They don’t make baseball players like Moe Berg anymore. Judging by Aviva Kempner’s authoritative and engrossing documentary “The Spy Behind Home Plate,” they likely never did.

Known as “the brainiest man in baseball,” Berg spoke numerous languages, studied at the Sorbonne and during his 15 years in the major leagues traveled with a suitcase full of newspapers, books and magazines. Berg had a law degree from Columbia, and, though not especially gregarious, an intriguing mixture of friends and acquaintances, including Ian Fleming, Albert Einstein and Chico Marx. He was, said sometime-roommate Dom DiMaggio, “a very complicated individual.”

And none of that touches on the most compelling part of Berg’s story: his tenure as a World War II spy for the OSS, precursor to the CIA.

Berg’s exploits have attracted media attention previously, including Nicholas Dawidoff’s nonfiction book “The Catcher Was A Spy” and last year’s dramatized version of the story starring Paul Rudd.

But Kempner, whose previous docs include another baseball subject, “The Life and Times of Hank Greenberg,” finds new ways to intrigue us.

First off, she personally interviewed anyone who might know anything about Berg, including veteran sportswriters Ira Berkow and Larry Merchant and former Major League Baseball Commissioner Bud Selig. Then she arranged for the use of interviews with some of Berg’s now-deceased former baseball teammates as well as the late CIA Director William Colby that were done by filmmakers Jerry Feldman and Neil Goldstein for a never-completed 1990s documentary.

Finally, Kempner and editor Barbara Ballow made adroit use of both stock footage and Hollywood spy movies such as the Alan Ladd-starring “O.S.S.” and Gary Cooper’s “Cloak and Dagger.”

Berg grew up in Newark, N.J., where, much to his father’s disgust, he took to baseball early. He ended up playing for five major league teams, including Brooklyn in the National League, and Chicago, Cleveland, Washington and Boston in the American.

Proving to have brains to match his brawn, he wrote an article for the Atlantic on the pitcher/catcher relationship in which he compared the catcher to “the Cerberus of baseball,” with eyes on everything. He also caused a sensation when he appeared on the radio quiz show “Information Please,” a newspaper headline noting that this “walking encyclopedia startles radio fans as he has Red Sox teammates.”

Most authorities agree that Berg likely engaged in espionage-type activities even before the war. When he accompanied players such as Babe Ruth and Lefty Grove on a goodwill tour of Japan in 1934, he donned a kimono (there are photos) and clandestinely filmed a panorama of the Tokyo skyline that might have aided Gen. James Doolittle on his famous raid years later.

Once Berg was recruited for the newly formed OSS, his most famous assignment was to track down German nuclear scientist Werner Heisenberg (whose son, Jochen, is interviewed on camera) to determine how far Germany had gotten in making an atomic bomb. He was given a green light to kill the man on the spot if he felt the danger was there. And he was issued a cyanide pill for his own use should the mission go bad.

We have to agree with sportswriter Merchant when he asks in genuine astonishment: “Has there ever been a professional athlete who had that kind of reach in his life? Can you make that up?” No, you can’t, and thanks go to filmmaker Kempner for putting all the pieces together in such a satisfying way.