Steve Nash is an efficiency expert

Steve Nash can be tough on coaches.

Scheming to stop his relentless pick-and-roll game often leaves even the best tacticians futilely scribbling on whiteboards.

“The agony he caused before games, during games and after games trying out how to figure out how you were going to do it better ... “ former New York Knicks and Houston Rockets coach Jeff Van Gundy said, his voice trailing off, “He’s taken years off coaches’ lives.”

The newest Laker has also left heartache in his wake.

One of the most difficult losses that Don Nelson endured in a 34-year, Hall of Fame coaching career involved Nash leaving the Dallas Mavericks in the summer of 2004 to sign as a free agent with the Phoenix Suns.

“It deflated my desires there because he was my favorite player,” Nelson recalled in a phone interview from his home in Maui. “To lose him killed me. I tried my best to deal with it. It’s not that I stopped trying or anything, but there was a little something cut out of my heart losing Nash.”

Now there’s presumably a massive bounce in Lakers Coach Mike Brown’s step after Nash agreed Wednesday to a three-year, $27-million contract as part of a sign-and-trade deal with Phoenix.

Brown can’t comment until the free-agent moratorium ends Wednesday, but Kobe Bryant was ebullient when the Lakers star met with reporters Friday in Las Vegas after Team USA’s first practice in preparation for the Olympics.

“He gives us a much, much better chance,” Bryant said of the Lakers’ title hopes.

Those who have coached Nash say the two-time most valuable player does more than provide Bryant with a dynamic point guard, something that has been missing for most of his 16 seasons with the Lakers.

“It really goes beyond that,” saidMike D’Antoni, who coached Nash in Phoenix from 2004 to 2008. “The way Steve is as a teammate, the way he sets the tone, the way the team kind of takes on his persona. As a coach, that’s the best thing in the world. It’s easy to coach. He’s taking care of the chemistry. You just coach.”

Of course, it’s hard not to be popular when your primary focus is getting others the ball.

And Nash, 38, has done it better than anyone besides Jason Kidd since turning pro in 1996. His 9,616 assists rank fifth on the NBA’s all-time list, and he has led the league in that category in each of the last three seasons and in six of the last eight.

He’s hardly one-dimensional, though.

Nash is routinely among the top three-point shooters in the NBA (career 42.8%) and is second all-time in free-throw accuracy.

“He’s an unbelievably efficient offensive player,” said Van Gundy, who is now an analyst for ABC and ESPN. “You just don’t see guys shoot 50%, 40% from three and 90% from the line and make the passes he can make. It’s pretty amazing.”

Van Gundy said he anticipated the Lakers would run far more pick-and-roll plays with the ambidextrous Nash, who always seems to be able to make the right pass to players cutting toward the basket in heavily congested areas.

Though the Lakers’ roster is configured differently than that of the Suns, who spaced the floor with three-point shooters, it does offers something Nash has never previously experienced: a pair of 7-foot targets in Andrew Bynum and Pau Gasol and an MVP teammate in Bryant.

“It’s a perfect scenario,” Nelson said. “Kobe really needs someone to get him a shot every once in a while. He’s one-on-two about half the time.”

Nelson said Nash’s game hasn’t changed much since the veteran coach convinced him to become more of a scorer during his six seasons with the Mavericks from 1998 to 2004.

Not that it was an easy sell.

The pass-first point guard was a reluctant shooter, Nelson said, who modeled his game after John Stockton, the NBA’s all-time assist leader. The coach told Nash that he was a better shooter than the Utah Jazz legend and needed to score more to help Dallas win the Western Conference.

“I was trying to get him to be a 20-10 guy,” Nelson said, referring to his proposed breakdown of averages for points and assists, “but he’s so unselfish that he could care less about the scoring. He would rather pass and have other people enjoy the moment of scoring.”

Nash eventually complied and his scoring average took a big leap, going from 8.6 points a game in his second season with the Mavericks to 15.6 points in his third season and 17.9 in his fourth.

Two years later, with the Suns, he won the first of back-to-back MVP awards.

Though Nash probably would never make it onto anyone’s list of top defenders, Nelson said the perception that he is a liability is overblown.

“How many point guards are great defenders anyway?” Nelson said. “You can count them on two fingers probably. There isn’t anybody who plays the angles better than he does, so he’ll be a very smart defender, but physically he isn’t going to be the best defender in the league.”

He could also be the smartest guy in the (weight) room.

Casey Jacobsen got a feel for Nash’s ability to maximize his physique during 6:30 a.m. workouts in the summer of 2004.

“He comes in the weight room and he does this crazy stuff with the Physioball,” recalled Jacobsen, the former Glendora High and Stanford star who played with Nash for half a season with the Suns before being traded to New Orleans. “He can stand on it and balance or you could throw him a medicine ball and he won’t fall down. It’s pretty incredible.

“He does everything with a purpose. He was the kind of guy that led me to question, why am I doing this and for what purpose? Will it help me get better in my position?”

Nash was an unassailable leader in the locker room, Jacobsen said.

“He’s a guy that can relate to every type of player,” said Jacobsen, who now plays for Brose Baskets Bamberg, a German team in the Euroleague. “And that’s a skill that you don’t always see. Some guys stick to their own or have a little clique on the team. He has good relationships with the coaching staff, the training staff and the players.”

Phoenix Coach Alvin Gentry helped Nash combat his advancing age last season by curtailing his minutes to 31.6 a game, his lowest average since his fourth NBA season.

Nash responded by averaging a double-double in points (12.5) and assists (10.7) for the seventh time in the last eight seasons. The Lakers are hoping for similar production after making what might be described as a pretty good move to acquire a player probably bound for the Hall of Fame.

“Not pretty good. Real good,” said D’Antoni, an assistant coach for the U.S. Olympic team. “I think he’s got a lot more in the tank. Having the possibility to compete for a title will stimulate him even further. I think it’s terrific.”

ben.bolch@latimes.com

Times staff writer Mike Bresnahan contributed to this report.