NEW YORK — “Are you a Jew?”

“Well, I’m Jew….ish.”

It’s a joke you’ve probably heard a hundred times before, but not delivered by Paul Rudd in the middle of a World War II spy thriller.

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One of the more jaunty and entertaining films that debuted at this year’s Sundance Film Festival was an adaptation of Nicholas Dawidoff’s successful 1994 biography, “The Catcher Was A Spy: The Mysterious Life of Moe Berg.”

The screenplay by Robert Rodat, whose credits include “Saving Private Ryan” and, surprisingly, “Thor: The Dark World,” is eager to juice the adventure aspects on a very curious life.

The movie takes some liberties — compressing some elements, leaving out some facts, teasing audience expectations a bit — but it’s all to the betterment of an enjoyable yarn. You exit the theater chewing on the mysterious Berg, thinking what Marlene Deitrich said about Orson Welles at the end of “Touch of Evil” — “he was some kind of a man.”

“The Catcher Was A Spy” never met a pre- or post-film card it didn’t like, so it opens by giving away what could have been teased out. As the United States raced to create the first atomic bomb, there was great worry that the Nazis would beat them to it. So they sent a former professional ball player to assassinate its lead scientist.

When we first meet Moe Berg in 1938, he’s already an outcast on his current team, the Boston Red Sox. He’s old, he isn’t the best player, but he’s all-seeing from his position calling the pitches as a catcher, and cocky when his instincts are proven correct.

He speaks a slew of languages, reads foreign newspapers, appears on radio quiz shows (and blows everyone away) but reveals nothing about himself. He doesn’t socialize with the rest of the team, and some think he may be a “left-handed batter,” code for a homosexual.

Later, we’ll see that even in this bigoted era, Berg prefers absolute privacy than defending himself against this charge. (As it happens, he lives with a woman without being married, an ignoble thing for this time period, but certainly “preferable” to the other claim.) There are implications that Berg’s self-perception as an outsider springs from his earliest days on a baseball team, the only Jew on a church-organized squad.

Berg joins baseball’s most notable figures, like Babe Ruth and Lou Gehrig, on a goodwill tour of Japan. His stats didn’t really merit it, but the Princeton graduate who later attended Columbia Law School and the Sorbonne had a reputation among sportswriters as being “the Professor.”

Japanese was one of the few languages his didn’t speak, but the wags thought he did, so he ended up on the trip. He brought a small movie camera with him and, seizing an opportunity, he shot footage of an air field from the roof of a hospital. He had a hunch this could come in handy down the line. (The movie fudges the years of this a little bit, but this isn’t a legal document, it’s a movie.)

When the war breaks out, he uses his old Princeton contacts to present this material to the OSS and look for patriotic work befitting a man of his intellect. Rudd plays Berg as obviously 10 steps smarter than everyone else, but among the Princeton alumni he’s a little bit unsure of himself.

There’s a fascinating moment when one of his friends apologizes if the choice of chorus songs make him uncomfortable (“it could be worse, it could be ‘Onward Christian Soldiers’”) but Berg shakes it off. Even when he’s ensconced in elite spaces, he is an outsider.

Despite that his OSS recruiter (played by Jeff Daniels) isn’t too keen to hire Jews or possible homosexuals, he can’t deny that Berg has the goods. He gets the job and, eventually, his big assignment.

The movie (directed by Australian-Jewish director Ben Lewin, whose other work varies to extremes in terms of quality) makes it seem like Berg was dispatched to Switzerland with a license to hunt and kill a Nazi scientist.

It’s both true and untrue. He was sent (in a roundabout fashion that involves Paul Giamatti racing through a hail of bullets in Italy, don’t ask) to ascertain just what was going up with the German bomb, and then, if the situation was truly dire, make a hard call.

Turns out his quarry wasn’t just any scientist. It was the elusive and inscrutable Werner Heisenberg, played by Mark Strong. Yes, this is the same Heisenberg from the Heisenberg Uncertainty Principal, which stated that the very act of observing quantum particles would alter them, therefore making their true nature unknowable. How about that for a perfect alignment of a man and his myth, huh?

“The Catcher Was A Spy” leans into this little storytelling crutch, especially in its second half, as Paul Rudd (looking very handsome in a suit and fedora) walks the rainswept streets of Zurich.

Though Berg is the very picture of an early 20th century Jewish scholar (with a little American Northeast schoolyard in him), there’s not much in the story here that reveals an inner Jewish life. There is a shot inside a synagogue toward the end, but it could just be because it looks dramatic. A dinner conversation arguing about Nazis being cruel to “the Poles, the Danes and especially the Jews,” hangs heavy in the room, but Berg has no specific reaction. He isn’t The Wandering Jew, he’s The Invisible Jew. Or, maybe, the Jew who wishes he were invisible.

Dawidoff’s book is 455 pages and, quite possibly, loaded with curiosities and strange, tangential stories. But for a movie you need discipline and direction, so the Heisenberg story steamrolls over most everything else. As such, I suspect a lot of the flavor of Moe Berg’s life is missing. But I’m glad that book is out there. This film leaves you itching to know more about this crafty, mercurial man — and that’s likely just the way Berg would want it. It’s as if he’s still calling the pitches from beyond the grave.