COOPERSTOWN, N.Y. — You don’t become the subject of an exhibit at the Baseball Hall of Fame by being a catcher who never played a full season and finished with a career batting average of .243.

You need to have done something unusual.

That catcher, Moe Berg, was a spy (code-name: Remus) during World War II for the Office of Strategic Services, the forerunner of the CIA.

If a catcher’s role is to help the pitcher deceive hitters, then the astute, defensive-minded Berg found his trade in baseball. But in spying, he found a true home for his penchant for secrecy, wide-ranging intelligence, talent with languages, and ability to blend into his surroundings in a dark suit and dour expression.

Berg’s mysterious life was detailed in Nicholas Dawidoff’s book “The Catcher Was a Spy” (1994), which was adapted into a film with the same title, starring Paul Rudd, which was released last month.

And in late August, the Hall is expected to open “Moe Berg: Big League Spy,” an exhibition that offers a glimpse at the double life he led.

“We knew the movie was being made and before we even saw it we decided that we had the ability to tell a really interesting story about Moe,” said Tom Shieber, senior curator at the Hall. “And we had a really cool collection with which to tell that story.”

The Berg exhibit — which will be on display for about a year — is part of the Hall’s role as a museum dedicated to tracing the history and culture of baseball. With a vast trove of artifacts, equipment, images and ephemera, the Hall maintains a variety of permanent and temporary exhibitions that, for instance, describe the life and exploits of Babe Ruth and Hank Aaron and tell the story of African-American and Latino baseball.

Many of the Hall’s nearly 300,000 annual visitors are attracted to its gallery of bronze plaques that describe the achievements of all the inductees and know little about its vast collections. The Hall built the Berg exhibit largely from those collections, which included donations made in the 1970s by his sister Ethel and his brother Sam. But it also has props from the movie.

Berg’s baseball history is chronicled with artifacts like his catcher’s mask (with a hole positioned at the mouth for spitting), a bat (likely from his time with the Boston Red Sox), his official notice of release from the Washington Senators in 1934, and the letter from American League president Will Harridge asking him to play in the game that followed the first induction at the Hall on June 12, 1939.

Berg loved baseball — it probably appealed to his love of strategy — but he lived a buttoned-up, nomadic life, traveling when he pleased, and never establishing roots with a wife or children. Perfect for a spy.

“Moe Berg was a fascinating person,” Dawidoff wrote in an email, “a gifted man whose abilities shone in two difficult and widely divergent (if equally glamorous fields). He was an excellent baseball player especially before his knee injury, and an even better spy.”

Educated at Princeton in modern languages and at Columbia Law School, Berg traveled to Japan twice with other major league players in 1932 and ’34. His nearly pristine All Americans road uniform suggests he did not get much playing time on the latter trip.

While the Americans were romping over the Japanese in a game in Omiya, Berg went off to Tokyo on an audacious mission of his own: with a Bell and Howell camera he had hidden under his kimono, Dawidoff wrote, Berg shot film of the city’s shipyards, military installations and industrial complexes from the roof of a seven-story hospital.

After his playing days, he went to work in 1942 for the federal Office of Inter-American Affairs, an economic and propaganda agency that worked to promote cooperation between the United States and South and Central America. He would resign a year later and apply to the OSS. The exhibition displays a photocopy of his application in which he noted that his proficiency in French, Spanish and Portuguese is “fair” and his facility to speak Italian, German and Japanese was “slight.” He also detailed peripatetic trips to China, Burma, Iran, Syria, Egypt, Palestine, Germany, Crete and England; some of those stops are memorialized in a passport that is on display.

The exhibition uses photocopies of declassified documents from Berg’s years in espionage. In one partially redacted document, he demonstrates his knowledge of languages (“Folaga is the Italian name for the type of radar apparatus, corresponding to the Freya, made in Italy,” he wrote in a 1944 report) and applied physics (describing “diffraction of ultra-short waves on a hilly terrain”); in another, a telegram transcript, a decision was made by the OSS to send Berg and another agent to Sweden.

He showed his film of Tokyo to the OSS, but there is little evidence to show it was useful.

There is nothing in the exhibition on his most-celebrated assignment: a trip to Zurich for the OSS in December 1944, to attend a lecture by Werner Heisenberg, the brilliant German physicist who won the 1932 Nobel Prize. Berg, who brought a gun to the lecture, was to shoot Heisenberg if anything he said suggested that Germany was developing an atomic bomb. Berg came to believe on the secret trip that Heisenberg was not supervising a German counterpart to the Manhattan Project in the United States. He did not fire his gun.

But a faint echo of that mission is in the Hall’s files. In 1968, Berg received a holiday greeting card from Lt. General Leslie Groves, director of the Manhattan Project (which had worked closely with the OSS on plots to kidnap or kill Heisenberg).

“Why don’t you run for baseball’s top job?” Groves asked Berg, probably referring to the vacancy caused by the ouster of William Eckert as baseball commissioner in early December 1968. “I could give you a lot of advice on what ails the game today.”

Berg’s exploits were the subject of a letter nominating him for the Medal of Freedom by Howard Dix, an OSS colonel. Berg was awarded the medal, but he rejected it.

“I do so with due respect for the spirit with which it is offered,” he wrote in a letter shown in the exhibit. He was typically mysterious about not wanting the medal but instead asked for the return of his movies — including the one he took in Japan that had been exhibited to “several interested” agencies. But it was not of any military value after the Japanese attack on Pearl Harbor.

After his death in 1972, Ethel Berg accepted the medal on her brother’s behalf. Later, she gave it to the Hall of Fame.