous sailing fastball for a three-hitter to win 2–0. It was the ultimate display of Koufax’s strength-against-strength style, with his disdain for guile. 

Admittedly, if Jim Gilliam hadn’t made a great defensive play in the fifth inning, Koufax might have lost the seventh game, and a hundred thousand bar mitzvah speeches would have needed a different illustration. But there was nothing foreordained about Koufax’s ultimate triumph, which only made his taking the risk more heroic.

Sailer elaborates on Koufax's ethnic popularity as a Jew:

Another part of Koufax’s appeal to Jews has been his intensely Jewish good looks. A half decade ago, I went to see a documentary movie about Wall Street at an Encino art-house cinema with a mostly Jewish audience. A trailer was shown for a documentary called Jews and Baseball: An American Love Story. When Koufax, then in his mid-70s but wearing a great suit and looking as dapper as ever, appeared on screen for an interview, the middle-aged Jewish ladies in the crowd gasped in delight. ... 

One reason the New York-born Koufax was so renowned was that he and his Los Angeles-born teammate [Don] Drysdale epitomized the golden age of the Golden State. .... The Brooklyn Dodgers had moved to Los Angeles in 1958, the central event in a long cultural war among Jews in the media industries over whether to stay back east or to head west (a conflict amusingly articulated in Woody Allen’s Annie Hall). The entertainment businesses, such as music, tended to go, while the news media stayed. The 1963 World Series, in which the Los Angeles Dodgers, behind the 25–5 Koufax, swept the long-dominant New York Yankees, was seen as a passing of the torch. 

In Los Angeles, Koufax and Drysdale became baseball’s Paul Newman and Robert Redford. (Indeed, Drysdale and Redford had been classmates at Van Nuys H.S.) The two Dodger pitchers, the Jew from New York and the gentile from Los Angeles, made a nice pair, symbolic of American pluralism. 

Fans liked that Koufax and Drysdale were friends and held out together in spring 1966, forming their own cartel against Dodgers owner Walter O’Malley. The two signed movie contracts with Paramount to give credence to their threat to sit out a year during this era when owners held all the cards. Drysdale and Koufax even agreed to appear on the TV variety show Hollywood Palace: 

“Don is expected to sing with his own guitar accompaniment,” a show spokesman told The Times. “Koufax will concentrate on humor.” .... 

Even though Koufax’s background was stereotypically Jewish-American (he was Brooklyn-born and Long Island-raised), he was also movie-star glamorous in a not typically Jewish manner: tall, handsome, athletic, strong and silent, like John Wayne or Gary Cooper.
He triumphed through physical superiority, courage, and suffering rather than through being brighter than his opponents. .... 

Sailer's separate blog article about Koufax is followed by a very amusing series of comments.

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I was attending a Lutheran parochial school in 1965, when Koufax declined to play the World Series game because of Yom Kippur. Our teachers praised Koufax for placing his religious holiday higher in his priorities than the World Series game.