A few minutes after 8 p.m. on Wednesday, a camera at Disney/ABC Times Square studio in New York will pan across the face of owner Ted Leonsis’s son, Zach, and his expression will reveal whether or not the Washington Wizards have won the No. 1 overall pick in the NBA draft for the second time in three years.

A huge smile, and they will add another Kentucky alum to the fold in shot-blocking big man Anthony Davis, the gem of the 2012 draft class. An uncomfortable smirk or frown, and they will have to pick elsewhere — as the Wizards have all but two times before.

With the second-best odds at winning the rights to draft Davis — 19.9 percent — the Wizards will select no lower than fifth in the June 28 draft. In the weighted lottery era, two teams have moved up from the second spot to win the top selection – in 1992, when Orlando picked Shaquille O’Neal, and in 1996, when Philadelphia picked Allen Iverson.

“I think regardless of what the ping-pong balls give us, we’ll add a nice piece to our team,” Wizards President Ernie Grunfeld said. “Obviously, everyone would love to get the No. 1 pick — and there’s probably one player that stands out to most people — but we feel there are some solid players available.”

Grunfeld brought a tiny gold chain with a gold ball attached to the end two years ago when the team earned the right to draft John Wall, but he won’t have it in his suit jacket Wednesday when the ping-pong balls shoot through the drum.

“That was used already,” Grunfeld said, refusing to reveal his good luck charm.

As recent draft history has proved, few selections can immediately turn a lousy franchise into a playoff contender. Two years with Wall has yet to produce any more than a 23-win season. Blake Griffin, the top choice in 2009, didn’t make his playoff debut with the Los Angeles Clippers until three years later.

And, Grunfeld knows the team will need more than just luck to avoid making a fifth consecutive trip to the draft lottery after this season. Ted Leonsis gave Grunfeld an extension last month because he had confidence in the direction of the franchise and the financial flexibility of the team moving forward.

The Wizards currently have about $59 million committed to 10 players — not including a high lottery pick and two second-round selections (Nos. 32 and 46) next month — for next season, but the team has several options to potentially clear cap space and add talent through free agency or from absorbing salary through trades.

“We’re going to explore every option at our disposal,” Grunfeld said. “It’s different ways to try to add players to your team, whether it’s though the draft, through free agency, or could be through a trade. Last year, we added, what we think is a free agent in Nene, but we did it through a trade. You have to be prepared for every scenario.”

Rashard Lewis has had a disappointing, injury-riddled 1½-year stint in Washington and is slated to be the second-highest paid player in the league next season, but the Wizards can buy out the 14-year veteran by June 30 for $13.7 million, which would reduce the payroll by roughly $10 million.

The team could also free up more money if it chooses to cut ties with Andray Blatche by using the one-time amnesty provision in July. Blatche has failed to contribute at the level expected when he signed an extension nearly two years ago and was shut down for the final month of the season to work on his conditioning. He is still owed $23 million over the next three years.

But according to multiple league sources, the team will look to move Lewis and Blatche prior to the draft before paying them not to play for the organization. Grunfeld intimated last month that Blatche could return.

The Wizards will owe $52 million over the next four years to veteran big man Nene, whom they acquired at the trade deadline in a three-team deal with Denver and the Los Angeles Clippers. Nene had an immediate influence on the team, with the Wizards going 7-4 in games he played and the level of professionalism increasing. His arrival also raised the importance of adding veterans with more significant roles to help expedite the growth of one of the NBA’s youngest rosters.

“I think we found out, it is important to have veterans,” Grunfeld said. “If we can add some veterans, obviously that is something we’ll be looking at, but also, every year that our younger players have in the league, they become that much more experienced. That group with John, Kevin [Seraphin], [Trevor Booker] and Jordan [Crawford], now they will be going into their third year; they’ve gained some valuable experience.”

The last time the Wizards had the second-best odds was 2009, when the team dropped to fifth and wound up trading the pick before the draft to Minnesota in an ill-fated deal for Randy Foye and Mike Miller . The pick turned out to be Ricky Rubio .