DALLAS — When the Warriors’ road trip concludes Monday in Minneapolis, Shaun Livingston will have played as many games for Golden State as he has for any other franchise during his 12-year NBA career.

His 145 games with the Clippers from 2004 through ’07 were filled with the promise of a lanky point guard, the likes of which the NBA had not seen. His 145 games with the Warriors will have been the fulfillment of that potential a decade later, having completely remade his career.

In between his two longest tenures, Livingston suffered one of the league’s most gruesome injuries ever — a left knee injury so severe that amputation was considered. In between his two longest tenures, Livingston has worn eight other NBA jerseys.

In between his two longest tenures, Livingston learned this:

“Don’t let them tell you what you can’t do,” he said. “Make them pay you for what you can do. I’m not a three-point shooter, and I’m not viewed as a perimeter player. People always want to pigeonhole you.

“But I like to think about what I can do to help a team win.”

That idea was imbued in him by Kevin Garnett during a one-year stay in Brooklyn. Livingston picked up other life- and career-changing advice from Scott Brooks, Jason Kidd, Flip Saunders and Erik Spoelstra during a seven-year whirlwind that whisked him through Miami, Oklahoma City, Washington, Charlotte, Milwaukee, Washington and Cleveland before Brooklyn.

Once he stopped trying to be the one to change a franchise, he could become the one to complete a franchise.

“Sometimes guys don’t want to do it. Some guys aren’t capable,” Livingston said. “It’s about your mind-set. You have to use your IQ to figure out how you can help a team. I can’t put up 20 shots like I used to, but I can stick in this league and make a career out of it. I can figure out whatever it takes to help teams win games.”

A year after the Warriors tried Toney Douglas, Nemanja Nedovic, Kent Bazemore, Jordan Crawford and Steve Blake before settling on swingman Andre Iguodala handling the backup point-guard duties, they signed Livingston.

He stabilized everything. His 3.07-to-1 assist-to-turnover ratio is seventh among players with at least 50 games this season.

If the Warriors go two or three possessions without a basket with him in the game, you can bet Livingston is driving to the baseline for a turnaround jumper or getting to the free-throw elbow for a shot he rarely misses.

Opponents know that, too, but they can’t stop it. At 6-foot-7 and with point-guard handles, Livingston can get anywhere he wants on the court and shoot over any defender.

Livingston is shooting an absurd 48 percent on pull-up jumpers, because he doesn’t shoot from anywhere but his spots. He’s shooting a ridiculous 52 percent when he’s defended within 2 to 4 feet, because he knows no one can block his shot.

“You can game plan for it, but if I’m getting to my spots, your game plan doesn’t really work,” Livingston said.

Ask Warriors executive board member Jerry West, general manager Bob Myers or head coach Steve Kerr about the backup point guard and within the first sentence, each will include praise of Livingston’s IQ.

Livingston is averaging 6.1 points on 53.1 percent shooting this season, and the Warriors outscore opponents by an average of 2.3 points per game when he’s on the court. Against the league’s best teams — San Antonio, Cleveland and Oklahoma City — Livingston is averaging 10.2 points on 74.3 percent shooting, and the Warriors are outscoring their opponents by 8.3 points per game when he’s on the court.

After the Warriors fell behind Memphis 2-1 in last season’s Western Conference semifinals, they outscored opponents by 90 points during Livingston’s minutes in the postseason’s final 14 games.

“I have always believed this: If you win, everybody looks good,” Livingston said. “There are going to be guys who get more attention, and that’s OK. Andre (Iguodala) might not get the MVP without all of the attention paid to Steph (Curry). I’m sure we make the game easier for Steph, at times.

“We all serve a purpose.”

Rusty Simmons is a San Francisco Chronicle staff writer. E-mail: rsimmons@sfchronicle.com Twitter: @Rusty_SFChron

Friday’s game

Who: Warriors (61-6) vs. Mavericks (34-34)

When: 5:30 p.m.

Where: Dallas

TV/Radio: CSNBA/680

What to watch for

The Warriors lost 114-91 on Dec. 30 in Dallas, with Stephen Curry sitting out because of a bruised left shin. This marks the first time the Warriors have returned to a place where they’ve lost this season.

At 29-6 away from home, the Warriors have the NBA’s best road record and have set the franchise mark for road wins. Only 21 teams in NBA history have won as many road games.

Draymond Green’s week of top-level power-forward matchups continues. During the past six games , Dallas’ Dirk Nowitzki is averaging 25 points on 52.4 percent shooting and seven rebounds.

Dallas has lost six of its past seven games to fall into the Western Conference’s eighth spot. The Mavericks have lost by fewer than four points in three of the games.

Dallas forward David Lee averaged 16.7 points and 9.3 rebounds per game in five seasons with the Warriors.

— Rusty Simmons