If you have the best record in baseball in mid-August, as the Washington Nationals do now, what is your chance of being in the World Series or winning it? I expected this simple exercise to show that it’s too early to think about October or count even a single unhatched chicken. But I was wrong.

Since wild cards arrived in 1995, the team with MLB’s best record on Aug. 15 went to the World Series in eight of 17 seasons — almost half. That team won the World Series in five of 17 years — almost a third.

It’s a small data sample, and the playoffs now include more wild cards. The MIT math faculty might say the true odds of a World Series visit for a team in the Nats’ position is 1 in 3 and maybe 1 in 5 to win. But that’s the ballpark.

The Nationals now have a 98.6 percent probability of making the playoffs, according to coolstandings.com. Feel free to round off to 99. If they go 22-22 the rest of the way, they’ll finish the regular season with 95 wins. If they go 15-29, they’d probably still snag the last wild-card spot. There are times to be sensible and, once every few generations, times to yell until you pop a vocal cord. Frankly, this is the latter.

So if you want to get excited, at least until a losing streak or injuries change the mood, I can’t stop you. A pennant race is about to come to D.C. for the first time since World War II. And the team with the best record in baseball has “Washington” on its uniforms for the first time since 1933. The Atlanta Braves, fourgames behind the Nats in the NL East, come to town for their final visit next Monday through Wednesday. The last time there was a series that important, Nats owner Ted Lerner, 86, was 7 years old.

One key person knows exactly how realistic the Nats’ chances are right now. Asked how Stephen Strasburg’s shutdown would impact the Nats’ year, Manager Davey Johnson said: “A lot of our guys have been shut down this year, through injury. We’ll overcome it.” Period. The manager’s been ahead of the curve in Nats analysis all along. He’ll brook no low-expectation excuses now.

After the Nats beat the Giants in San Francisco on Wednesday, finishing an 8-2 road trip, Johnson was asked if his team had gained confidence through its recent success. That is like asking Houdini if he thinks his same old tricks will still fool people. Johnson’s teams always have confidence and if they don’t, he gets new players who possess it. It’s an old trick, but one with a long record of success back to Davey vs. Goliath.

“They’ve been confident all year. The hard part was early in the season — for two months we had nothing but nail-biters. We were banged up,” Johnson said. “We’re getting healthy. We’re getting in the fun part of the year. Everything is magnified in a pennant race. And these guys are primed for it.”

Primed for it. Does he write this stuff out and memorize it, then pretend he’s just riffing and drawling? Or is 50 years of proper baseball breeding just so deep in him that he hits the right notes and avoids wrong ones by nature?

This spring, I asked Johnson what the most important thing was in managing. “Be right,” he shot back, laughing. “That’s the job. The more you’re right — in game decisions, in player evaluations — the more you win. And the more your players believe that you’re right — and right about them.”

Johnson has been hotter than pocket aces since February. No one, not even General Manager Mike Rizzo, has seen the team’s immediate future so clearly. Before the first spring game, he’d compared his entire roster — position by position, right down to Bobby Ojeda’s stuff vs. John Lannan — to his ’80s Mets powerhouse. “This team has more talent. I can see it,” said Johnson, who’d studied the club for two years. “But right now, it’s still potential.”

In the last five weeks, that potential has started turning into reality. As the Nats played 35 games in 34 days and won 24 of them to get on pace for 100 wins, they’ve changed the basic reality of where they stand in baseball.

At the trade deadline, the Phillies and Marlins quit on 2012, dealt away stars for prospects and, in doing so, made themselves less appealing destinations for future free agents. They acted like teams that, in their closed-door heart of hearts, know the next couple of years in the NL East belong to the Nats and Braves. The Madoff-ed Mets, buried under bad contracts, are worse off.

In public, the Phils and Fish will talk bravely. But only actions speak. You can’t untrade Hanley Ramirez, Omar Infante, Anibal Sanchez, Hunter Pence, Shane Victorino, Joe Blanton and others. You can chat up your chances to sign Michael Bourn, but unless you vastly overpay like the Nats did for Jayson Werth, he’s not coming. He sees the standings. The Mets are dying to dump Johan Santana’s and Jason Bay’s contracts. No takers. If all this gives you whiplash, join the club. The Nats are now among the “Haves.”

Maybe things won’t work out as Johnson expects. But his mischievous expression at the road trip’s end seemed to say, “I know something you don’t know.” Maybe it’s that, of the Nats’ last 44 games, 27 are at home and 28 against teams that are at least six games under .500.

Maybe having Thursday off, plus four more days off on tap, ensures that the Nats will have proper stretch-run relief. The dog days and short-handed months may be ending. Key stars such as Michael Morse, Ian Desmond (due back Friday), Werth, Drew Storen and Ryan Zimmerman have had so much rest the Nats have one of baseball’s freshest everyday lineups.

Maybe it’s pondering all the young arms and bats that’ll be called up on Sept. 1. Johnson loves a deep bench. His will soon be bottomless. He even hinted Anthony Rendon might arrive: “That stroke will hunt,” Johnson said.

The Nats as a group are now dogs that will hunt.

All five of their starters are in the top 13 in the National League in average fastball velocity. Rookies flourish. When Desmond was hurt for 25 games, rookie Steve Lombardozzi played every day, hit .308 and duplicated his 2011 statistical “slash line” from the minors.

The team’s hidden improvement is its defense on batted balls. Three years ago, the Nats were, by miles, the worst — with the most errors (143) and unearned runs (83) in baseball combined with the third-worst defensive efficiency rating in the National League. (That’s the ratio of defensive outs to defensive opportunities.) They got to nothing; dropped it if they did. This year, they’re on pace for only 93 errors, 41 unearned runs and are No. 1 in baseball in defensive efficiency (range). They get to everything; miss little.

Baseball seldom lets “giddy” last for long. Sooner or later, the Nats are headed toward heights where first-timers, and even vets, sometimes can’t get their breath. “Remember to breathe” is not a late-season joke but a basic tip.

For now, it’s still only August, so just open your lungs and gulp it all in. The baseball air in Washington is the freshest and sweetest in 79 years.

For previous Thomas Boswell columns go to washingtonpost.com/