The Post Sports Live crew recalls the highlights from the year in Washington sports. (Jayne Orenstein/PostSportsLive/The Washington Post)

Have the Washington Nationals lost their minds? Were they clobbered in the head with a bench? Or are they quietly exploring the potential in what may be baseball’s next semi-secret weapon: the collective power of the game’s least-respected citizens — the “scrubs?”

This month, the Nats signed Nate McLouth for $10.75 million over two years as a fourth outfielder. Last year they added Scott Hairston, who’ll make $2.5 million as fifth outfielder. They’re rumored to have interest in catcher John Buck ($6 million last year) and corner infield slugger Eric Chavez ($3 million), who won six Gold Gloves at third base. They just traded away versatile Steve Lombardozzi, which opens a path for Danny Espinosa, who has had a 20-homer and 20-steal year, to be their utility man.

If the Nats do land Chavez, whose on-base plus slugging average in 506 at-bats the past two years (.829) edges Ryan Zimmerman (.817), or Buck, who was once an all-star, they might have so much talent on the pine that many in baseball could say, “They misallocated cash.”

More likely, the Nats think they’re on the verge of maximizing a disguised team-building edge that too few franchises understand: Every year, MLB’s bench “bums” get to the plate more often than each team’s top three hitters — those “heart of the order” heroes.

Last season, the three top hitters (by OPS) on five NL East teams batted 6,990 times combined. But the players who came off the bench, swarms of them, many almost anonymous, had 8,734 combined at-bats. Pitchers batted 1,691 times, too. Combined, that’s 10,425. So the guys you hope hit when you’re in the pizza line bat far more often than the stars.

Yet players such as Robinson Cano or Jacoby Ellsbury — both at least 30 years old — are getting $240 million or $153 million contracts, while solid players such as McLouth, Hairston, Chavez and Buck are stacked like unwanted cordwood with few takers.

Baseball is constantly looking for the next subtle edge, the newest way to squeeze two or three more wins a year out of a tiny advantage. Maybe it’s in defensive positioning or Fielder Independent Pitching that spots pitchers whose bad luck may turn.

But one of the biggest advantages, especially in the National League, hides in plain sight. Guys who call themselves the Goon Squad or the Stunt Men or “scrubeenies” are constantly asked to sub, sometimes for a month or more, for stars. And their late-inning pinch-hit spots are often among a close game’s most crucial “high-leverage” at-bats.

Teams obsess over the glamorous work of upgrading their stars. But it’s just too boring, too devoid of credit, to improve the 10 to 15 players who rotate through most team’s benches in a season. Last season, the Nats used 15 bench players, in part because so many failed and had to be replaced. The last three years combined, the Nats’ bench has 4,733 at-bats to 4,650 for the team’s top-three OPS hitters in those seasons.

If this isn’t an opportunity to find “value at the margin,” what is? It’s incredibly hard to raise the slugging average of your 3-4-5 hitters by 50 points over their 1,550 at-bats, much less by 75 to 100 points. Yet bench production fluctuates wildly year to year. The Nats have learned the “deep” lesson the hard way. They benefited enormously from their Goon Squad bench in 2012, a gang that hit .255 and slugged .385 in 1,544 at-bats. Last year, many of those same players flopped as the Nats’ bench hit an awful .209 and slugged a pathetic .284. Can’t start a rally, can’t finish one, either.

Mull this: The slugging average of the Nats’ bench fell 101 points and thus poisoned the equivalent of three full player-seasons worth of at-bats. That’s how a team goes from 98 victories to 86.

Who was the surprise postseason team last year, the so-called Nats of ’13? The Pirates. They won 94 games for many reasons, but one big element was 14 players who came off the Bucs’ bench for the heavy duty of 1,942 plate appearances and hit .252 and slugged .394. Those “stiffs” beat the NL batting and slugging norms of .251 and .388.

Constructing a bench is hard work. Some potential candidates are very old. Some still think they’re still starters and balk at signing up for “bench” roles. So maybe you need to pony up $10.75 million. Some have a gimp or can’t hit certain kinds of pitching.

But here’s a partial list of men who slugged at, or far above, the MLB norm (.396) last season yet remain unsigned: Raul Ibanez (29 homers, but 41 years old), Chavez (.478, a steal at 32), Omar Infante (.450, have bat will travel), Juan Uribe (.438), Michael Young (2,375 hits but now a bench-level hitter), Lyle Overbay (.393), Mark Reynolds (.393), Jason Bay (.393), catcher Miguel Olivo (.392), Michael Morse (.381), Travis Hafner (.378) and Buck (.362). Backup catcher Wil Nieves (.369), an ex-Nat, also has learned to hit a little the past two years.

Are they very good every day players? No. But before you scoff, last year the O’s Nick Markakis slugged only .356. For reference, McLouth, who stole 30 bases, slugged .399 in ’12 and Hairston .414 with 10 homers in 157 at-bats.

The Nats have already fixed their biggest bench fear. The past two years, they’ve had major outfield injuries that cost starters more than 220 games. You respect patterns. Now the Nats should have a quality backup platoon. A tandem of McLouth (career .763 OPS vs right-handers) and Hairston (.806 vs. left-handers) could allow you to adjust to an injury to Denard Span, Harper or Werth. (Harper could play center, if needed.) New manager Matt Williams says he wants to give his starting outfielders more days off, too.

In another bench twist, if Espinosa remembers how to hit, you could see Adam LaRoche resting for 15 or 20 games against left-handers with Zimmerman at first base, switch-hitting Espinosa at second and Anthony Rendon switched over to third base.

Every NL East fan knows Freddie Freeman, Werth, David Wright, Mike Stanton and Chase Utley. But they, and their 3-4-5-hitting ilk, had almost 2,000 fewer plate appearances last year than the combined work of more than 50 obscure pine brothers such as Jordan Schaffer, Josh Satin, Darin Ruf and Cristian Yelich. Yet the ability or ineptitude of those subs creates a big gap in production between teams. The savvy Braves had the best ’13 bench, batting .263 and slugging .406. Next came the Marlins (.235, .334), the Mets (.222, 337), the Phillies (.204, .364) and finally the putrid Nats (.209, .284).

Contending teams are built around front-line players and stars. But they are finished by depth. If you want to know what the Nats are up to these days, they’re just — yawn — finding those final not-so-vital pieces of their bench after their bravura Doug Fister trade.

That’s their company line any way. Believe it if you want.

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