The best bullpen in baseball also has been one of the more heavily leaned-on units across the first three months of the season.

The Yankees are proceeding carefully.

“There’s obviously a delicate balance,” pitching coach Matt Blake told Sports+ recently.

The predicament became a point of contention among the fan base last week during the Subway Series. During Wednesday’s game against the Mets, the Yankees entered the bottom of the seventh with a 3-1 lead after getting six strong innings from Gerrit Cole.

Four innings later, the Yankees had lost 4-3 in 10 innings without ever using their three best relievers in Clay Holmes, Michael King or Wandy Peralta because of their recent workloads, even with an off day looming Thursday and just having had one Monday before entering the series.

But Holmes and Peralta had pitched on three of the past four days. King had pitched on two of the last three, including that Tuesday, and the Yankees have not yet been willing to use him on back-to-back days since he fractured his elbow last season.

The loss to the Mets stung, but the Yankees stuck to their self-regulated reliever restrictions for a reason.

“It would have been four out of five for those guys, and [we] just didn’t feel comfortable pushing them, knowing we got the big picture in mind,” Blake said. “I know it’s hard to think about that when you have a win in your grasp. It’s something we wrestle with every night.

“We’re trying to win every night, [but] sometimes you just can’t sell out for that win right there. That’s just putting in some rules that we like to live by as a group, and it holds us to some accountability about how we push each guy. We listen to the feedback from them, too.”

The Yankees, who own the lowest bullpen ERA in baseball at 2.91, have the ninth-most innings pitched by relievers with 284 2/3 after mopping up behind Domingo German on Thursday night. That ranking had come down a few ticks thanks to a June schedule that features five off days.

After getting through a grueling May and finishing a West Coast trip on June 4 against the Dodgers, the Yankees had pitched the fourth-most bullpen innings in baseball with 233.

In the month of May, the Yankees had three of the five relievers who tied for most appearances in MLB: Holmes, Peralta and Ron Marinaccio each had 15.

“Obviously, it’s been a heavy workload,” Blake said. “We’ve just had so many games, and so many tight games, through May. It’s something we want to be mindful of, though, trying to solve for getting to October and having success in October.

“You gotta win now to get there. But at the same time, you can’t just run everybody hard and then like last year, where you lose Michael King, you lose Clay Holmes, you lose some of these guys.”

As was the case Thursday, the Yankees have been burned at times by short outings from their starters, which then puts a heavier burden on the bullpen. Outside of Cole, members of the Yankees rotation had completed six innings in just 14 of their 60 combined starts.

In part because of their struggling offense without Aaron Judge, the Yankees also have been involved in plenty of tight games, putting an extra strain on their high-leverage relievers. Before the lopsided Mariners series finale, 13 of their past 15 games had been decided by three runs or fewer.

“Obviously, if starters go a little deeper in certain spots, you use the seventh or eighth guy in the bullpen in certain situations, all that stuff adds up in the long run,” Blake said.

A number of factors go into the Yankees’ workload equation for relievers, including overall appearances, how many days they have pitched in a row, how many days out of the past five and past seven they have pitched, the amount of pitches they threw in an outing and how many ups they had.

“There’s some objectivity to it in terms of the total volume of work we can calculate and then the subjective component of how are guys recovering,” Blake said. “There’s a little bit of art and science to it, but you’re trying to put the pieces together in as clear a way as possible for them so they know the expectations. Then for the staff, so when we go into a game, we know what’s available to us.”

There also have been times this season when the Yankees have tried to stay away from certain relievers for more than a few days in a row — without revealing it in real time — to allow them to work through something physically. It happened with Peralta at the end of April. Boone alluded to him being “a little beat up” after Peralta did not pitch at all between April 25-28.

Even still, Peralta has made a team-high 34 appearances, on pace for a career-high 73 appearances.

It later happened with Jimmy Cordero as well: The right-hander did not pitch once during the Yankees’ West Coast trip from May 29-June 4.

“I think that’s the give and take of it,” Blake said. “If Wandy can be available in two or three nights, you want to take that shot and not wait 15 [days for an injured list stint]. But you also don’t want to put an extra burden on the bullpen if we’re trying to cover for him for five, six, seven nights and we’re playing short. That’s challenging.

“But fortunately, the way the schedule lined up for him and then for Jimmy after the Seattle series into the next one, sometimes you can find the situations where you give them three or four nights if they’ve been run hard. Hopefully give them a little reset and they’re good to go again.”

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Billy McKinney has evolved from a good story into a player who actually could help the Yankees — in addition to what he has done already.

When McKinney had his contract selected from Triple-A Scranton/Wilkes-Barre on June 7 as the injury replacement for Judge, it came as somewhat of a surprise. The Yankees passed over Franchy Cordero (on the 40-man roster) and Estevan Florial (not on the 40-man).

It was a full-circle moment for McKinney, who played two games for the Yankees in 2018 — neither at Yankee Stadium — and then got hurt before being dealt to the Blue Jays in a deal for J.A. Happ.

McKinney then tripled and homered in a June 8 doubleheader in The Bronx, and talked about what it meant to him to finally play there as a Yankee.

But he has not stopped hitting since. The 28-year-old outfielder hit homers on Tuesday and Wednesday against the Mariners, and he has reached base in each of his first 13 games as a Yankee. During that stretch, he’s hitting .318 with a .984 OPS.

It’s no secret the Yankees have been desperately lacking a left fielder, but suddenly McKinney and Jake Bauers — two non-roster invitees to spring training who started the season at Triple-A — are two left-handed bats providing some real impact at a time when the team needs it most.

“I’ve always believed in myself, but you gotta prove it in this game,” McKinney said.

It will take more than 13 games for McKinney to solidify his place with the Yankees, but so far, he has opened plenty of eyes.

“Consistent at-bats,” Boone said. “It’s really good at-bats. That’s what’s been exciting and encouraging and lines up with the reports we were getting for the last 4-6 weeks leading up to his promotion. I feel like he’s impacting the ball a little bit better than I’ve ever seen.”

In addition to catching an interesting staff of pitching prospects at Double-A Somerset this season, Austin Wells has gotten to work with a pair of rehabbing Yankees in Luis Severino and Carlos Rodon.

The Yankees’ top catching prospect, known more for his bat than his defense, has left an impression.

“I think Austin’s great,” Rodon said Wednesday after throwing to Wells on Tuesday in a three-inning rehab start. “I thought he received the ball well. That was our first real time working together. I thought he did a really nice job. He called good sequences.”