Clay Holmes had finally stirred on the off-day following a long West Coast trip and decided to walk to his local Starbucks for some fuel when his cellphone buzzed. He looked down and saw the name of his Pirates general manager, Ben Cherington.

He just knew what it meant, even though he was not highly coveted or involved in the week of trade-deadline rumors.

“Everybody in the locker room kind of knew [when you are with a second-division rebuilding team like Pittsburgh] that there’s at least a slight chance,” Holmes recalled Tuesday, the exact one-year anniversary of his trade to the Yankees.

The next call on July 26, 2021, back in his apartment now, was from Brian Cashman welcoming Holmes to a new team. And there was a conversation not long after he joined the Yankees in Tampa with pitching coach Matt Blake, bullpen coach Mike Harkey and a few of the organization’s analysts in which it was emphasized to the righty just how good his sinker was and that if he focused on it — when to throw it (basically all the time) and where (in the strike zone and just let it dive) — that success would follow.

But the Yanks wanted a soft first step for Holmes and inserted him for a debut on July 29 in St. Petersburg, Fla.; the ninth inning of a game they trailed the Rays 14-0. There was hardly a ripple, just like when they obtained a guy with a career 5.57 ERA. The big Yankee news that day was that they had completed their years-long pursuit by obtaining Joey Gallo. But even in a blowout, seeing him up close for the first time, Blake had an initial “aha” moment with Holmes.

“It was 95-96 [mph], over the plate, so even in low leverage, it was hard to watch and not think we might have something,” Blake said.

They had a lot. In fact, when the Subway Series began Tuesday, it was arguable that the New York teams had the best relievers in their respective leagues — Holmes and Edwin Diaz. Less debatable was that both the Yankees and Mets felt they had to further augment bullpens in front of their closers in the next week, before next Tuesday’s 6 p.m. trade deadline.

In that way, Holmes is emblematic of the modern game and how to pursue bullpen help. Yes, the Yankees and Mets are both interested in Cubs closer David Robertson due to experience and track record and the fact that, even at 37, he is throwing the ball well, with the extra benefit that he is both New York and postseason proven.

But like many teams, the New York clubs will see if the Holmes magic can be recaptured by focusing on perhaps underpublicized relievers with at least one pitch that is dominant.

“[Robertson’s] track record kind of speaks for itself above other guys because it’s so lengthy,” former Yankee and current Met reliever Adam Ottavino said. “But I think in every other case, teams are looking at their models and looking for some sort of outlier pitch that they can help exploit and see if maybe they can put their little special adjustment on the guy.”

For example, part of the surprise Oriole success is built on a deep bullpen that features one reliever after another with a superb offering — Dillon Tate’s sinker, or the four-seamer of Felix Bautista and Cionel Perez. Bautista wowed the Yankees in a recent series. Perez is the kind of power lefty that would entice the Mets.

The way the Met farm system sets up — well touted prospects at the top, but not great depth — you can imagine that for them to include, say, a Ronny Mauricio or Mark Vientos as the main component of a package, they would want to one-stop shop a bit. So, think of asking the Orioles for Trey Mancini and someone like Perez or closer Jorge Lopez, for example.

The Mets believed enough in their ability to find more relief help that they used Colin Holderman to acquire Daniel Vogelbach. Trevor May is nearing a return, but the Mets cannot be sure on him or that Seth Lugo finds the best of his past or that Drew Smith stops permitting homers or — if Jacob deGrom returns successfully — that David Peterson and perhaps Trevor Megill can integrate well into the pen. Thus, they are hunting at least one and probably two relief arms.

The Yankee bullpen took a devastating loss with Michael King joining Chad Green in being out for the year. They were Aaron Boone’s most versatile relievers. Aroldis Chapman hasn’t lost his stuff as much as his confidence. Can that be reclaimed? Can Jonathan Loaisiga rediscover 2021? Zack Britton (Tommy John surgery) is about a week from graduating to live bullpen sessions. Can he make it back for September — and October?

Albert Abreu, Lucas Luetge, Ron Marinaccio, Wandy Peralta and Clarke Schmidt reside between intriguing and insufficient. The Yanks’ big eyes seem to be on a starter such as Cincinnati’s Luis Castillo. They also want a bat, and the unvaccinated status of Andrew Benintendi has not yet discouraged them — perhaps they believe on a contender he would feel compelled to be inoculated to be able to play in Toronto. Could the Yanks do one-stop shopping with Kansas City for Benintendi and closer Scott Barlow and his impact slider?

The Tigers are loaded with intriguing relievers too, notably Michael Fulmer and All-Star Gregory Soto. But also Jason Foley (sinker) and Alex Lange (curve) have compelling pitches, as does Texas reclamation project Matt Moore. As a full-time reliever for the Rangers, Moore has de-emphasized his fastball to rely more than ever on his curve. His 44 ²/₃ innings this year without allowing a homer were the most in the majors.

Second on that list at 43 innings was not much more than a blip on the trade landscape a year ago.

Clay Holmes.