Dan Haren was a $13 million mistake, but the Nationals can correct it by spending more. (John McDonnell/THE WASHINGTON POST)

Baseball has always had a secret sauce for prosperous popular teams: money, in a light demi-glace of cash. It makes a long season taste better.

Washington has never had the experience of following such a team, one that has the wide fan support and, thus, the resources, to remain competitive when its offseason strategy and its in-season injuries don’t work out right.

That might change soon. In the next few weeks we may find out if the Nationals, who have a $13 million bust in pitcher Dan Haren and the next-to-worst offense in baseball, but just drew more than 140,000 fans to see the mundane Rockies, can make the transition to a team with the wherewithal, thanks to their fans, to execute mid-course corrections.

Just as the crowds grow at Nationals Park, boasting the biggest increase of any team in ’13, the air is steadily going out of the club that plays there.

This season the Nats’ average attendance of 33,894 is ahead of legendarily popular teams with national fan bases, like the Red Sox and Cubs. Washington has moved into the sport’s top 10 (ninth) for the first time since the quaint days when baseball only had 16 teams. Also impressive, only five teams — the avidly followed Giants, Cards, Red Sox, Phils and Tigers — fill their parks to a higher percentage of capacity than the Nats.

For decades, many asked how well Washington would support baseball. The answer appears to be: In D.C., you get the MLB attendance you deserve.

In many cities, a rise like the Nationals’ current spike hints at another jump to an eventual string of near-sellout years. That is, if the team plays well or, at least, does everything reasonable to contend and strengthen its bond with fans. Right now, the Nationals face an inflection point: just as they catch fire with the public after winning the NL East last year, how do they avoid dousing their prospects on the field? How do you revive a 37-38 year that has value in its own right but also has brand-building potential?

What moves can you make? And which do you avoid because you would have to trade away valuable players who could be long-term assets?

“Good crowds let the team make good money, and with good money you can get some good players when you need them,” first baseman Adam LaRoche said in his laconic way. “Our crowds are supportive and pretty patient. You don’t hear a lot of booing. Stay behind a player who’s struggling and they usually come around. They’ve come a long way from three or four years ago when I used to play [against the Nats] here. It’s a nice change.”

But it’s unwise to test patience and support to their limits. On Sunday, the Nats gave away 15,000 Bryce Harper bobbleheads and drew 39,307. Unfortunately, when you take the doll out of the box, it can’t bat third and play left field. For now, neither can Harper, who’s missed the last four weeks. At one point in a 7-6 loss to Colorado, the Nats’ outfield was Jeff Kobernus, Steve Lombardozzi and Roger Bernadina.

The Nats’ first, and also biggest need, is to find a fifth starting pitcher to replace Haren, who was put on the disabled list on Sunday with shoulder stiffness. Statistically, Haren was the worst starting pitcher in MLB this year, in ERA, homers allowed and other categories while always remaining a class act.

“Right now, I’ve got to wear Haren,” General Manager Mike Rizzo said. “My name is on it. There was a reason it was a one-year deal. But he’s a pro. He went on the DL last year and had a 3.58 ERA after he came back. The final verdict’s not in. We’ll judge it at the end of the year.”

The Post Sports Live crew discusses whether the Nationals can win a wild card spot without Bryce Harper in the lineup. (Post Sports Live)

More likely, we’ll be judging in July. By then, the Nats will have filled their rotation with (in order of probability) Taylor Jordan (6-0, 0.73 ERA at Class AA), journeyman right-hander and Princeton grad Ross Ohlendorf or a revived Haren. “We’re not afraid to call people up from AA,” Rizzo said. The best bet is probably that none of them look like a half-season solution.

That’s when Washington will probably find out if Rizzo can be as “creative and aggressive,” as he says he will be if the Nats still have major needs as the trade deadline approaches.

“Management has allowed me to do what I need to do,” said Rizzo, whose payroll is now up to $115 million. “We work through the process together. But they’ve really let me do what’s best for the franchise.”

If that continues, then the Haren demotion — sorry, injury — is probably the signal for future fireworks. Nobody knows exactly which pitchers will be on the trade market between now and the July 31 deadline. But everybody knows the high quality of the names that might be on the list.

Three clear candidates, all pitching well, all in their walk years for going-nowhere teams and all major Nat upgrades are the Cubs’ Matt Garza and Scott Feldman and the Marlins’ Ricky Nolasco.

Tougher gets, which would cost more in trade but are possible if their teams become sellers, are Brewers ace Yovani Gallardo (signed through ’14) as well as two former Cy Young winners, the Phils’ Cliff Lee (guaranteed $50 million in ’14 and ’15) and the Rays’ David Price, under team control in ’14 and ’15 but having a bad year and on a rehab assignment in the minors.

Unless a Nats minor leaguer, Ohlendorf or Haren somehow steps up quickly and forcefully, the Nats absolutely have to acquire one of the best pitchers on the market before the deadline. Those 33,894 fans, and trending up, know that no team always wins but, to stay interested, they need to know that their support is matched by the team’s commitment to contend, even in a year of high expectations, pressure, injuries and yada-yada-yada.

One of the blessings of high expectations is that problems are addressed more quickly and bluntly. The Nats sent Danny Espinosa to Class AAA and now have him playing shortstop, showcasing him for a trade. That unleashed rookie Anthony Rendon, 30 for 90 and the second baseman in perpetuity.

The Nats released Henry Rodriguez and Zach Duke. That revealed lefty Fernando Abad (1.42 ERA) and Ian Krol, the southpaw who looks like he’ll make the Michael Morse trade a steal — for the Nats. So far, Krol has fanned 12 in 82 / 3 innings and acts like the one hit and one walk off him were an oversight.

Washington baseball has moved to a new novel point in its history. Mediocrity, a goal for a century, is now unsatisfactory. When you stack the park for four days to see the Rockies, you can eat $13 million and not even belch. Now, we’ll find out what the Nats order for their next course.

For Thomas Boswell’s previous columns go to washingtonpost.com/boswell.