Irene Pollin brought her late husband Abe’s 1978 NBA championship ring with her to Secaucus, N.J., last May and there was no denying its charm when she gasped with shock after the Wizards secured the right to draft John Wall with the No. 1 overall pick.

Wizards point guard John Wall may bring the gold jacket Irene Pollin, left, wore when she represented the team in last year’s draft lottery. (Bill Kostroun/Associated Press)

Grunfeld will bring the childhood gift from his father, Alex, with him Tuesday, and Wall is expected to pack some other items — possibly the gold jacket that Irene Pollin wore — to help as the Wizards attempt to become the first team since Orlando in 1992 and 1993 to win the top pick in consecutive years.

“Hopefully the Ping Pong balls fall our way again and it works out for us again,” Grunfeld said in a telephone interview as the Wizards make their third straight trip to the lottery after yet another 50-loss season.

Unlike last year, when Wall was projected by many as the No. 1 pick, there isn’t a consensus top choice this year. Most draft projections have Duke point guard Kyrie Irving rated as the best prospect available, but the Wizards certainly have a that position locked up for the next decade or so.

But if the Wizards get the top choice again, Grunfeld chuckled and said, “That would be a nice problem to have, although I don’t see it as a problem at all.”

Arizona forward Derrick Williams is also considered another option for the spot. “It probably will depend on which team wins it,” Grunfeld said. “There’s still a whole evaluation process that we have to go through before the draft starts. Most people had John as the number one pick last year, but some may have gone a different direction.

“Obviously, we are very pleased that we got the number one pick and we were able to have [Wall] become a part of our franchise. I think he had a terrific rookie season.”

The Wizards asked Wall to represent the team at NBA Entertainment studios and he obliged. The team has just an 11.9 percent chance of landing the No. 1 pick. “Now we’ll see how good he really is,” Grunfeld joked.

Minnesota has the best odds (25 percent) of winning the lottery, followed by Cleveland (19.9 percent) and Toronto (15.6 percent). If they fail to win the lottery, the Wizards can do no worse than picking seventh since they finished with the league’s fourth-worst record for the second year in a row. They won the lottery last year with the fifth-best odds (10.3 percent chance) after losing a tiebreaker against the Golden State Warriors. It was only the second time in 14 lottery trips in which the Wizards moved up — the other time resulted in Kwame Brown in 2001-- and the team has dropped 10 times.

Only one team has won the lottery with the fourth-best odds, with San Antonio earning the right to draft David Robinson in 1987.

Grunfeld said the Wizards will take the best player available, regardless of position. He mentioned that the Wizards have a player under contract at each position entering next season — Wall at point guard, Andray Blatche at power forward, JaVale McGee at center, Rashard Lewis at small forward and Jordan Crawford at shooting guard if the team is unable to re-sign restricted free agent Nick Young. But multiple league sources have confirmed that the Wizards plan to bring back Young.

“We have all the positions filled right now,” Grunfeld said. “So we don’t have to say we have to get such-and-such position. But obviously, anytime you can add some talent to your team, regardless of the position, it can help you.”

This draft class is considered to be among the weakest in recent memory, especially with Ohio State’s Jared Sullinger and North Carolina’s Harrison Barnes electing to return to school, but Grunfeld said the Wizards will still be able to find a good player.

“If you look at last year’s draft, which was supposed to be a strong draft, how many players came in and were difference makers from Day 1? When you’ve got rookies, it’s always a process with them, and some mature faster than others. You have to see who’s available at the spot you’re picking.”

And Grunfeld will make sure that he has his good luck charm with the hopes that it can yield the first choice once again. “If it helped, why not bring it back?” Grunfeld asked.