When Victor Robles caught the final out in center field, and fireworks exploded over South Capitol Street, M.L.B.’s vision for the city was illuminated: a perennial winner with a roster of stars in a ballpark that set off a neighborhood building boom.

“That was absolutely the dream,” said Jim Bowden, the Nationals’ first general manager after their move from Montreal. “When I came over, the team was owned by 30 clubs and run by the commissioner’s office. They wanted to find an owner that had the resources, lived in the D.C. area and had the pockets to build world championship-caliber teams.”

Under the principal owner Ted Lerner, the Nationals have spent lavishly, won consistently and watched new construction rise steadily around Nationals Park. But nervous tension in early autumn is also part of the team’s identity.

The playoffs have come to Washington five times in eight seasons, including Tuesday’s wild card showdown.

“The blueprint’s been pretty impressive,” Bowden said. “The only thing they’re lacking is winning a series and winning a world championship, which they’re still trying to do for Ted.”

This year’s effort seemed doomed through the first 50 games of the season. The Nationals were 19-31 through May 23, yet rallied to become the first team since the 1914 Boston Braves to finish with at least 93 victories after falling 12 games under .500. Those Braves beat the Philadelphia A’s in one of the greatest upsets in World Series history.

These Nationals are a hard sell as an underdog. Their payroll of roughly $195 million ranks among the highest in the majors, and their three top starters — Scherzer, Strasburg and Patrick Corbin — are signed for a combined $525 million.