Two of the NBA's worst teams will be rewarded at the draft lottery Tuesday, winning the chance to choose Greg Oden or Kevin Durant.

University of Texas basketball player Kevin Durant and Ohio State University basketball player Greg Oden are shown in recent handout photos from their respective schools. [AP]

Representatives from 14 teams will be in Secaucus, N.J., hoping they earn the right to select another Tim Duncan or LeBron James, players who went No. 1 in the draft and now have their teams deep into the postseason.

"Someone is going to get very smart in a hurry," Nets president Rod Thorn said. "There is going to be a GM who all the sudden becomes a guru and a coach that is going to be very good."

The Memphis Grizzlies, after finishing with a league-worst 22-60 record, have a 25 percent chance of landing the top pick. The Boston Celtics have a nearly 20 percent chance, and the Milwaukee Bucks will be looking to turn the league's third-worst record into their second lottery win in three years.

The Bucks took Andrew Bogut with the No. 1 pick in the 2005 draft and made the playoffs the following season, so they know the impact one player can make. And general manager Larry Harris has hinted that player would be Oden if Milwaukee beats the odds to win again.

"One player solves a lot of problems for us defensively," said Harris, who will be carrying a stone submitted by a fan in a contest the team ran to find a lucky charm. "I mean, we were 29th in defense, 30th in rebounding, 30th in shot blocking. One guy solves a lot of those issues, and defense wins game."

Oden could have been the top pick last year if not for the league's age requirement, so instead helped Ohio State reach the national championship game with his shot blocking and rebounding. Durant, a forward who was the college player of the year in his lone season at Texas, is the more polished offensive player.

With two potential franchise players heading this year's draft, there is more attention on the lottery than any year since James was the big prize in 2003. And there sometimes seemed quite a desire to be a part of it.

Strange substitution patterns and curious injury absences convinced people that some teams were losing games on purpose. Boston coach Doc Rivers opened one postgame news conference by stressing that he wasn't trying to lose. But conspiracy theorists thought they found proof in the final week of the season after the Celtics sat forward Ryan Gomes in the fourth quarter of a loss to the Bucks that clinched the second-worst record.

"I probably (would have played), but since we were in the hunt for a high draft pick, of course things are different," Gomes said after the game. "I understand that. Hopefully things get better. Now that we clinched at least having the second-most balls in the lottery, the last three games we'll see what happens. We'll see if we can go out and finish some games."

Intentional or not, those losses can come in handy with a bit of luck -- or a lot of it. Just ask Pat Williams, who won the lottery with Philadelphia and followed it with three more victories in Orlando, earning the right to draft Shaquille O'Neal in one of them.

"Those Ls, which are so gruesome during the season, they're beautiful in late May," the Magic's senior vice president said. "Those Ls are gorgeous come springtime in Secaucus."

The lottery determines the top three positions, with the rest of the 14 in inverse order of a team's record. So Memphis can do no worse than the No. 4 pick, but missing out on Oden or Durant would feel like another loss for a team that began the season without star Pau Gasol, is losing Jerry West after the draft and didn't have much to feel good about in between.

The Celtics are hoping for lottery luck after they missed out on Duncan 10 years ago. San Antonio won that lottery -- and the Celtics didn't beat the Spurs from that moment until late this season. The Spurs, meanwhile, have won three titles and are seven victories from another, and coach Gregg Popovich knows that wouldn't have been possible without some luck.

"I'd be coaching a third-grade team someplace in America," he said.

A couple of teams already good are hoping to get even better. The Chicago Bulls got the right to swap spots with New York in the Eddy Curry trade, and the Phoenix Suns will take Atlanta's pick as a result of the Joe Johnson trade unless the Hawks move into the top three.

Williams has won when the odds were in his favor, and as a long shot. And he knows how much a victory means to a franchise.

"It just triggers your whole offseason," Williams said. "It triggers your sales, it triggers your imagination. Above all, it triggers hope. The hope that the lottery brings you, you can't put a price tag on it."

AP sports writers Jaime Aron in San Antonio, Tom Canavan in East Rutherford, N.J. and Chris Jenkins in Milwaukee contributed to this report.