Rays and Twins (4 +3 games) are both having good years, and the Rangers (4 games) are above .500, so this is a pretty good test. I think the Sox split with the Rays, take 1 of 3 at Minnesota, take 3 of 4 from the Rangers and 2 of 3 at Baltimore. That's 8-6, which probably won't make up much ground with the Yankees, but also shouldn't give up too much.
The lineup, despite all our complaints, isn't that bad and is 4th in MLB in runs and 5th in OPS. The rotation is pretty good with two--Sale and Price--capable of being very good to great.
The big question, especially with all these back to back games including a doubleheader tomorrow, is the bullpen. On another thread (or page on this thread) I said Barnes, Walden, Workman, Brasier, and Hembree--maybe our five best--are being paid a total of $5.5M. The Yankees pay their four best relievers about $40M, and the Cubs just handed Kimbrel a $42M contract for 3 years.