Adapted by Robert Rodat from Nicholas Dawidoff’s book about baseball player Moe Berg’s second career as an OSS agent during World War II, Ben Lewin’s “The Catcher was a Spy” has a good deal in common with the game Berg played. It’s mostly slow-moving and frequently tedious, but marked by periodic outbursts of action. Too restrained and genteel to fully satisfy as an exciting real-life espionage tale, it’s also too speculative in its treatment of some major narrative elements to be entirely convincing. And yet the inherent interest of the tale—and of the man at its center—makes it a film one might want to check out, despite its flaws.

Berg is played by Paul Rudd, who holds his lighter side firmly in check as the admittedly unspectacular catcher whose career on the field was overshadowed by his formidable intellectual accomplishments: Berg was a linguist of note, holding an undergraduate degree in languages from Princeton as well as a law degree from Columbia. He appeared several times on the radio quiz show “Information, Please,” where he showed off his knowledge—something the film dramatizes in a brief scene.

The film begins, however, with a glimpse of a December, 1944 encounter Berg had in Zurich with Werner Heisenberg, the German physicist who headed the Nazi regime’s effort to build a nuclear bomb—a meeting that returns in longer form at the picture’s close as probably the most significant episode in his OSS career—before winding back to the catcher’s twilight years as a player. On a good-will trip to Japan with other players, Berg took the opportunity to slip onto the roof of a Tokyo hospital to film the harbor and navy yards—a show of enterprise that will later impress OSS Chief “Wild Bill” Donovan (Jeff Daniels, perhaps too mild for the role) when Berg applies for a spot with the newly-formed agency.

The focus then shifts to Berg’s post-baseball career with the OSS. After some frustrating months pushing papers in a desk job, he’s partnered with military man Robert Furman (Guy Pearce) and nervous scientist Samuel Goudsmith (Paul Giamatti) to make their way through war-torn Italy to meet with Edoardo Amaldi (Giancarlo Giannini), a friend of Heisenberg (Mark Strong), before proceeding to Zurich, where, with the help of physicist Paul Scherrer (Tom Wilkinson), he manages to meet the German himself in order to determine what his intentions about the bomb are are—and, if necessary, to deal with him summarily.

The picture does tinker with chronology at times, for example assigning the Japan trip to late in Berg’s on-field (career-closing) stint with the Boston Red Sox (1935-40), though it actually occurred earlier, in 1934, before he even joined that franchise. That’s irritating, but larger problems have to do with filling in blanks with speculation. Two examples stand out, one essentially gratuitous and the other dramatically necessary but nonetheless suspect.

The first has to do with Berg’s personal life. He was undoubtedly an unusual man, and some have suggested he was gay. The evidence for that is scanty, though, so Rodat has confected some. While allowing a note of ambiguity by depicting Berg’s relationship with a woman (Sienna Miller), he coyly indicates it was purely platonic. And he not only includes an episode in which Berg assaults a younger teammate who was trying to get dirt on him, but an extended sequence in which he enjoys a night with a Japanese man while in Tokyo. Topping it off, when asked on that quiz show whether he has a wife, Berg dodges the query, and when Donovan asks him directly if he’s “queer,” Berg merely replies that he can keep secrets. In short, while Berg was unquestionably a complicated man, the script is far blunter on the matter of his sexuality than the actual record supports.

Second, there is little direct evidence regarding Berg’s meeting with Heisenberg, beyond the fact that he allowed the physicist to go home unharmed, but Rodat and Lewin contrive to turn it into an elaborate cat-and-mouse dance, complete with skulking Gestapo agents, tart-tongued anti-Hitler dinner guests, an Allied gunman (Pierfrancesco Favino), and even a chess match played by the two men by memory alone. All of that is highly fictionalized, but it might nonetheless have made for a suspenseful denouement had Lewin staged it with any real energy. Instead the entire sequence simply meanders before coming to a flat close, and with it so does the movie.

It might also have helped if Rudd and Strong been able to bring genuine intensity to their face-off. But all that Rudd manages to invest Berg with throughout the film is a generalized smug imperturbability; it seems that in his determination to damp down his likability, Rudd turns Berg into a curiously bland fellow, which he definitely was not. The film boasts a strong supporting cast, but like the star they all seem unduly constrained by Lewin’s laid-back directorial approach and Mark Ypshikawa’s stately editing, which drain even the few action scenes of excitement. On the other hand, production designer Luciana Arrighi and costumer Joan Bergin have managed a strong sense of time and place on what was probably a quite limited budget, and cinematographer Andrij Parekh endows the images with an attractive burnished glow.

Moe Berg’s wartime service in the OSS is a fascinating subject. One wishes that “The Catcher Was a Spy” was more compelling, and accurate, in dramatizing it. Still, the story is undoubtedly an intriguing one, and that could justify giving the film a look.