Seven of the 10 oldest teams in the major leagues made the postseason this year, which isn’t a shock since contending teams usually move to supplement youthful cores with free-agent veterans. The youngest teams to reach the playoffs this season — the Tampa Bay Rays (28), Oakland Athletics (27.9) and Minnesota Twins (27.8) — are in the bottom half of M.L.B.’s payroll rankings. The youngest teams in baseball — the San Diego Padres (25.8) were the youngest, and finished 70-92 — were rebuilding and had shed most of their more experienced, better-paid players.

Many players on the Astros, one of the most unapologetically analytics-driven teams, said they would not have won the 2017 World Series without Carlos Beltran, a designated hitter who was 40 at the time and hit .231 with 14 home runs, and Brian McCann, a catcher who was 33 and hit .241 with 18 home runs. Their production wasn’t commensurate with their combined salaries of $33 million, but they still added value.

Beltran, who retired after that season, helped young hitters learn to game plan against opposing pitches, while McCann, who retired after two seasons later, mentored young pitchers.

“It felt like a winning atmosphere,” said Astros shortstop Carlos Correa, now 25 .

“They gave us a lot of confidence and made us believe that we were the best team out there and had to compete like it,” Correa continued. “Having veterans on the team is huge. It helped the younger guys set the tone, and to speak when they had to speak in meetings or when the team is not playing good.”

The Nationals saw that firsthand this season. In late May, when they sat at 19-31, it was difficult to imagine them making the playoffs, let alone being up two games to none in the World Series against the juggernaut Astros.