VIERA, Fla. — The Washington Nationals’ biggest offseason addition is not Daniel Murphy or Ben Revere. The instant bang, maybe a large one, will be pitching coach Mike Maddux, whose impact on previous staffs in Texas and Milwaukee was legendary.

In 11 seasons before Maddux arrived in Texas in 2009, the Rangers gave up 888 runs a season. MLB orthodoxy: “It’s impossible to pitch in Arlington.” Hitter and homer heaven. In Maddux’s seven seasons, they gave up 707 — 181 fewer runs a year. Or about an additional 20 wins a season.

In 2011, the Rangers allowed 290 fewer runs than they had in 2008 and went to their second straight World Series. Maddux did it without new free agents or trades for stars. His rotation was C.J. Wilson, a 27-year-old reliever with a 6.02 ERA when Maddux got to town; obscure Colby Lewis, plucked from Japan; less-than-mediocre journeyman Scott Feldman; and a raw kid named Tommy Hunter.

In Maddux’s six years in Milwaukee, the Brewers allowed 77 fewer runs a season than they did in the previous seven. The Brewers went from 106 losses before he came to 90 wins and the playoffs in his final season. He was given only one new star: a half season of CC Sabathia, who’s never had an ERA under 3.00 in any season anywhere — except in 17 starts with Maddux, when he went 11-2 with a 1.65 ERA.

That’s 13 straight seasons of doing what should be impossible. Nobody thinks any coach or manager is worth 20 wins a year in Texas or eight in Milwaukee. But the Nats, instead of getting stuck on “What exactly is he worth?” went straight to “Forget the money. Get that guy!”

Pitchers Yusmeiro Petit, left, Joe Ross and Max Scherzer talk to pitching coach Mike Maddux during training camp at Space Coast Stadium in Viera, Fla. (John McDonnell/The Washington Post)

[Nationals hire Mike Maddux as pitching coach]

For the Nationals, that’s a sea change. The first thing Bryce Harper said here was, “I can’t be more excited to have Dusty Baker, Davey Lopes and Mike Maddux here.”

If the Nationals play with more confident relaxation because of Baker, with more stolen bases because of Lopes and with fewer allowed because of Maddux, it will be because the team finally decided to spend what it takes to get the best teachers.

Since the Lerners bought the Nats, they’ve studied where money can be wisely spent and where it’s superfluous. The family’s been slow to grasp that managers and key coaches have significant value, even though it’s harder to quantify to homers and ERAs. And to get those men, you have to pay them well. The Nats never have. For Max Scherzer, $210 million, yes. But more than $3 million total for a manager and two coaches, no. In some years, a third that much.

With their payroll down by $50 million this season, the Nationals have followed the advice that they’ve been hearing for a decade from baseball people. When the idiot Rangers fired Maddux after last season, baseball rendered its collective opinion. Maddux’s phone blew up with six offers in four days.

Because the Nats pounced fast, and to some degree independent of their manager search, some think Maddux may be, in part, an insurance policy, protecting Nationals pitchers from Baker’s reputation for blowing up arms. But that’s not how it’s playing here, where the pair seem to walk together constantly.

“Dusty and I spoke one time in a dugout a few years ago. Right away, we were like-minded. Maybe we’re two peas in a pod. We just hit it off,” Maddux said this week. “We’re both from military families. Both baseball lifers. I said, ‘Be fun to work together someday.’”

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Now the Nats can’t wait to learn from the older brother of 355-win Hall of Famer Greg Maddux. The pencil-thin Mike, who could hide behind a flag stick, pitched 15 years in the majors and won 39 games. If he had to go to the minors (12 years), he went. But he kept coming back.

“Mike might’ve had the toughest job in baseball. It’s hard to compete if your brother is Albert Einstein,” said Bronson Arroyo, a 15-year veteran. “Mike’s carved out a really respected place in the game for himself.”

Maddux’s approach combines many elements. First, there’s “the mental game of accountability,” mastering every detail of your job. “Greg always said fielding practice is not punishment. It’s an opportunity — to hone your craft,” said his brother. “You don’t have to do it; you get to do it. ‘Seize the moment.’ ”

Mental toughness, a refusal to lose focus or be distracted by breaks, is a core tenet. “It’s not a beauty pageant. It’s okay to be ugly,” said Maddux. “But it’s a W or L next to your name. Be responsible for it. Take charge.”

[What to expect from the Nationals’ rotation in 2016]

GM Mike Rizzo, who pursued and signed Maddux, considers him a master of pitching mechanics right down to the varying pressure of each fingertip on the ball. “In a side session I threw a bad curve that just spun,” said lefty Sean Burnett. “He said, ‘See your hand out directly in front of your nose’ at the release point. I’d never heard that in my whole career. The next pitch, my curveball was back.”

Maddux and his pitchers love to analyze opposing lineups. “Where do I get my outs?” said Maddux. “Sometimes the best hitter can’t hit you — maybe he just doesn’t ‘see’ you right. Manage the lineup. You’ve got to pick your fights.”

Late movement on a pitch beats mere speed. “The highway is littered with velocity,” said Maddux. Of PitchFX, which shows how much every pitch breaks to the inch, Maddux says, “It’s not in 3-D. When does it move?” So the Nationals will hear about “extension” for late movement as well as grip or pressure points to get different kinds of swerve. All of it while seldom changing a man’s basic mechanics, which Maddux thinks are often a unique, personal gift.

Finally, don’t let hitters dig in. This is Nolan Ryan’s guy, after all. Many modern hitters have to be attacked inside to open up the rest of the plate. The minors seldom teach it.

“The minors are not a get-rich place. Hitters are diving across the plate. If you hit one, it causes a ruckus,” Maddux said. “They don’t want fights in the minors. So the pitcher gets suspended and fined five days’ pay. That makes guys reluctant to go inside.” Mike isn’t reluctant to teach them how. “It’s just part of the game.”

A game that people named Maddux seem to understand remarkably well.

For more by Thomas Boswell, visit washingtonpost.com/boswell.