FORT MYERS, Fla. — What happens when the third-hardest-throwing left-hander in the majors scraps his old breaking ball for a new one, taught to him by Chris Sale?

Answer: the kind of spring training hype that has Eduardo Rodriguez being built up as a Cy Young Award contender instead of just another back-of-the-rotation arm.

“Everyone is in the best shape of their life, but Eddie really is in the best shape of his life,” Red Sox Manager Alex Cora memorably declared as camp opened last week.

On Tuesday, the 25-year-old Rodriguez took the mound for his first live batting practice session against some teammates.

Rodriguez flashed his signature mid-90s heater, one of the game’s best change-ups and a reinvented slider that looks bigger and sharper than any breaking ball he’s thrown.

“I worked with Sale and most of the guys, asked everyone the way they throw the curveball and slider and how they finish,” Rodriguez said. “But mostly Sale, because he has the best slider in the game, so that’s how we do it.”

With the rest of the rotation watching, along with most of the Red Sox front office, Mookie Betts and a few other teammates, Rodriguez’s unveiling of the new pitch turned heads.

For four seasons, Rodriguez has only teased the Red Sox with his potential while simultaneously disappointing with poorly timed injuries and no third pitch.

“It was like, an in between slider-cutter,” Cora said. “Now it’s a real slider.”

During his career, hitters have a .218 average against his signature change-up, and a .242 average off his four-seam fastball, which he throws as hard as 98 mph. But they’ve hit .277 with a repugnant .517 slugging percentage off his slider, a pitch once considered so ineffective Rodriguez stopped throwing it.

Injuries haunted him again last year, but when he returned from the disabled list after missing six weeks, Rodriguez struck out 12 against the White Sox on his way to a 36-strikeout month in just 25 innings (though he allowed 15 runs in that span).

“I think he showed a lot of people in baseball that this guy has the ability to go through teams, go through lineups a few times,” pitching coach Dana LeVangie said.

In the postseason, it was more of the same, with Rodriguez dazzling for the majority of his World Series start against the Dodgers, only to give it all up with a three-run homer off the bat of Yasiel Puig (culminated by Rodriguez’s now-infamous glove throw).

That pitch might have changed his career.

“You can tell he’s had some drive this offseason,” Sale said.

Added postseason hero Nathan Eovaldi, “I feel like he’s taken it to a whole new level.”

Though the other starters are being held back in camp after a long postseason, Rodriguez, who threw just 10 innings in October, is ahead of schedule.

“For him to be as crisp and clean as he is now at the beginning of spring training, give him a little more time and he’s going to be even better,” Eovaldi said. “I like the fact that he locates his fastball.

“His slider and his fastball, when he locates his pitches like he has, and I feel like he’s been working the ball up in the zone as well. With him and his velocity, I feel like it’s going to get him a lot of quick outs.”

Rodriguez is known for talking a lot, which prompts a lot of good-natured teasing in the locker room. But the veteran starters around him think his outgoing personality has helped him build relationships.

“Besides giving him a hard time all the time, they want him to be great,” Cora said. “They see it. At one point in their careers, Sale and Price were that guy. They’re hard on him because they know how talented he is. Sometimes he gets caught up on who he wants to be. He wants to be Chris one day, and Rick (Porcello) the next day, and David (Price) the next outing. We want him to be Eduardo. Eduardo is a good big league pitcher. That change-up, we saw it in Game 4. When he has that combination of fastball up, change-up down, he’s lethal.”

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