CLEARWATER, Fla. — A few days before Bryce Harper left Las Vegas this week for spring training, his wife asked him if he thought the Phillies had done enough this winter to improve.

The team’s upgrades this offseason were mostly limited to a one-week span in December when the Phillies signed a frontline starter and a shortstop. They finished 2019 in fourth place with a .500 record and Kayla Harper isn’t the only one wondering if the team that arrived this week to Clearwater is good enough to reach the playoffs.

“She’s super into it and everything like that,” Harper said Sunday morning, his first day in camp.

Harper, before signing last year to the richest free-agent contract in the history of baseball, wanted assurance from managing partner John Middleton that the Phillies were committed to building a championship team. He’ll earn $330 million over 13 years, but Harper also wants to win.

And he told his wife this week that he believes the Phillies did enough this offseason to be better in 2020.

“We were able to get the guys that we needed to,” Harper said.

The Phillies spent $132 million on right-hander Zack Wheeler and shortstop Didi Gregorius and will have the most expensive payroll in franchise history. But there would be less discussion if the Phillies did enough if they were able to trade for Kris Bryant, the superstar third baseman who the Cubs are shopping.

The Phillies halted their spending in early December as their payroll neared the $208 million threshold of the competitive-balance tax. They could have used an additional starting pitcher and an arm in their bullpen, but the Phillies seemed set this winter on avoiding the tax. Team president Andy MacPhail said last week that the Phillies could exceed the threshold with an in-season acquisition.

And that is one reason that they seem lukewarm this spring on adding Bryant, who grew up with Harper in Las Vegas and will earn $18.6 million this season. Bryant, 28, is set to be a free agent after the 2021 season, and acquiring him would also require the Phillies to part with the top of their farm system, which Baseball America ranked this week as the fifth-worst in baseball.

Bryant would be a huge addition, but a trade remains unlikely. Even Harper, who openly courted Mike Trout last spring before he signed an extension with the Angels, understands why.

“Any time you’re able to add an All-Star player you’re going to want to add an All-Star player,” Harper said. “But you have to be able to know that you developed a player in the minor leagues that can also help you at third base, and Alec Bohm could be that guy for us. He could come up and be one of the best third basemen in the second half or whatever it is. As a team, you have to have guys like that, that are only making the minimum so you can go and spend at the deadline.

“If the Cubs aren't where they are, you never know at the half what they're going to be doing. Bryant could be cheaper at that point. But I can't give up Spencer Howard and Bohm, and possibly give up our whole future, for a year and a half of KB if we don't sign him to an extension.”

Even without Bryant, Harper likes his team’s chances. He said Jake Arrieta, who will slot behind Aaron Nola and Wheeler in the rotation, is a “Cy Young contender” now that he’s healthy. He’s excited to play for Joe Girardi, who will be Harper’s sixth manager in nine seasons, and is a fan of new hitting coach Joe Dillon, who worked with Harper for one season in Washington.

“He understands what it takes to win,” Harper said of Girardi. “He's had a lot of superstar players. He's had a lot of fringe players as well that have helped him. He's been in this game for a long time. I think as a team, as an organization, we're thrilled to have him in our clubhouse and being the leader of our staff.”

Harper is enticed by Howard, who could join the rotation at some point, and is keeping tabs on the cast of hard-throwing relief prospects in camp like 6-foot-5 left-hander Damon Jones. Harper is confident in the bullpen, which is counting on the return of several injured relievers, and expects new pitching coach Bryan Price to help the staff.

The Phillies signed just one major-league free agent - Tommy Hunter for less than $1 million - after curbing their spending in December. They signed a cast of veterans to minor-league deals as they tried to finish their bullpen on a budget. Harper likes Drew Storen, who he played with in Washington, and thinks Bud Norris “could be a gold mine for us.”

“Everybody talks about our bullpen. ‘We need to add, we need to add,’ ” Harper said. “Hector Neris was really good for us and then we’re getting back guys that were not healthy.”

The Phillies will have their first full-squad workout on Monday and they’ll play their first Grapefruit League game on Saturday. Opening day is five weeks away. The Phillies will then be able to learn if they did enough this offseason. But their star player already thinks they did.

“As a team, we do have a chance of getting deep in the playoffs, if that’s our goal which it should be every single year,” Harper said. “Then we’ll make the moves we need at the half as well before the deadline. I’m excited about what we do have right now and looking forward to getting to know the guys in spring and get going again.”

Extra bases

Outfielder Tyler Garlick, acquired Saturday in a trade with the Dodgers, was scheduled to arrive in Clearwater on Sunday night. Each of the team’s other 69 players have reported to camp. ... Andrew Knapp, Joe Girardi said, continues to make progress from the ribcage injury he suffered on Wednesday. ... Girardi will address the team Monday before the first full-squad workout of camp.