More than 70 years on, the summer Olympics of 1936 are popularly remembered for the exploits of the American track star Jesse Owens, and for the legend of Adolf Hitler’s refusal to shake Owens’s hand, which probably never happened. The best-known images of those long-ago German games are still those captured by Leni Riefenstahl in her epic documentary “Olympia,” which, while produced with lavish funding from Joseph Goebbels’s Nazi Propaganda Ministry, remains the most influential sports film ever made.

But another legacy of those games is less often traced to Hitler’s Berlin: The great symbol at the heart of the modern Olympics — that of a series of torch-bearing runners carrying the inspirational flame cross country to the stadium for the lighting ceremony — was an “invented tradition” of the Nazis in 1936. The torch relay was devised to draw the link Hitler saw between the Olympiad’s classical origins and its modern rebirth in the Aryan ideal.

Using 3,000 runners to cross seven countries “was but one of many ways in which the Nazi games helped define the modern Olympic experience as we know it today,” writes the American historian David Clay Large in “Nazi Games” (Norton, 416 pages, $27.95). The relay “turned into an advertisement for the new Germany across southeastern and central Europe, a region coveted by Nazi proponents of Lebenstraum (living space) — and eventually overrun by the Wehrmacht. The seemingly innocuous torch trek to Berlin from Olympia prefigured the naked aggression to come.”

Biographies of Hitler, Owens, and Riefenstahl have fully treated their subjects’ roles in the “Nazi Games” of 1936 (Germany also hosted that year’s Winter Olympics in the Bavarian towns of Garmisch-Partenkirchen). But this book is devoted to the large and small moments of the games themselves and their accompanying politics, especially the international boycott movement during the stormy run-up to the Olympics. Decades after Owens’s four gold medals in Berlin, Mr. Large does his best to re-create the full urgency of the boycott movement, which had two looming targets as Hitler’s regime worsened from the time he became chancellor in 1933: The coming Winter Games would showcase Bavarian culture within a particularly strong region of Nazi support, while the summer Olympics held in Berlin would be surrounded by newly commissioned monuments to Hitler’s power. By the fall of 1935, when the Nuremberg Laws stripped German Jews of many rights of citizenship, African-American newspapers were divided on the boycott issue. On the one hand, the presence of American Olympians would add to the legitimacy of Hitler’s racist regime. On the other hand, certain glory awaited the Americans, especially its magnificent squad of black track athletes. The Amsterdam News published an open letter to Jesse Owens and his Olympic teammates urging them to support a boycott. In congratulating Owens on public comments he’d made sympathetic to the boycott movement, the NAACP’s Walter White admitted a common ambivalence about keeping black Olympians home: “There have been times when I have felt that there might be a certain psychological value in having blond Nazis run ragged by yourself and others.” Indeed, although he wouldn’t have been able to legally compete against whites anywhere in the Jim Crow South in 1936, Owens ultimately decided there was some value in running Germans ragged on a world stage after all.

If viewed through the prism of appeasement and coming world calamity, then it remains a minor tragedy that the world couldn’t summon the will to boycott Hitler’s games, as Mr. Large implies in recounting the movement’s defeat, primarily at the hands of the American Olympic Committee’s President Avery Brundage, who is a deserving villain of the book. (And who, decades later as head of the International Olympic Committee, gave the infamous order that the 1972 Munich Games “must go on” despite their interruption by terrorist bloodshed).

If, however, you view the Nazi games as a menacing backdrop for Jesse Owens’s assault on Aryan bigotry, then Brundage’s ignoble role becomes more complex. As Jeremy Schaap puts it in his fluent, compact retelling of the Owens story, “Triumph: The Untold Story of Jesse Owens and Hitler’s Olympics,” “If not for Brundage’s pigheadedness, cunning, Germanophilia, anti-Semitism, and deep-rooted bigotry, Jesse Owens would never have become an Olympian.”

By the time the Winter Games arrived in Garmisch-Partenkirchen, the ugliest public displays of Nazism had been toned down for the sensibilities of the foreign press. But the ski-town streets were thuggishly policed by Blackshirts whose tactics made no friend of the Chicago Daily News columnist Westbrook Pegler: “It was a magnificent display of strong-arm authority wholly corroborating the old tradition that the German people’s favorite sport is to be shoved around by men in uniform.”

Mr. Large’s narrative is often weighted down with bland, faithful summaries of each day’s events, which doesn’t make for vivid storytelling. (As if to dramatize a suspicion of slick writerly techniques, the most famous witness to the Berlin games, the director Leni Riefenstahl, doesn’t make her big appearance in the narrative until all the races are run, some 300 pages in, as if her editing Olympic footage were more interesting than the two weeks her crew had just spent in the thick of its drama.) There are no such lapses in Mr. Schaap’s well-wrought telling of the Jesse Owens story in “Triumph” (Houghton Mifflin, 288 pages, $24). While hardly “untold” (Owens has previous biographers, including his own trio of memoirs), Mr. Schaap does present Hitler’s games memorably, if at a compressed length.

But what of the lasting political value of running “blond Nazis ragged” before the world? Although Paul Gallico and others reported Hitler giving a kind of seated salute as Owens left the stadium in triumph after the 100 meters, much of the African-American press deplored a perceived “snub” of black athletes by the Führer. Since this is the way many people have come to remember the Berlin games, imagining an enraged Hitler storming from the stadium, it would seem that a boycott would have deprived the world of a small but much-needed victory in a frightening time. “As events have turned out,” wrote Westbrook Pegler from Berlin, “it would have been a great mistake for the Americans to withdraw … for they have had the luck to figure in certain incidents which have redounded to the honor of democracy and the shame of the dictatorial concept of sport.”

Mr. Ward last wrote for these pages on A.J. Liebling.