CINCINNATI -- Around the same time Robert Stock was walking off the Great American Ball Park mound with a right hamstring injury on Tuesday, Carlos Carrasco was wrapping up his own abbreviated five-run outing for Triple-A Syracuse. Earlier in the day, Noah Syndergaard threw off flat ground, though he’s more than a month away from a return. As for Jacob deGrom, who knows? Mets officials say his right forearm injury is minor, but he hasn’t thrown a baseball since it happened.

Such is the state of the Mets’ rotation, which has become so ragged that the team has called up four pitchers in the last two days alone. One of them was Stock, who injured his hamstring about an hour after the Mets promoted him from Triple-A Syracuse. The Mets spent the rest of the night simply trying to survive what became a 4-3 loss to the Reds.

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And so New York continues to find itself in an unenviable position, despite living in first place for more than 10 consecutive weeks. With deGrom, Carrasco, Syndergaard, David Peterson, Joey Lucchesi and others all sidelined, the Mets are relying regularly on the Stocks and Jerad Eickhoffs of the world. And while they’ve mustered more than their share of wins in spite of that quandary, their injuries are piling up at such a significant rate -- they’ve now placed 28 players on the IL, with Stock perhaps about to become the 29th -- that their current rate of success seems all but unsustainable.

Fortunately for the Mets, help is almost certainly on the way. Earlier Tuesday, general manager Zack Scott reiterated on the “Big Time Baseball” podcast that starting pitching “is our top priority” and “has been for a while.” In other words, the Mets will add an arm by July 30, full stop.

“I always say I do subscribe to that old adage that you can never have enough pitching,” Scott said. “I do think in the seasons, in my experience, that have fallen apart, that’s been the main reason why they have fallen apart.”

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But the Mets haven’t acquired that starter yet. Until they do, they face issues in the short-, medium- and long-term future.

Short term

Simply put, it’s not going to be easy for the Mets to get through the next week. Although the team can roll out starters Marcus Stroman, Tylor Megill and Taijuan Walker from Wednesday through Saturday, it doesn’t have anyone lined up for Sunday against the Blue Jays or Game 2 of Monday’s doubleheader against the Braves.

Carrasco had been a candidate to make his season debut in one of those games, and perhaps he still is. But the Mets can’t feel wholly comfortable using him after he allowed three home runs in his second rehab start, stretching out to only 41 pitches.

As for other options, the Mets on Tuesday designated Eickhoff for assignment to make room for Stock. Now, Stock is injured, as are depth options Jordan Yamamoto, Corey Oswalt and Thomas Szapucki. Nick Tropeano and Anthony Banda are healthy enough to log significant innings for the Mets, but both are veterans who have struggled in recent big league action. For a team trying to win as many games as possible, it’s not ideal.

“I think the biggest thing is when your name’s called, be ready,” said reliever Stephen Nogosek, who took a tough-luck loss on Tuesday after allowing back-to-back homers in the third. “I wasn’t necessarily expecting to get called up, but when I did, it was, ‘All right, get out there and compete and give it everything I’ve got.’”

Medium term
Here’s where the Trade Deadline comes into play. The Mets will be in on just about everyone, though it’s not entirely clear how many top-flight pitchers will actually be available at the Deadline. Names to dream on include José Berríos of the Twins; Germán Márquez and Jon Gray of the Rockies; Kyle Gibson of the Rangers; Kyle Hendricks of the Cubs; John Means of the Orioles; Tyler Anderson of the Pirates; and more. Not all of them will be moved, but some will. And the Mets will be as motivated as any club to grab one.

Beyond that, Carrasco should return by the start of August if not sooner, theoretically giving the Mets another healthy arm. If this roster can survive the next week-plus, it’s likely to be in far better shape by the first of the month.

“We have some really talented guys that we’re just really anxious to get back,” first baseman Pete Alonso said.

Long term
Surviving the short- and medium-term future is so important because in autumn, the Mets’ dream can become even more vivid. Imagine a postseason rotation headlined by deGrom, Carrasco, Syndergaard, Stroman, Walker or a Trade Deadline acquisition. Perhaps an established arm goes to the bullpen at that time. Perhaps the Mets find some other way to align their top arms. Perhaps another injury changes even the best-laid plans. In any event, the Mets have enough pitching to compete with anyone on an October stage, and they know it.

They simply have to get there first.

“All of us are pulling in the same direction in there,” Alonso said, when asked about the difficulty of routinely playing games like Tuesday’s. “They played better than us tonight, but we’ll go out there and take the series tomorrow.”