ATLANTA — Every team relishes a trip to the NBA playoffs. Is there any team that appreciates it more than the Atlanta Hawks?

Well, maybe. How about the Miami Heat?

Both teams experienced life at the bottom of the league in the not-so distant past, which makes them especially grateful to still be playing at this time of year.

"I savor every moment of it," Hawks forward Josh Smith said. "You’re more appreciative going from the bottom to the top than you are going from the top to the bottom."

Try telling that to Miami.

The Heat reached the pinnacle in 2006, winning its first NBA title with a team led by Shaquille O’Neal and Dwyane Wade. Just two seasons later, with Wade battling injuries and O’Neal having been dealt to Phoenix, Miami plummeted all the way to the bottom of the standings with a 15-67 record.

It was an awful experience, but one that taught a valuable lesson about the fleeting nature of championships. No one wants to forget what happened, even those who were fortunate enough to be playing somewhere else last season.

"All season long, those guys, we’ve felt their pain," rookie forward Michael Beasley said. "We weren’t here, but we know what they went through."

No one was more motivated than Wade. He returned from two injury plagued seasons with a vengeance, leading the league in scoring (30.2 a game) and pushing himself into MVP contention — all for the shot at another ring.

"The regular season, it’s a warm up to this," Wade said. "The lights are brighter. I feel it already. I enjoy these moments. Our crowd’s going to be rocking when we get back to Miami. Their crowd’s going to be rocking in Atlanta. This is what we play for."

In contrast to Miami’s rapid up-and-down-and-back-up-again journey, the Hawks took a much more tortuous trip to this best-of-seven series, which begins Sunday night in Atlanta.

The franchise actually went off course a full decade ago when a perennial postseason team decided to transform itself with youth and speed. Ohhhh, what a mess of things they made. The trade for Isaiah Rider is a good starting point for how NOT to rebuild a team. By 2004-05, the Hawks were just a step above the D-League, winning only 13 games in coach Mike Woodson’s first season.

"I knew we would eventually turn the corner, but it takes time," Woodson said. "I’ve been in this 27 years. If you thought we should have been in the playoffs two or three years ago, you’re crazy, you’re out of your mind. No young team in the history of this game has ever done that."

Indeed, there were times when the Hawks seemed to be standing still, but they were really making progress all along. They drafted Smith, Marvin Williams and Al Horford. They signed Joe Johnson. They rounded out the starting five by trading for Mike Bibby. On the court, the wins improved from 13 to 26 to 30 to 37 to this year’s 47-35 mark, Atlanta’s first winning season since 1999.

"It means a lot to me," said Smith, one of the holdovers from the worst season in franchise history. "To go from 13 wins to 47 wins is unbelievable."

The Hawks actually got a valuable sampling of playoff basketball a year ago, when they broke the NBA’s longest active postseason drought, albeit with a record eight games below .500. No one gave them much of a chance in the opening round against eventual NBA champion Boston, but they took the Celtics to the limit.

Three wins at home showed the Hawks they were capable of hanging with the NBA’s elite. Four blowout losses in Boston showed them just how far they had to go.

The season ended with a dismal 99-65 loss in Game 7.

"That definitely left a sour taste in all our mouths," Smith said. "No one played well that game. We want to write a different story this year. We want to end on a positive note. We’re not going to be satisfied just getting out of the first round. We want to try to reach our goal, to one day bring an NBA title to Atlanta."

Coming into this season, Woodson talked over and over about the importance of having home-court advantage to start the playoffs. Atlanta reached that goal as the best team in the Eastern Conference beyond the Cleveland-Boston-Orlando power triumvirate, which ran away from everyone else.

"I hope like hell there’s a carry-over from last year’s run," Woodson said. "That taught us how to play playoff basketball. When we to Boston, we had no clue. That’s why the games were so lopsided. Then we came home and won Game 3. We grew up awfully fast and were able to make a series out of it."

While much of the focus in this series will be on the Wade-vs.-Johnson matchup, there’s always room for others to step up.

Beasley could play a huge role for Miami off the bench, giving the Heat scoring punch when Wade is not on the court. The rookie was the team’s second-leader scorer at 13.9 points a game.

For the Hawks, keep an eye on much-traveled Flip Murray, who finally seems to have found a home in Atlanta. The combo guard averaged 12.2 points filling in for both Johnson and Bibby, providing the sort of instant offense the Hawks lacked a year ago from their reserves.

"We would not be in this position without Flip," Williams said.

Williams also played a key role before a back injury sidelined him for 16 games. He returned for the final week of the regular season and will be in the starting lineup Sunday night.

"That’s 14 points and six or seven rebounds a game," Woodson said. "It’s good to have him back."