PHOENIX — Bryan Shaw is back.

The 36-year-old right-handed reliever put up some pretty good numbers after most of the baseball world stopped paying attention to a White Sox team that was steaming toward 101 losses late last season. He was an oft-used arm out of Pedro Grifol’s bullpen, taking the ball 18 times in the season’s final month – including, at one point, on five consecutive days – and allowing just two runs from Sept. 1 on, looking like the guy who three times, including as a 33-year-old in 2021, led baseball in pitching appearances.

Despite doing some stuff that might have generated some interest in a major league deal, Shaw returned to the White Sox on Saturday, the team announcing a minor league pact that made him the 70th player to join their spring camp.

“Any time you can bring a guy that just wants to pitch every day and actually performs, (he is) a really good clubhouse guy and understands what it takes to win. It’s great,” Grifol said Saturday. “We are adding a bunch of those guys to this clubhouse.”

Even with his advanced age, there’s little reason that Shaw shouldn’t find himself right in the middle of a wide-open competition for spots in the South Side bullpen. Heck, he’s not even the oldest guy in the running for a big league relief gig. Jesse Chavez, similarly added on a minor league deal less than a week ago, is 40. He, too, though, is coming off a strong showing, posting a microscopic 1.56 ERA with the Braves last year.

This time a year ago, the White Sox’ relief corps was seemingly loaded with sure things, the Kendall Gravemans and Joe Kellys and Reynaldo Lópezes of the world, with All-Star closer Liam Hendriks on a remarkable road back from beating cancer. Of course, things didn’t turn out as anticipated, and much of that group was gone, in one way or another, by the trade deadline.

Things are much different now. While Chris Getz added to the bullpen with major league free-agent deals for John Brebbia and Tim Hill this winter, those could be the only two names being written in pen when it comes to forecasting an eight-man group for Opening Day.

Outside of that duo, it would seem jobs are very much up for grabs, which is why guys coming to camp on minor league deals four days after pitchers and catchers reported seemingly have as good a shot as anyone.

Shaw and Chavez might find themselves among the favorites, though their low-risk minor league contracts mean that the White Sox aren’t attached to either should their springtime performance not be up to snuff. Certainly, two guys with a combined 29 years of major league service time know what it takes to make a roster, and Chavez, in particular, is already impressing his manager.

“He’s been unbelievably impressive,” Grifol said Friday. “There’s a reason guys like him play 17 years. And when you go out and watch it, you realize it’s impeccable makeup and character. The ultimate teammate, selfless, teaching, leading and leading by example. He’s not telling people to jog from station to station, he’s jogging from station to station. He’s not telling people to come in early, he’s getting here early. He’s rolling up when I’m rolling up.

“He’s a true professional. He brings a dynamic to the clubhouse that every single player in there understands what he’s done in his career and why he’s done it. And that’s got to permeate through our clubhouse, because he’s got the recipe for longevity in this league, and it stems (from) character and integrity and execution at the end of the day, which he does.”

While none of that had anything to do with throwing strikes and getting outs, it’s high praise and strikes as particularly important as the White Sox embark on an overhaul of the organization’s identity and the clubhouse vibe.

Past Chavez and Shaw, there are others. Corey Knebel, a former All-Star closer, and Dominic Leone, who has history with White Sox pitching czar Brian Bannister, were added on minor league deals within the last week.

Joe Barlow used to close for the Rangers. Prelander Berroa is a hard-throwing youngster acquired in the recent trade of Gregory Santos. Jordan Leasure, brought in in last summer’s trade with the Dodgers, put up impressive minor league numbers.

Deivi García was a waiver claim last summer. Alex Speas was a waiver claim in October. Tanner Banks, Jimmy Lambert and Matt Foster have been with the organization for years. Edgar Navarro, Nicholas Padilla and Lane Ramsey all pitched for the major league team last season.

And then there’s whoever of the 14 or 15 guys the White Sox are stretching out as potential starters this spring doesn’t make the limited spots available in the Opening Day rotation. Could the bullpen be the landing place for Rule 5 pick Shane Drohan, free-agent signing Chris Flexen, 2023 holdovers Jesse Scholtens and Touki Toussaint or non-roster invitees like Justin Anderson, Chad Kuhl or Jake Woodford?

Just a handful of days into a six-week decision-making process, making projections seems a fool’s errand given the amount of question marks. Grifol said Saturday that in this early stage of the spring, he’s not even thinking about how the White Sox will put together their roster for Opening Day.

“We are not even thinking about the roster right now. We are thinking about competition. We are thinking about guys going out there and proving to us these are the guys we want to go to Chicago with. And that’s where we are at right now,” he said. “As far as building a roster or a bullpen right now, we are not even close to thinking about that.”

So this could go any number of ways, including a bullpen full of guys who were added on minor league deals, which is happening all over the White Sox’ roster this spring.

“You’re looking for competitive advantages, and I think one of the competitive advantages we had this offseason was the opportunities (for jobs),” Getz said Thursday. “I think that has shown with some of the players that have been willing to come here, whether it be minor league deals or even major league deals. There’s a long list of players that can offer a lot to a major league club, and we’re going to take advantage of that.”

The uncertainty in who will populate the ‘pen stands in stark contrast to where things stood a year ago, when the White Sox intended to set out on a campaign in which they challenged for an AL Central title. Those aren’t the expectations anymore, and the unknown of how the relief corps will look come Opening Day is a perfect example of where the team sits these days.

Will Grifol be calling on Shaw over and over again, like he did in September?

“Some of those times we used him, you get a little uncomfortable because it’s not everyday you see somebody throw five days in a row. (But) when he comes into your office and he’s been around the block a few times, he’s approaching 800 appearances, and he tells you, ‘Skip, I’m ready to go,’ you’ve got to trust him. And I do. And I did,” Grifol said. “He did a really good job. To be able to add him here to the mix and have him compete for a job, it makes this camp even more interesting.”