Denver’s Andre Miller hasn’t played in nearly seven weeks following an argument with Coach Brian Shaw on the sideline. Miller, 37, joined the Wizards in a three-team trade on Thursday. (Matt Slocum/AP)

When Jan Vesely stood up and kissed his girlfriend on the night of the 2011 NBA draft, the Washington Wizards thought they had selected a high-flying, athletic big man destined to catch alley-oop lob dunks from John Wall for years to come.

Less than three years later, the Wizards shipped the disappointing Vesely, the No. 6 pick in that draft, to the Denver Nuggets for a soon-to-be 38-year-old backup point guard who hasn’t played in seven weeks.

Wizards President Ernie Grunfeld said he was thrilled about acquiring Andre Miller for Vesely, Eric Maynor and a future second-round pick before Thursday’s trade deadline in a three-team deal that also involved the Philadelphia 76ers. A crafty, 14-year veteran with a proven track record for reaching the playoffs, Miller addresses the team’s desperate need for a suitable backup behind Wall.

“Any time you can improve your team, you look to do that, and Andre is a proven player. He’s a proven veteran with a lot of experience,” Grunfeld said in a teleconference Thursday night. “He became available to us, and we pursued it, and we feel he’s going to add some really good things to our team.”

Miller’s arrival signals the urgency of the franchise as it attempts to reach the playoffs for the first time in six years. It also ends the Vesely era, one marked by a failure to develop much skill aside from providing the occasional highlight dunk.

Maynor, the Wizards’ first free agent commitment last season, also did not deliver what the franchise had hoped.

Vesely came to Washington to become a foundation piece.

Yet he struggled with his confidence and limited skills. His future within the organization became tenuous when the Wizards declined to pick up his fourth-year option in October, which made him a free agent this summer.

Chris Singleton, also poised to enter free agency this summer, stands as the only pick remaining from the 2011 draft class.

Vesely was the only trade chip Denver was willing to take for Miller, who had been apart from the team since around New Year’s after engaging in a verbal spat on the bench with Nuggets Coach Brian Shaw. A prideful competitor, Miller lashed out at Shaw after receiving the first DNP-CD of his career. He was suspended for two games before Denver sent him away altogether.

The two sides couldn’t even come together for a compromise after the Nuggets lost Nate Robinson for the remainder of the season with a knee injury.

Grunfeld called the situation “an isolated incident” and said he didn’t have any concerns about Miller after talking with some of Miller’s former teammates and coaches. Miller started his career playing for Randy Wittman in Cleveland and played with current Wizards Nene and Al Harrington in Denver and Martell Webster in Portland.

“Everybody speaks highly of his professionalism and his dedication and work ethic,” Grunfeld said, adding that Miller told him that he had lost 10 to 12 pounds while sitting out. “He’s very familiar with our team. He wanted to be in the playoff hunt, and when he looked at things, he saw us as an up-and-coming team. He thought that he could help us in our push to make the playoffs. . . . Obviously, it’s going to take time to get used to our system and to get used to game shape once again, but he’s been under a lot of different systems and seen a lot of different things and he has a high basketball IQ, so I’m certain he’ll pick up things pretty quickly.”

Miller has made the playoffs in nine of the past 10 seasons, but he has not advanced beyond the first round. He has career averages of 13.6 points and seven assists but averaged career lows of 5.9 points and 3.3 assists in 30 games this season.

Miller will make $5 million this season but only $2 million of his $4.6 million salary is guaranteed for next season. Vesely makes $3.5 million and Maynor earns $2 million, so the Wizards wind up saving money and move almost $1.5 under the luxury tax line. They have a roster spot available and the financial flexibility to sign a free agent or call up a player from the Developmental League for a 10-day contract.

The Wizards have made deadline deals with Denver in two of the past three seasons after acquiring Nene in a three-team deal involving JaVale McGee and Nick Young in March 2012.

They sent the second-round pick that they received in that trade to Philadelphia, which also got a second-round pick from the Nuggets and absorbed Maynor’s $2 million salary for next season.

Vesely had a successful offseason in which he performed well during NBA summer league in Las Vegas and the European championships in Slovenia.

But he was unable to have that production translate to the regular season. He fumbled an early opportunity with Emeka Okafor out with a neck injury during training camp, which prompted the Wizards to make a deal with Phoenix for Marcin Gortat. His confidence continued to wane and was most apparent at the foul line, where Vesely shot a career-low 26.7 percent (8 for 30).

“You have a first-round pick, you’d like to see him have some consistency and develop,” Grunfeld said. “He just didn’t develop as much, up to this point, as much as we would like to see him do. I think he has some abilities, as far as athleticism and strength and running the floor and defensive abilities.

“Offensively, he was very inconsistent for us. He had some real good moments, and you never know what’s going to happen for him in the future.”

Grunfeld said he expects to have Miller in uniform to make his debut Saturday, when the Wizards host the New Orleans Pelicans. The Wizards felt the need to snag Miller after the Maynor signing quickly proved to be a blunder. Maynor averaged 2.3 points and 1.7 assists in 23 games for the Wizards, lost his job to Garrett Temple and appeared in one of the past 26 games.

“Garrett did an outstanding job from a defensive standpoint, but we really wanted to have someone who was more creative from an offensive standpoint with that second group,” Grunfeld said. “Eric didn’t do the kind of things of running the team the way we really wanted him to, and when we saw this opportunity to get someone who has proven that he can do something like that, we felt like we had to take advantage of it. [Miller] is very excited about coming back to play. He’s what you call a baller. He loves to play basketball. That’s what it’s about for him.”