On they came, one after another, making the walk from the bullpen to the pitcher’s mound. It was the first night of the American League playoffs, one year ago this week, and the Baltimore Orioles’ starting pitcher hadn’t lasted through the fifth inning. Six relief pitchers followed as a 2-2 stalemate with the Toronto Blue Jays stretched toward midnight. By the end, Buck Showalter, the Orioles’ manager, had put every available pitcher into the game except his best one: Zach Britton, the league’s leader in saves that season.

Britton is a closer, the pitcher charged with protecting a lead at the end of a game. Showalter had used him all season in the way that nearly every big-league manager deploys his closer, which is almost always to start the ninth inning and only with a lead of three runs or fewer, a situation in which a pitcher can earn a save. This was a one-game playoff between the A.L.’s two wild-card teams — a loss meant elimination. But Showalter didn’t change his tactics. In the bottom of the 11th, the Blue Jays broke the tie with a towering home run off one of Baltimore’s least reliable pitchers, a starter who rarely worked in relief. That the Orioles’ season ended without Britton’s ever entering the game struck baseball players, commentators and fans as inexplicable, bordering on absurd.

For years, analytically adept observers have been asking why a manager would limit one of his best pitchers to a couple of dozen pitches every two or three games, and no more than 70 innings a year. Top relievers should be used, they argue, as often as possible during those inflection points when the game’s outcome hangs in the balance. Managers have resisted. It isn’t always easy to identify an inflection point, for one thing. And giving your best reliever the lead with one inning to go is seen as the culmination of a plan. “He puts in a closer,” says Trevor Hoffman, who saved 601 games over an 18-year major-league career, “and basically says, ‘My work is done.’ ” Most closers, who are paid far better than other relievers, also aren’t keen to expand their duties. They’re baseball’s equivalent of fighter pilots. Giving up the chance to earn a save is a sacrifice that few are eager to make.

One afternoon this summer, I asked Dave Roberts, who manages the Los Angeles Dodgers, about Showalter’s decision not to use Britton. Roberts is preternaturally polite, yet he couldn’t help rolling his eyes. During his two seasons’ managing the Dodgers, he has come to believe that a team’s most effective relief pitcher should be used not just to finish games but whenever he can have a decisive influence on them. “You can make a strong, strong case to pitch your best reliever in a nonsave situation,” he said. “I’m moving toward that.”