As the Boston Red Sox begin a four-game series against the New York Yankees this weekend, one that includes a Saturday doubleheader, they find themselves with a chance to leapfrog the Yankees for first-place in the American League Wild Card standings.At 73-60 coming off a 4-0 loss in Miami on Wednesday night, the Red Sox are 13 games over .500, just 2 1/2 back of New York for the top wild card spot. It’s been an unimaginable turnaround and a very different spot than the last time the Red Sox played New York two months ago.On June 25, the Red Sox arrived home around 6 a.m. after a severely delayed flight from Colorado with no off day ahead of a four-game series against the Yankees. The Red Sox were coming off one of their worst series of the season, losing two of three to the Rockies, and had very much reached their nadir, the likes of which the franchise hadn’t seen since the 2011-2012 debacle.They’d fired manager Alex Cora and six coaches in April and things hadn’t gotten much better under interim manager Chad Tracy in the ensuing two months. They owned the worst record in the American League when they walked off that plane and sat 14 games below .500 at 32-46, with FanGraphs projecting a meager 9.4 percent playoff odds.But starting that night against New York, their season began to change. Their pitching remained strong and the work the Red Sox had been putting in behind the scenes to find their rhythm at the plate took hold. Four games later, they had completed an improbable four-game sweep.“I think just beating a team four times in general is so hard,” outfielder Jarren Duran said. “We know how hard it is to win a three-game series, let alone beating a really good Yankee team four times. I think that’s something that we kind of leaned on.”That sweep set in motion the most dominant stretch in baseball for any team this season. After a fight-fueled series against the Washington Nationals, the Red Sox swept three straight series on the road entering the All-Star break and stretched their winning steak to 15 games after the break. It marked the longest in the majors this season. Even after the streak ended, the good play did not, as they followed it up shortly thereafter with another nine-game winning streak. Even after losing seven of nine games during an inevitable August swoon, the Red Sox have bounced back to win five of their last six games.Since the start of that last series against the Yankees, the Red Sox have gone a remarkable 41-14, vaulting themselves from 14 games below .500 to 13 games above .500.