REGIMES have often used sport to showcase their military and political might. Adolf Hitler did as much with the Berlin Olympics, and Vladimir Putin and the Sochi Olympics of 2014 provide another vivid example. The post-war Soviet government threw its weight behind the development of star athletes as a manifestation of power and superiority. "Red Army", a new documentary by Gabe Polsky, shows how ice-hockey became a big part of this propaganda machine. The film tells the story of the Soviet army's extraordinarily successful ice-hockey team, CSKA Moscow, and the Soviet national team that it fed. It is rare among sports documentaries in managing to unravel the stories of the sport, the team, its stars and its history to offer a new take on the rivalries of the Cold War.

Mr Polsky, the son of Ukrainian immigrants (and talented enough to play ice-hockey for Yale), makes good use of archival footage while ensuring the film keeps its sense of humour. Along with scenes of grand athletic pageantry, urgent political speeches and boys crawling across ice rinks, one clip shows a choir singing about the "Ice Brotherhood" and the fact that “Real men play hockey.”

The focus of the film's three arcs—the personal, the historical and the athletic—is Viacheslav Fetisov. One of the country's greatest players, he fought publicly with the authorities in the 1980s over his wish to play in the National Hockey League in North America. He eventually got there, then made an unlikely return to Russia in 2002 when Mr Putin invited him back to serve as Minister of Sport.

Mr Fetisov's ice-hockey story begins with the training he received from Anatloy Tarasov, who coached CSKA from 1947-1975. Widely considered the father of Russian ice-hockey, he studied chess and dance in his bid to find a competitive sporting edge, and his team's fluid style reflected these artistic influences. Between 1955 and 1989 CSKA won the Soviet League on all but six occasions, and between 1969 and 1990 only failed to win the European Cup twice. The team had pretty much the pick of all Soviet players, since men had to do military service, and the best ice-hockey players simply joined CSKA as they performed that service.

From the mid-1970s, CSKA and the national team made several trips to North America, usually to embarrass their opponents, with results including an 8-1 win against a Canadian team that included Wayne Gretzky, Guy Lefleur and Gilbert Perreault. The national team may have won a mere silver medal in the 1980 Olympics, behind the underdog Americans, but they were otherwise dominant through the 1980s.

The young stars did not travel unaccompanied. KGB agents joined them on every trip, making sure that none of the titillating materialism of the West lured their young compatriots away. A bright idealism did indeed seem to hold them together—Mr Fetisov reflects that he was never tempted to defect on those trips and proudly represented the Soviet Union.

Soviet politics did intrude, though, when Leonid Brezhnev himself replaced Tarasov with Viktor Tikhonov, a protégé of the head of the KGB. The film presents Tarasov and Tikhonov as polar opposites. The latter was authoritarian and abusive and isolated his players in training camp for 11 months a year. Mr Fetisov recounts how the players often discussed whether it would be worth losing the world championship so that the authorities would fire the coach and end their suffering. Tikhonov caused Mr Fetisov particular pain, publicly allowing him to leave to play in the NHL in 1988 and then privately reneging.

In the last days of the Soviet Union, the lure of Western cash proved too strong for both players and government alike. After the defection of Alexander Mogilny, who told international television audiences that he “lived like a homeless dog” in the Soviet Union, political pragmatism finally prevailed. In 1989 players were permitted to join the NHL, as long as they sent at least half their earnings to the Soviet government. Most were happy with the arrangement and promptly left, but Mr Fetisov's dispute was only settled when he was allowed to sign directly with the NHL, and special dispensation was made for some of his earnings to be used specifically to pay for hockey equipment, and not to replenish government coffers.

The story of the sport's development in the Soviet Union could easily have been lost under all the political and social details. To his credit, Mr Polsky has made the game as integral to the film as the Cold War and Mr Fetisov’s personal struggle. He resists straying towards a heavy-handed retelling of international rivalry and propaganda, and manages instead to weave together three related elements into a more complete and more compelling tale.