One team’s excess is another team’s ecstasy. The Giants dumped Gerardo Parra after a month, and now he’s headed to the World Series as the Washington Nationals’ inspirational leader and dugout celebration administrator.

The Nationals are a loose bunch, and Parra’s a big reason. Bruce Bochy loved him in San Francisco for his positive vibe and clubhouse jollity, and Parra has taken his act to the nation’s capital, albeit with a big difference: The Nationals still are playing.

Parra has appeared in just three of the Nationals’ 10 postseason games, going 1-for-3 as a pinch-hitter, but he remains influential. The Nationals lacked veteran leadership before he arrived in early May, and he has taken the role seriously.

And not so seriously.

Parra is at the center of the Nationals’ dugout craze that features dancing, hugging and even shark clapping, a spin-off on Parra’s “Baby Shark” nickname, which wasn’t a deal in San Francisco because his teammate was Daddy Shark, Jeff Samardzija.

Plus, silliness doesn’t play on a losing team. On a winning team, it’s everything. It’s the rally cry. Check the 2010 Giants. So when Parra walks to the plate as the children’s song “Baby Shark” blares over the speakers, it’s not annoying for Nationals fans. It’s embracing. They extend their arms, one over the other, and do the shark clap.

So do teammates, an amusing ritual. If the jingle is good enough for Parra’s 2-year-old daughter, he figures, it’s good enough for him. Parra ups the ante by hanging a stuffed baby shark from the dugout rail, and his strangely tinted glasses are all the rage.

Then there are the hugs. Giants fans are familiar with Buster hugs, which come after winning a postseason series or finishing off a no-hitter. They’re demonstrative and quick. By comparison, Parra’s are long and tender.

This hug never wanted to end pic.twitter.com/K7WYVSYk8f — Dan Steinberg (@dcsportsbog) October 15, 2019

Pitcher Stephen Strasburg came out of Game 3 on Monday, and Parra greeted him with a two-armed embrace and rested his head on Strasburg’s shoulder for several moments. Anibal Sanchez joined the hug-fest, as did other teammates, which put a rare smile on Strasburg’s face.

“I’m not much of a hugger,” he said, “but they kind of just surround me. So I just have to take it.”

All the way to the World Series.

John Shea is The San Francisco Chronicle’s national baseball writer. Email: jshea@sfchronicle.com Twitter: @JohnSheaHey