Yankees starting pitcher Gerrit Cole warms up in the top of...

Yankees starting pitcher Gerrit Cole warms up in the top of the first inning against the Blue Jays at George M. Steinbrenner Field on Friday. Credit: Newsday/J. Conrad Williams Jr.

TAMPA, Fla.

Gerrit Cole made his scheduled start Thursday long before the Yankees played their actual Grapefruit League game later that night at Steinbrenner Field. It lasted roughly three innings and involved battling mostly Ben Rortvedt, who amounted to his personal catcher down the stretch last season.

But to think Cole’s workday ends when he throws his last pitch would be a mistake. Or that his efforts to get the Yankees to an elusive World Series take place only on the mound.

Aaron Judge may be entering his second season as the official Yankees captain, but this is the fifth year of Cole basically wearing the rotation’s “C”. And he embraces the idea that as the ace, it’s also his responsibility to help squeeze the best from this staff beyond merely his days to pitch.

Whether he’s studying a teammate’s bullpen session, breaking down someone’s mechanics on video or hashing things over with the analytics crew — yes, Cole is a voracious consumer of cutting-edge data — the reigning AL Cy Young Award winner is all about using whatever’s at his disposal to improve on the margins.

Although he already is at the very top of the sport, a peerless combination of durability and dominance, the Yankees are still trying to get there. And Cole understands that he needs plenty of help to make that happen.

“There’s probably a role aspect to it,” he said Thursday afternoon. “I would say it’s partially part of the job, too. We win collectively as a team and each one of us can’t pitch every single day. But we can be out there to support our teammates, so that’s the culture that we’re trying to foster.”

Last season, Cole led the AL in starts (33), innings pitched (209) and ERA (2.63). His 0.98 WHIP was tops in the majors. It all led to his first career Cy Young Award — he also has two second-place finishes — and was painfully squandered in the Yankees’ 82-win season, their first playoff whiff since 2016.

The Yankees didn’t sign Cole to a nine-year, $324 million contract to be the ace of a fourth-place team. He was supposed to be the missing piece, the bona fide No. 1 starter they didn’t have when they fell short against Cole & Co. in the 2019 ALCS loss to the Astros.

Cole has lived up to that responsibility. The rest has been a system failure, and now he again is shouldering the load for a rotation that still has some question marks once you get past the top spot. With the Yankees resisting the temptation to go after more pitching help — primarily Blake Snell, who, like Cole, has Scott Boras as his agent — Cole’s $36 million annual salary feels like a bargain compared to where the market has gone during the past five years. And not just for his performance between the lines.

“To be an ace, you have to be an alpha dog,” general manager Brian Cashman said Thursday. “And to be an alpha dog, you have to have leadership qualities. So to me, I can’t recall any ace, whether it’s Roger Clemens or David Cone or CC Sabathia, that didn’t have those leadership-quality, alpha-dog mentalities. That’s how they got to the top of the mountain. So I expected that to be part of the package with Cole.”

Cashman conceded that Cole has shot past what he imagined as far as the overall impact on the Yankees — from the mound, through the clubhouse and upstairs to the front office. Hal Steinbrenner repeatedly has mentioned consulting with Cole during the offseason in trying to fix the problems of a year ago, so it’s clear that this ace appears to wield more clout than most.

“He’s the smartest one we’ve ever been associated with,” Cashman said. “Obviously he comes with a great physical package. But the intellect is at such a higher level. The game has evolved in a way that you can do as much of a deep dive into the pitching world as you want, and he’s an experienced deep-water diver in terms of the pitching knowledge . . . He’s all-in. We’re invested in him, but simultaneously he’s invested in us.”

Cole discussed that investment Thursday down to the smallest details, such as just going down the bench during a game, recognizing a teammate who might be having a tough night and trying to provide some kind of boost. Sounds basic. But only if you’re staying aware of what’s happening with the people around you. And that’s often taken for granted. For Cole, it’s second nature.

“Every player should ask themselves, by the time the game goes on, what can I do to positively affect the outcome today, whether you’re in the game or not,” Cole said. “But you have to be paying attention, know where your teammates are and have a rapport with your teammates in order for something like that to be effective.”

From a pitching perspective, Cole never stops working — almost to the point of being another coach when he’s not on the mound.

“Probably like I’ve never seen,” manager Aaron Boone said. “He could give you a good scouting report probably on every guy in [the clubhouse]. And what, in his mind, that guy could do better, and that’s because he loves pitching. He’s invested his whole life in it.”

The Yankees paid big for Cole the ace. Consider everything else a bonus.

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