Bradley Beal, the third overall pick in the 2012 NBA draft, will represent the Wizards in New York for Tuesday night’s draft lottery. (Julio Cortez/Associated Press)

Making their fifth consecutive appearance in the NBA draft lottery, the Washington Wizards will try to land the No. 1 overall pick with just the eighth-best odds (3.5 percent). But no matter what the Ping-Pong balls reveal Tuesday night in New York, Wizards President Ernie Grunfeld is hopeful the team is done making the annual May trip up Interstate 95 because of another disappointing season.

“As we said, we made some progress in the second half of the year and we want to build on that. If we continue to build on that, we’ll have a good shot to make the playoffs next season,” said Grunfeld, who watched the Wizards win half of their final 50 games after a dreadful 4-28 start.

Since the NBA began utilizing a weighted lottery system to determine the No. 1 overall pick in 1990, a team with the eight-best odds or worse has moved up to claim the top choice three times. The Wizards can take some encouragement in that it has happened twice in the past five years. Chicago won the right to draft Derrick Rose with the ninth-best odds (1.7 percent) in 2008, and Cleveland moved up to snag Kyrie Irving with the eighth-best odds (2.7 percent) in 2011.

“There is always a chance,” Grunfeld said.

In 14 of their 16 trips to the NBA draft lottery, the Wizards have stayed in the same spot or moved down, including last season, when they dropped one spot to No. 3. The two times the Wizards moved up, they claimed the top choice. They had the third-best odds (18.7 percent) in 2001 when they selected Kwame Brown and the fifth-best odds (10.3) in 2010 when they landed John Wall.

But unlike previous years, the team isn’t placing as much importance on draft position with a core already being established. Bradley Beal and John Wall, the 2010 No. 1 overall pick who produced all-star-caliber numbers the final six weeks of the season, appear to be the back court of the future with Nene manning the middle.

Beal, who last week was named to the NBA’s all-rookie team, will represent the team in New York on Tuesday night.

After the season ended, Wall and several other players expressed a desire for the team to use the draft pick to acquire more veteran talent.

Grunfeld has traded away two lottery picks during his tenure with the Wizards. In 2004, he used the fifth pick as part of a package to acquire Antawn Jamison from Dallas, which contributed to four consecutive playoff appearances. And in 2009, Grunfeld used the fifth pick as part of a package to acquire Randy Foye and Mike Miller from Minnesota, which contributed to four more years in the lottery.

When asked whether he feels as compelled to keep the pick as in past seasons, Grunfeld said: “Everything is on the table. We’re going to explore our options and prepare for any scenario. I think it’s a little bit different [this year]. We’ll see what’s out there for us. But at the same time, regardless of where we end up, we’ll be prepared to make a pick.”

If Beal is enough of a good-luck charm on Tuesday, the next question is what the Wizards would actually do if they win the lottery for the second time in four years. Kentucky freshman center Nerlens Noel is considered the favorite to go first, but Kansas freshman guard Ben McLemore or even Michigan sophomore point guard Trey Burke could be in the mix.

“I don’t think there is a clear-cut number one right now. This year, I think it’s a little more open than it has been in the past,” Grunfeld said. “I don’t know if you can get the same player at three or eight, but you can still get a solid player. You can never depend on a rookie to come in and have an impact right away. But what we’re going to try to do is get a player that can help us down the road, if not next year.”

Washington has a 12.4 percent chance of moving up to one of the top three slots. The Wizards will slide down to 11th in the worst-case scenario, but that would require three of the six teams below them to move in front of them (a 0.01 percent chance). Washington has a 70.3 percent chance of landing the eighth pick.

The Wizards also will have two second-round picks — No. 37 and No. 54, which was acquired from the New York Knicks in a three-team deal involving Ronny Turiaf — but Grunfeld doesn’t plan to hold on to all of those selections.

“I don’t think we want to have three rookies on the roster next year. We’ll see what we do with those second-round picks and how they could become an asset. Maybe package them to move up a little bit,” Grunfeld said. “Most years there is some movement. I’m sure there will be a lot of discussion, a lot of speculation, a lot of rumors flying, but we feel comfortable wherever we end up that we’ll be able to find somebody to help us and do some things for us.”

NBA draft lottery

8:30, ESPN