NBA basketball players, from left, Detroit Pistons' Andre Drummond, Portland Trail Blazers' Damian Lillard and New Orleans Pelicans' Anthony Davis mingle onstage before the NBA draft lottery in New York. (Jason DeCrow/AP)

If the Washington Wizards felt securing a top three pick was the only way for the franchise to make progress, then claiming the eighth pick or lower in the NBA draft lottery Tuesday would’ve been a serious disappointment.

But this is an organization that already believes a postseason berth is soon on the horizon, so their stunning move up five spots to claim the third pick in the upcoming draft — despite just 4.79 percent odds — only raises the optimism.

Instead of hoping for a player to slide or taking the best of what’s left, the Wizards can now focus simply on the best.

“Obviously, we’re in a better position now than we were an hour ago,” said Wizards President Ernie Grunfeld, who sat in the sequestered room where Ping-Pong balls determined the fate for the 14 non-playoff teams. “We did get lucky.”

Cleveland won the No. 1 overall pick for the second time in three years and Orlando will select second in a draft that many scouts and executives believe is short on immediate impact players. At three, the Wizards will likely have a chance to select Georgetown’s Otto Porter Jr., who could join an impressive young trio with John Wall and fellow Missouri native Bradley Beal.

Other options include UNLV freshman big man Anthony Bennett, Maryland sophomore center Alex Len or Indiana swingman Victor Oladipo (DeMatha). And depending on what the Cavaliers or Magic do, the Wizards might even be able to pick one of the players projected on most draft boards to go first and second — Kentucky big man Nerlens Noel or Kansas guard Ben McLemore.

“We’ve said all along, next year, our goal is to make the playoffs and that’s still going to be our goal. We’ll still bring in a lot of players but maybe not as many as we would’ve,” Grunfeld said with a laugh. “We can address every position at three. I don’t think we’ll lock into any certain position but I know there will be some solid players there for us.”

One of the reasons the Wizards are encouraged about their future and the direction of the franchise was seated in the second row of a stage at Disney/ABC Times Square studios. Beal, the shooting guard who finished third in rookie of the year balloting, represented the organization and wore the same tie that he donned on June 28, when the Wizards selected him third overall in last year’s draft. The tie will likely go on the shelf until a special occasion after the Wizards overcame overwhelming odds to move up for just the third time in 16 lottery appearances.

Grunfeld, who brought a gold chain with a ball attached when the Wizards landed the top pick three years ago, wasn’t ready to give credit to a tie: “Bradley was our good [luck] charm.”

Last year, the Wizards had the second-best odds and fell one spot to third. In 2010, they had the No. 1 overall pick and took Wall.

“You can’t go wrong with any of those picks. There are a lot of talented guys in this draft. We’ll be able to make a wise decision,” said Beal, who is friends with two of the top prospects, McLemore, his former AAU teammate, and Porter. “Ben is a great shooter, super athletic. And Otto is a grimy player who can slash and score and play great defense. All those guys are great. Terrific.”

The Wizards no longer have to cast a wide net.

“It gives us a bunch of options,” Grunfeld said about the Wizards, who only had 3.5 percent odds of winning the No. 1 overall pick, but 70.3 percent odds of getting the eighth pick. “It’s a nice place to be. I think there will be a nice player for us.”