LOS ANGELES -- There is a trophy case inside the Los Angeles Clippers’ training facility.

It is a floor-to-ceiling glass display outside the practice court, and it houses more basketballs than trophies for a franchise that has yet to make it out of the second round of the playoffs.

There are two game balls painted to commemorate the team's two Pacific Division titles and another painted to remember a 17-game win streak in December 2012. But the centerpieces are the two game balls painted to celebrate Game 7 wins over the Memphis Grizzlies in 2012 and the Golden State Warriors in 2014, both in the first round.

They are the two most significant wins in the franchise’s star-crossed history, but both would have to be moved aside to make room for a new game ball if the Clippers defeat the San Antonio Spurs in Game 7 of their first-round series Saturday in Los Angeles.

In many ways, this is the most important game in Clippers history -- not just because it is an elimination game, but also because of the domino effect the result could have on the future of the franchise.

This is the fourth season Chris Paul, Blake Griffin and DeAndre Jordan have been together. Although the Clippers’ Big Three have produced the most successful four-year run in team history, they also have failed to get out of the second round of the playoffs. If this season were to end with a first-round exit for the second time in three years, there would be some serious questions this offseason about the core of this group and returning the same nucleus for a fifth season. That decision might not even be the Clippers’ to make if Jordan decides to spurn the Clippers and leave as a free agent this summer.

But a win Saturday could also prove to be a turning point for this group. They would likely be favored in a second-round matchup with the Houston Rockets. Winning that series would send them to their first conference finals. It would be the kind of step forward the team has been looking for after seemingly hitting a ceiling the past three seasons.

Although the Clippers have won two Game 7s in the first round the past three seasons, a win Saturday would be bigger than both, largely because of the team they are facing. The Spurs are the gold standard by which teams in the NBA are judged. Vinny Del Negro, who played under Gregg Popovich in San Antonio, used the Spurs as his blueprint for success when he coached the Clippers during the first two years this roster's core was together. It’s also a blueprint that Doc Rivers, who also played in San Antonio, isn’t shy about admitting he has been attempting to duplicate with the Clippers since he arrived two years ago.

“They are the best,” Rivers said. “San Antonio is the benchmark. They're clearly, in my opinion, the franchise everyone wants to be. They've done just an amazing job on and off the floor with the way they pick their players. They have been the model.”

It’s way too early to say the proverbial torch would be passed if the Clippers knock off the Spurs, but it’s hard not to think about the league’s past and future while watching Blake Griffin and Tim Duncan square off against each other in the fourth quarter of games in this series.

“They are a great team in every sense of the word,” Griffin said. “I don’t think you can look at a team over the past 20 years or so that has been better. Duncan is a great player and one of the best players of all time. They have been in this situation. They went into a Game 7 with Dallas last year in the first round, and they ended [up] winning the whole thing. They have been in this situation, and they know not to panic.”

Three years ago, the Clippers saw firsthand what kind of a machine the Spurs can be, as San Antonio swept them out of the playoffs following their Game 7 win over Memphis. It was the first postseason Paul, Griffin and Jordan experienced together in Los Angeles, and their growth since then is evident in the way they fought back from heartbreaking losses at home in Games 2 and 5 to earn big road wins in San Antonio in Games 4 and 6.

“We’re so much more resilient now,” Jamal Crawford told ESPN.com. “We have so much to draw from now, in the past having been in these situations and not willing to settle and not giving in and not letting go of the rope, as Doc says. We’re going to hang on, and we believe in each other. He has confidence in all of us, and we have confidence in him.”

Rivers doesn’t break out the motivational tools as much as he used to, but before the series, each player was given a sheet of paper with 47 predictions from analysts around the country on the Clippers’ first-round series against the Spurs. Only one had the Clippers winning. He told them that if they kept “pulling the rope together” as a team and not letting go, they would put themselves in position to win the series and get to places they had never been before.

“I have been saying it all year: This team is tough,” Rivers said. “They are mentally tough. We hear all of the stuff about them, but this team is mentally tough. We have got to come and do it again. This series in some way should go seven [games]. It is almost like it is right. That is what should happen in this series, and it is.”