When Bradley Beal gleefully walked down from his seat in the back row of the stage at the Disney/ABC Times Square studios to stand next to Cleveland Cavaliers owner Dan Gilbert’s son, Nick, and Orlando Magic senior vice president Pat Williams, he only had one thought on his mind.

“Hopefully we’ll be able to get one,” Beal said.

(Associated Press)

Beal wasn’t satisfied that the Wizards had already made the biggest and most improbable leap at Tuesday’s NBA draft lottery, from the eighth spot into a top three pick. He wanted to get greedy and become second team in the past three years with the eighth-best odds to win the top overall pick in the June 27 draft.

But setting for the third pick was a decent consolation prize — especially when the team only had a 4.79 percent chance of moving up that high.

“You’re projected to be eighth but you never know how the lottery balls are going to fall. They fell in our favor and now we’re a top three team again,” said Beal, whom the Wizards claimed with the third pick last June.

The Cavaliers won the top choice for the second time in three years, winning with the third-best odds after winning with the eighth-best odds (with a pick acquired from the Los Angeles Clippers) in 2011. Wizards President Ernie Grunfeld was in the room when he found out that his team was moving on up and said Cleveland’s number combination came up for top choice and again for the third choice. The Ping Pong balls were dropped back in the drum for another run and the Wizards’ combination popped up.

“It was a good feeling,” Grunfeld said with a grin. “We were happy with it.”

Franchise building blocks are often found among the top three picks and Grunfeld appears to have hit on his two choices in that range. But he faces an intriguing decision with the third pick this season. Grunfeld is entering the final year of his contract and the Wizards will have to make considerable progress next season — as in, put a stop to five straight seasons in the lottery — to convince owner Ted Leonsis to retain him.

This draft doesn’t have any players projected to have an immediate impact, which makes dealing the pick an option. But such a move would probably be unpopular without bringing back a stud veteran in return — especially with Georgetown’s Otto Porter Jr., Indiana forward and DeMatha product Victor Oladipo and UNLV power forward Anthony Bennett possibly available at the third pick.

Bennett was in attendance at the lottery, with his surgically repaired left shoulder in a sling and said he probably won’t be able to begin participating in basketball-related activities until August. A physical, low-post bull with the range to step out and convert long jumpers, the 6-foot-8 Bennett is arguably the most polished offensive big man in the draft and some NBA talent evaluators believe he could be the best player to emerge from this draft.

“I feel like any pick in the top five is best for me,” Bennett said. “I heard [Washington] is a great organization. Great city. Great fan base. I’m pretty sure it’s going to be a great season next year.”

Immediately after the draft order was determined, two Western Conference executives felt that the Wizards would surely pick Porter, with one calling his selection a “no-brainer” for the team.

Porter would seem to be an ideal fit to pair with Wall and Beal, giving the Wizards an intriguing trio with complementary skills to build around going forward. Grunfeld hasn’t had to go very far to scout Porter since he played his home games in the same building as the Wizards. And it would be hard to think that Georgetown alum Leonsis wouldn’t want to add the school’s first first-team all-American since Allen Iverson — and an easily marketable player — to his NBA franchise.

Moving up gives the Wizards better talent options but also significantly affects the team financially next season. The difference between cost of the third pick and the eighth pick is $1.36 million ($3.57 million, compared with $2.21).

Since teams usually pay first-round picks 120 percent of their rookie salaries, the difference will actually wind up being $1.73 million ($4.38 million, to $2.65 million).

And if the Wizards select Porter, retaining unrestricted free agent small forward and last year’s resident marksman/comedian Martell Webster would be more a challenge after both Wall and Beal expressed a desire to have him back with the team.

The Wizards could also attempt to move down to acquire a big man such as Indiana’s Cody Zeller or Maryland’s Alex Len.

Kentucky center Nerlens Noel and Kansas guard Ben McLemore could also slide down to three, depending on what the Cavaliers do with the No. 1 pick (they could trade it or even address a need a small forward with Porter) and Orlando does with the No. 2 pick (Michigan point guard Trey Burke is under consideration).

Grunfeld said he wouldn’t be confined to drafting based on position alone. “In this league, players win. Regardless of what position they are at, we’re going to continue to evaluate and see who is available when it’s our turn to draft and we’ll take the person that we feel can help us in the short term and long term.”

The Wizards have only had a top three pick eight times in franchise history and those selections have yielded three Hall of Famers (Wes Unseld, No. 2 in 1968; Earl Monroe, No. 2 in 1967; and Walt Bellamy, No. 1 in 1961), some promising prospects (Beal and Wall) and a glaring bust (Kwame Brown; No. 1 in 2001).

Billy McGill (No. 1 in 1962) had a mostly forgettable career. Gary Bradds (No. 3 in 1964) had his best success in the ABA and Rod Thorn (No. 3 in 1963) is more known for his successes as an executive, which includes drafting Michael Jordan — with the third pick for Chicago in 1984.

Beal paid out twice for the Wizards, producing a solid rookie season and now a top-three pick. The pressure is now on the Wizards to take the next step and Beal, who has yet to be cleared from his season-ending stress injury, believes they were already headed there after finishing the season winning half of their final 50 games.

“Even if we would’ve had a lower pick, our expectations were going to be high,” Beal said. “We expect our team to do well from the jump, with all our players healthy and ready to go from Day One.”