Toronto Blue Jays slugger José Bautista’s defiant gesture during the seventh inning of Game 5 of the American League Division Series was one of 2015’s most memorable moments in sports. Photograph by Tom Szczerbowski / Getty

An average American football game takes about three and a half hours, but after you cut out all the referee huddles, official reviews, timeouts, injury stoppages, commercials, booth chatter, and endless shots of players standing around waiting for something to happen, you're left with just about eleven minutes of actual gameplay.

The same principle applies to any given year in American sports. More than half a million minutes filled end-to-end with news, analysis, commentary, and debate—with a few feats of stunning physical agility or memorable narrative drama mixed in to keep things just on the right side of interesting. In 2015, there was plenty that we would have preferred to skip, or, now, looking back, to forget: the days given over to Deflategate, the endless daily-fantasy commercials, the particulars of the latest multimillion-dollar contract, and who said what about whom on Twitter. As such, here is the year in sports, whittled down like a D.V.R.’d football game, to the eleven most compelling minutes.

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Forty-eight seconds: The amount of clock time in the fourth quarter of Super Bowl XLIX during which the Seattle Seahawks appeared to have beaten the New England Patriots thanks to a miraculous catch by Jermaine Kearse—only to have the game stolen away a few plays later on a stunning goal-line interception by the Patriots rookie Malcolm Butler. The responses on either sideline told the story: the New England quarterback Tom Brady jumping up and down like a little boy, whooping, as Seattle’s head coach, Pete Carroll, shouted, simply, "Oh no!" before absently dropping his headset to the ground.

One second: How long it took for Riley Curry, the then-two-year-old daughter of the Golden State Warriors star Steph Curry, to earn the title of cutest child in America, after telling her father to "be quiet" while at the podium for a postgame press conference at the Western Conference Finals. Her father's Warriors would go on to beat the Cleveland Cavaliers in the N.B.A. Finals, and Steph would emerge as the best player in the league, shooting with devastating efficiency and seemingly in scoring range anywhere across half court.

Two minutes, seventeen seconds: The amount of time at the beginning of Game 4 of the Finals during which it seemed that, somehow, with his best teammates injured and out of the series, LeBron James might single-handedly win an N.B.A. championship. James had led the Cavaliers to a surprising 2-1 series lead, averaging 39.5 points and playing nearly every minute in the two wins; as the Cavs rushed to a 7-0 lead to start Game 4, it appeared as though the young Warriors might be on the other side of a remarkable upset. Instead, they pulled even, won three straight games, and demonstrated why a well-composed team almost always beats a single opponent, however herculean.

Three seconds: The combined time by which the racehorse American Pharoah won the Kentucky Derby, Preakness Stakes, and Belmont Stakes, becoming the first horse in thirty-seven years to complete the Triple Crown. American Pharoah won narrowly at the Derby, and then going away in the slop at the Preakness, and, three weeks later, in bright sunshine at Belmont. If the whole thing felt a bit anticlimactic, after such a long wait, that is due more to the diminishment of horseracing in American sports culture than to any particular deficiency in the horse. And even skeptics had to be won over by the rousing call by the track announcer Larry Collmus, who bellowed, in the stretch run, "American Pharoah is finally the one."

Two minutes, twenty-five seconds: The length of the ovation that Novak Djokovic received at the French Open, following a losing effort in the final to Stan Wawrinka. Djokovic had what Gerald Marzorati argues was the greatest season of any athlete in 2015, winning three major titles and an astounding eighty-two of eighty-eight matches. His principal blemish, however, came at the French, where he was beaten in four sets by an opponent playing what everyone agreed was once-in-a-lifetime tennis. Yet, after the match, the crowd swelled in support of Djokovic, who, as the cheers lingered, was moved to tears. Djokovic has never won a title at the French Open, which remains the missing piece of a career Grand Slam, and his quest for a win there next summer will be one of the bigger sports stories of 2016.

Two minutes, twenty seconds: The time it took the for the U.S. midfielder Carli Lloyd to score twice, in the third and fifth minutes of the World Cup Final match against Japan. After her third goal of the game, in the fifteenth minute, which she struck all the way back at midfield and sent floating just over the out-of-position goalkeeper's head, the rout was on—the United States women's national team won its first Cup in sixteen years, and reminded the world that, when it comes to women's soccer, the sport is still America's game.

Two seconds: The time it took Boston Mayor Marty Walsh, on July 27th, to utter the phrase "about ten people on Twitter," referring to those whom he imagined to be the critics of the city's bid to host the 2024 Olympic Games. An immediate and widespread outcry on Twitter and other social-media platforms revealed that the Mayor had underestimated the local opposition, and that same day, citing onerous demands from the International Olympic Committee, the city dropped its plans to submit a bid. Boston's failed bidding process demonstrated the mounting skepticism from people around the world of the financial benefits promised by the Olympic movement, and was a victory for Web-based social activism. But, for some, the allure remains: Los Angeles stepped in quickly to replace Boston as the United States' bid for 2024.

Five seconds: The length of the apology offered by the Italian tennis player Roberta Vinci to the crowd at Flushing Meadows, in New York, following her world-shocking defeat of Serena Williams in the semifinals of the U.S. Open. The light-hitting, unheralded Vinci came from behind to derail Williams's summer-long march toward history, and felt compelled to soften the blow for the crowd, saying, "Sorry guys, sorry." No such demurral was necessary; Vinci's gutsy performance had already charmed the crowd, which laughed and cheered as she declared the victory the best moment of her life.

Three seconds: How long the Toronto Blue Jays slugger José Bautista spent admiring his go-ahead three-run home run and then flipping (or, to be more precise, heaving) his bat during the seventh inning of Game 5 of the American League Division Series against the Texas Rangers. That exultant, defiant gesture was the most memorable of a string of wild moments during an inning that also included an odd error by Toronto’s catcher, made while tossing the ball back to the pitcher; a prolonged deliberation from the umpires over an arcane rule that awarded a run to the Rangers, followed by a revolt from the home crowd; and then, in the bottom of the inning, three consecutive errors by the Rangers, Bautista's home run, and an argument among the players that caused both benches to clear while excited fans threw debris field-ward. In all, the inning was nearly an hour of baseball madness, but the bat flip, a contentious international phenomenon that delights many and horrifies a few, was its signature moment.