NEW YORK — The Philadelphia 76ers lost plenty the previous two seasons, though never managed to lose the most.

This season they finally fell all the way to the bottom.

The potential payoff comes today, when the 76ers have the best chance to win the NBA draft lottery — and could walk away with two top-four picks if the pingpong balls bounce their way.

“It’s a big day on Tuesday,” said new president of basketball operations Bryan Colangelo. “We’re going to know where we are and no matter how it comes out, we’re at least going to know where we stand and what we have to play with with respect to building this team.”

The Lakers and Celtics, the NBA’s most storied franchises, have the next-best odds of getting the No. 1 pick and the chance to draft the type of player who could get them back to the lofty positions they used to occupy.

But nobody is set up like the 76ers, who used to be regular winners themselves but have done nothing but lose — which seemed to be their plan — in recent years.

The team with the worst record normally has a 25 percent chance of winning the lottery, but the Sixers’ odds are even better. They have the right to swap picks with Sacramento from a trade involving Nik Stauskas, so adding the Kings’ 1.9 percent chance of moving up to No. 1, Philadelphia actually has a 26.9 percent chance.

“To win it is a euphoric feeling,” said Colangelo, who did just that 10 years ago with Toronto. “Obviously there’s a lot of chance involved. We have likely more chances than anybody else, which is a good thing.”

And there’s more: If the Lakers don’t remain in the top three, their selection would also go to Philadelphia, a pick the Lakers originally dealt to Phoenix for Steve Nash that the 76ers later acquired in another trade. It makes lottery night the highlight of what’s been three miserable seasons for the 76ers.

The 14 teams that didn’t make the playoffs go to the lottery, which sets the top three picks. The remainder of the order is determined in inverse order of the teams’ records.

Jimmy Butler will represent the Bulls, who have the 14th and smallest odds of getting the No. 1 draft pick or moving up into the top three places as the best team to miss the playoffs with a 42-40 record.

The Lakers had the No. 2 pick last year and are right back in the same spot in the lottery after going 17-65 in Kobe Bryant’s final season. The Celtics were a 48-win playoff team who will take the Brooklyn Nets’ spot on stage as part of the payment from the Kevin Garnett and Paul Pierce trade in 2013.

The lottery debuted in 1985 when the Celtics, Lakers and 76ers were in the midst of claiming nine straight NBA championships, so any of them, with good history and strong fan bases, would be a welcome landing spot for this year’s top talent.

“Those are franchises that have won many championships. Those organizations, they’re big-time,” said Marquette center Henry Ellenson, an expected lottery pick. “And just playing for something like that, it would be something special.”

The Sixers, though, have been an embarrassment in recent years. They lost 26 straight games in 2013-14, then started 0-17 in 2014-15.

But they didn’t have the worst record in either season and last year that proved particularly costly, with Minnesota cashing in its 25 percent chance and getting Karl-Anthony Towns, the Rookie of the Year who appears to be a franchise player.

It’s unclear yet what the Sixers have, as they ended up with the No. 3 pick both times and drafted Joel Embiid — who still hasn’t played because of a foot injury — and Jahlil Okafor, who had some rocky times as a rookie. Nobody was beating Philadelphia to the bottom this season, after an 0-18 start and 28-game skid spanning the previous season sent the Sixers to a 10-72 finish that was barely better than the worst ever in an 82-game schedule.

So they’re in great position for a shot at LSU’s Ben Simmons or Duke’s Brandon Ingram — or perhaps one of them and another building block.

The Sixers have been bad. Now they want to be lucky.

“It’s been a long time coming,” O’Neil said. “We’re finally going to get a chance to have some fun.”