The Yankees are looking for bullpen help, and given that they hope to have a large chunk of their offseason spending going to Aaron Judge, they appear unlikely to be involved at what’s left of the top of the free-agent reliever market.

So how might they go about adding reliever reinforcements?

Perhaps by finding their next Clay Holmes or Wandy Peralta.

When the Yankees acquired Peralta in April 2021 (from the Giants in exchange for Mike Tauchman) and Holmes in July 2021 (from the Pirates for Diego Castillo and Hoy Park), neither deal was met with much fanfare. Peralta had a career 4.72 ERA and Holmes a career 5.57 ERA.

And yet, by the end of the 2022 season, Peralta and Holmes were the Yankees’ two best (healthy) relievers.

Of course, not every pitcher the Yankees acquire instantly turns into gold. For every Holmes and Peralta, there is an Andrew Heaney. The Yankees’ magic touch does not apply to everyone.

But what’s the secret sauce under pitching coach Matt Blake — whose contract expired after this season, though both he and the Yankees hope to sign a new one — and how might it offer some hints on whom the Yankees could look to acquire this offseason?

The Yankees like relievers with a sinker-slider arsenal. They also try to identify pitchers who have a quality pitch that may be underutilized and direct them to throw it more often — a philosophy for which Holmes and Peralta are perfect examples.

Before the Yankees traded for Holmes, the most he had thrown his sinker was in 2019, when it accounted for 51.6 percent of his pitches, according to FanGraphs. It did not grade out as a strong pitch that year — it had a below-average pitch value of -4.2, per FanGraphs — but it did have the kind of terrific movement (its 6.7 inches of vertical movement versus average was the third-best in the majors) that could be lethal if Holmes could figure out how to harness it.

So when the Yankees acquired Holmes in the middle of 2021, they immediately had him start throwing his sinker more often. Throwing it pitch after pitch allowed him to get a better feel for it, and the results followed: With a 73.2 percent usage rate (as a Yankee) in 2021 and 79.7 percent in 2022, Holmes’ sinker became one of the best in the league. From the first day he pitched for the Yankees until the end of the 2022 season, Holmes’ pitch value on his sinker was an MLB reliever-best 17.2. During that span, it graded out as the sixth-best pitch by a reliever in baseball — behind only Kenley Jansen’s cutter and the sliders of Edwin Diaz, Andres Munoz, Emmanuel Clase and Camilo Doval.

The left-handed Peralta arrived in The Bronx with an above-average changeup that he threw for a career-high 31.4 percent of his pitches in 2020 and a sinker with decent horizontal movement that he did not throw all that often.

Once Peralta put on the pinstripes, the Yankees increased his changeup and sinker usage — to 53.4 percent and 27.9 percent in 2021 and 42.5 percent and 40 percent in 2022, respectively. The results: From the first day he pitched for the Yankees through the end of the 2022 season, Peralta’s pitch value on his changeup is second among all MLB relievers at 17. His sinker pitch value during that span is a not-too-shabby 4.8.

So who’s next? There’s no exact formula — at least not one that the Yankees are willing to share publicly — for how they find reliever gems in the rough. But given what they did with Holmes and Peralta, here’s a look at four relievers who could fit the bill as an offseason acquisition:

Andres Machado

The 29-year-old right-hander, who made his MLB debut in 2017 with the Royals, had a solid season for the Nationals in 2022, posting a 3.34 ERA across 59⅓ innings while battling some command issues. But his sinker was elite. Machado threw the sinker for 33.7 percent of his pitches, and opposing batters hit just .164 against it with a .164 slugging percentage. He also threw a changeup (15.7 percent of his pitches) that limited hitters to a .158 average and .184 slugging percentage.

Machado’s four-seam fastball (30.6 percent) led to much of the damage against him, and the Yankees have tended to shift their relievers away from a heavy reliance on that pitch. Would an increase in sinker usage, and perhaps his changeup, too, allow him to reach the next level?

Mark Leiter Jr.

The New Jersey native, and nephew of Al, pitched in the big leagues this past season for the first time since 2018. He did so as a 31-year-old right-hander for the Cubs, initially as a starter before transitioning back to the bullpen and pitching well enough (3.99 ERA) that Chicago might not be interested in giving him up if they are trying to contend in 2023.

But if he is available, Leiter could be an interesting pickup. His two best pitches were his sinker and his changeup — opponents hit .196 with a .333 slugging percentage against the sinker and had a .090 average with a .135 slugging percentage against the changeup. But he combined to throw them for just 45.8 percent of his pitches. He gave up more damage on his four-seam fastball, curveball and cutter, which he combined to throw 49.2 percent of the time.

Jason Foley

The Athletic’s Ken Rosenthal reported the Tigers are a popular target for teams looking for relievers via trade, with two-time All-Star lefty closer Gregory Soto, Joe Jimenez and Alex Lange as possible candidates to be dealt. They are three appealing names, but if they require too costly a return, let’s look at another option in Foley.

The 27-year-old right-hander, who hails from Manhasset, recorded a 3.88 ERA across 60⅓ innings this year. He threw a sinker 60.8 percent of the time and held opponents to a .348 slugging percentage with a pitch value of 6.5, per FanGraphs, which ranked 15th among all relievers. Where the Yankees might see room for improvement is by refining his slider (opponents slugged .423) or by having him throw more changeups (6.9 percent usage, .278 opponent slugging percentage).

Michael Fulmer

If the Yankees want to use their financial might instead of prospect capital, they could go after the free agent Fulmer — a former Tigers and Twins reliever and former Mets first-round pick. Injuries forced him into a full-time relief role in 2021, but the 29-year-old right-hander has taken well to it.

In Fulmer, the Yankees would like his slider — he threw it a career-high 63.4 percent of the time in 2022 and held opponents to a .342 slugging percentage — and could wonder about increasing the usage on his sinker. He threw it for just 13.2 percent of his pitches, but held hitters to a .263 slugging percentage.

What the IKF?

A week has passed since the Yankees and Isiah Kiner-Falefa agreed to a $6 million contract for 2023 to avoid arbitration.

The move did not go over well with Yankees fans, but perhaps with a week to digest it, there’s room for explanation.

Rather than non-tendering Kiner-Falefa and losing him for nothing, the Yankees paid $6 million to retain him (at least for now) and keep their options open, which isn’t a terrible idea considering their infield next year has several question marks.

Perhaps the most pressing question is whether DJ LeMahieu will be ready by Opening Day. He missed the playoffs due to a toe injury that he has decided to treat conservatively for now. But if that does not work, surgery could be on the table later this offseason, which would threaten to delay his start to the 2023 season.

The Yankees also don’t know yet whether they will be able to find a taker for third baseman Josh Donaldson (and his $21 million salary for next year plus a $6 million buyout of a mutual option for 2024) or whether Gleyber Torres might fetch them something in a potential trade that would make it worth dealing the second baseman who is two years away from free agency.

Then there is the question of whether Anthony Volpe or Oswald Peraza will show enough to force his way onto the roster — whether that is as the starting shortstop or in the second-base job, depending on what happens with Torres.

If all of those scenarios work out in the Yankees’ favor, Kiner-Falefa easily could become expendable, and perhaps they find a way to trade him. But until then, he could be worth having around as a placeholder/backup/utility player, even at the price of $6 million.

Around the Winter League

The Dominican Winter League is underway, and a handful of Yankees (mostly minor leaguers) are spread out across the six teams.

Leones del Escogido has the roster most populated by Yankees farmhands, including catcher Ben Rortvedt, reliever Jimmy Cordero and outfielders Estevan Florial and Michael Beltre.

Through 12 games, Rortvedt was batting .114 with a .387 OPS. He is there to get reps following a season in which he was limited to just 48 games (all in the minors) because of oblique and knee injuries. Rortvedt, 25, landed with the Yankees along with Kiner-Falefa and Josh Donaldson in the blockbuster trade that sent Gary Sanchez and Gio Urshela to the Twins.

Cordero, who had only pitched in one game through Wednesday, was added to the Yankees’ 40-man roster earlier this month, and could have a shot to impact their bullpen next year — featuring that sinker-slider combination the Yankees like.

Twice this week, Escogido played Toros del Este, a team that features Yankees pitching prospect Jhony Brito (who was also just added to the 40-man roster) — along with former Yankees Miguel Andujar and Jackson (Clint) Frazier.