Do they have a run in them?

That’s one of the two major questions surrounding the Yankees as they start the season’s second half Friday night at the Stadium.

Because if they don’t, the other question that has been swirling around the club for the better part of two months will dominate: Will they actually pull the plug on the season and be sellers before the Aug. 1 trade deadline?

“I think it’s really important,” manager Joe Girardi said of the 10-game homestand. “I don’t think it’s the end of the end, but I think it’s really important because of who we’re playing.”

The Yankees, who pulled into the All-Star break at 44-44, open the homestand against two of the teams ahead of them in the AL East. First up are the second-place Red Sox (49-38) for three over the weekend, followed by a four-game visit from the first-place Orioles (51-36), whom the Yankees trail by 7½ games. After that the NL West-leading Giants (57-33) come in for three.

A poor homestand could grease the skids for general manager Brian Cashman getting the green light from ownership, reluctant to this point, to trade marketable commodities such as relievers Aroldis Chapman and Andrew Miller and outfielder Carlos Beltran. Such moves could infuse the system with young, athletic talent.

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A homestand in which the Yankees build on what they accomplished in Cleveland just before the break — taking three of four from the AL Central-leading Indians — likely puts them in acquisition mode.

Not surprisingly, Yankees players want to keep the band together, hoping for a sustained spurt of quality baseball that didn’t occur in the first half.

“We know that we’re better as a whole than we’ve shown for most of the year,” third baseman Chase Headley said. “There’s a lot of professional hitters here that have done a lot of good things. So we’re just grinding, we’re keeping going and hopefully that needle’s going to turn and we’re going to really catch fire because we haven’t to this point, really, had that stretch that you expect. You go through the cold and usually you go through the hot, and we really haven’t had too much hot. So hopefully that’s coming.”

But the kind of extended hot streak Headley referenced typically happens only with good teams. And the Yankees did not show indications of having much more than an average team the first half and being capable of that kind of run.

“I just don’t see it,” an opposing team executive said before the break. “The lineup looks old, everyone knows that, but forget about that for now. That rotation . . . won’t allow them to really get it going.”

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Offensive inconsistencies aside, the rotation has been the club’s greatest disappointment. Throughout spring training the feeling around the club was the starting pitching would be a strength if it stayed healthy. It has stayed mostly healthy but has not produced. At the break three-fifths of the rotation have ERAs of 5.00-plus — Michael Pineda (5.38), Nathan Eovaldi (5.18) and Ivan Nova (5.18) — often making it difficult getting to the stellar big three of Dellin Betances, Miller and Chapman at the back end of the bullpen.

Masahiro Tanaka is 6-2 with a 3.23 ERA, but his numbers on regular four days’ rest (5.33) compared to five days (1.05) are concerning. CC Sabathia helped anchor the staff early and is 5-6 with a 3.77 ERA, but the lefty, who turns 36 July 21, is 0-2 with an 8.22 ERA in his last four starts.

And then there is the offense, which has struggled to score. The Yankees are 11th in the AL in runs (371), 13th in on-base percentage (.313) and 14th in slugging (.398) and OPS (.711).

They have a minus-34 run differential (405-371), so one could argue their record is actually better than it should be.

“We’ll have a message when we come back,” said Girardi, whose team plays 49 of its remaining 74 games in the division. “We have our work cut out for us, that’s the message. Be ready to go when we get back.”