No one could have blamed the Baltimore Orioles for the sense of hopelessness that must have washed over them during the first inning of Monday afternoon’s game against the Yankees. A familiar script was rolled out the moment Didi Gregorius’s three-run home run cleared the right field wall, and the tale didn’t change throughout a day-night doubleheader sweep: another unforgiving attack against Orioles pitchers, seven Yankees home runs (three by Gleyber Torres), two more victories in the Bronx for the home team, another pinstriped step forward in an unfettered path to October.

According to Fangraphs, the Yankees have a 99.9 percent chance of getting to the postseason and a 98.2 percent likelihood of winning the American League East. This year’s Yankees have the second-best record through 120 games of any Yankee team since 1962 (only the ’98 edition fared better). Monday’s sweep — an 8-5 victory over the Orioles in the first game, followed by a similar 11-8 battering in the nightcap — lifted the Yankees to a season-high 38 games over .500 and a remarkable 46-16 record within the division.

Unlike the many clubs engaged in fierce battles for division leads or wild-card berths, like the Mets, the Yankees have the luxury of coasting over the final six weeks if they so choose. But Manager Aaron Boone is still busy, mostly overseeing the various rehab schedules of his several injured players.

The prevailing sentiment in the clubhouse remains fierce and forward-directed.

“This club hasn’t won the division in a number of years. A lot of guys talk about that as motivation,” D.J. LeMahieu said, referring to the drought that began after the 2012 season. LeMahieu, a heavy-hitting infielder who was with the Colorado Rockies before signing with the Yankees as a free agent last winter, added: “I’ve been on teams that had to win every game down the stretch just to get to the playoffs. It’s exhausting. You get there and you have nothing left.”