PHOENIX — Just a week into spring training, with Opening Day still six weeks away, temperatures barely climbing out of the 60s in the Valley of the Sun and only a couple of flat-ground bullpens and one live batting-practice session under his belt, Lucas Giolito had already proved himself to be indispensable to the Chicago White Sox: He was an obvious choice to organize the traditional rookie skits. Given Giolito’s background, these just might be the greatest rookie skits in baseball history.

“You guys ready for rehearsal?” he barked one morning this week to a handful of fellow rookies in the White Sox’s clubhouse at their Camelback Ranch spring headquarters.

The son of accomplished actors Rick Giolito and Lindsay Frost — and the grandson of the late Warren Frost, who appeared in five “Seinfeld” episodes as George Costanza’s prospective father-in-law — Giolito has a Hollywood pedigree that made its way into the White Sox’s consciousness long before anyone had gotten a look at his right arm.

What the White Sox see when they look at Giolito is a 6-foot-6, 255-pound specimen with a live arm, a congenial and coachable 22-year-old prospect and a guy who clearly knows his way around a comedy script. What they don’t see are the scars, because his are of the invisible type.

Widely considered the best pitching prospect in baseball as recently as last summer and presumed to be a major piece of the Washington Nationals’ future, Giolito, the team’s first-round draft pick in 2012, flamed out in his first taste of the major leagues, posting a 6.75 ERA in 21 1/3 innings with the Nationals in 2016, while allowing opposing batters a .988 OPS and shuttling between Washington and the minors four times.

By the winter, the entire industry seemed to know the Nationals had soured on Giolito, and in December, they sent him and two other pitching prospects — Reynaldo Lopez and Dane Dunning — to the White Sox for center fielder Adam Eaton.

“Last year, struggling in the big leagues and being up and down was a whirlwind, and I never got to settle in at any point. I was dealing with that failure and my mechanics being out of whack,” Giolito said, leaning against his locker. “I didn’t accomplish anywhere near what I and the [Nationals] expected me do — make it to the big leagues, help make an impact on a winning team, and win some games. I didn’t do that at all. It makes sense they would sour on me, or whatever term you want to use.”

Regardless of why it happened, the time was probably right for a split between Giolito and the Nationals. And if he was going to be someplace else in 2017, the White Sox were the perfect landing spot, committed as they are to a rebuilding process that is still in its opening stages, with the December trades of Eaton and Chris Sale netting them seven prospects and management vowing to proceed cautiously.

“He’s not walking around here as ‘first-round pick Lucas Giolito,’ ” White Sox General Manager Rick Hahn said. “For all the guys who get picked that high, there’s always that level of expectation that comes with it. He doesn’t have that added pressure over here. And secondly, unfortunately for us, we aren’t currently at the same spot in our success cycle as Washington is. Odds are, we’re not exactly trying to set our October rotation today. So we have time to be more patient with him.”

To that end, the White Sox have penciled Giolito into their Class AAA Charlotte rotation, with performance, more than need, dictating his advancement. Among the things they are asking him to work on, Manager Rick Renteria said, is throwing his curveball for strikes, especially as a first-pitch weapon, instead of always seeking to “bury” it out of the strike zone.

“They’re human beings,” Renteria said, “and confidence is a big thing. We’re trying to get him to feel comfortable with us as quickly as possible.”

Hahn said the White Sox, despite Giolito’s 2016 struggles, still project him as a front-of-the-rotation starter in the big leagues. But they won’t be in a hurry for him to get there.

“He’s still 22 years old,” Hahn said. “So this is a guy who would’ve been drafted last year if he had gone to college. . . . He still has the same physical tools, and age on his side, as when he was drafted.”

By the time Giolito walked off the mound for the last time in 2016, after two ineffective innings of mop-up relief duty in a 14-4 loss to Arizona, he seemed a shell of the pitcher who had captivated scouts and prospect-rankings mavens in years past. His fastball, which had touched 100 mph in his top-prospect days, was now sitting in the low 90s, and batters were teeing off on it. His breaking pitches were flat and lifeless, and he couldn’t seem to command any of them. Always a swing-and-miss pitcher, he was striking out batters at the lowest rate (4.6 per nine innings in the majors) of his career.

“Last year my stuff was not nearly as good as it should be,” Giolito said. “My mechanics were way off. When I’m throwing across my body, I lose the life on my fastball. I lose the angle on my fastball, which is my bread and butter — throwing downhill, using my height to my advantage. I didn’t have any of that. Not good.”

The Nationals, Giolito said, had made some small alterations to his mechanics, in the front (or “loading”) half of his delivery. In his offseason throwing program, and this spring, the White Sox have stressed getting back to basics and a more natural motion.

“I never caught on to it very well,” Giolito said of the alterations. Asked whether his struggles in Washington were the result of having too many voices in his head, he said, “To a certain extent. But most of it is on me. I would get in own head. I really overcomplicated things. I would try too hard, instead of letting it happen . . . I’m a big guy, so I have to really be able to repeat my mechanics well. It’s one of the most crucial parts of being able to be consistent and throw ball where I want.”

As Giolito’s corner of the White Sox’s clubhouse filled with his fellow rookies, at the end of another workout on another sleepy morning in the quiet days of early spring, they all started making their way toward him, and Giolito excused himself with a handshake and a “nice talking to you.”

Giolito, the Hollywood kid, needed to get this rehearsal underway, because before you know it, it would be time for the show.

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