Joc Pederson doesn’t relish the attention generated by his climb from Palo Alto High School to the Los Angeles Dodgers. He also wanted to include his brother, Champ, when he was honored at the Santa Clara Hot Stove Banquet in January.

So there went Champ Pederson, cheerily stepping to the podium to speak on behalf of his “baby brother.” Champ has Down syndrome and does relish attention — and he talked passionately to the crowd of more than 500 people, preaching baseball’s value in coming together with friends and urging his audience to play every game with joy and verve.

Champ received a standing ovation when he finished.

“He stole the show,” said Tyger Pederson, his other brother. “People can feel his emotions — they’re drawn to him. Almost every time he speaks, people are cheering or crying.”

As the Giants and Dodgers renew their rivalry Monday night, it’s worth knowing the family story behind the center fielder in blue. Joc Pederson not only carries Champ’s deep influence, but he also comes from a Bay Area clan of athletic renown.

No fewer than three Pedersons — dad Stu, Tyger and Joc — were drafted by the Dodgers. Stu played in eight games for Los Angeles in 1985; Tyger played for San Rafael and Vallejo in a Bay Area independent minor league this past season; and Joc, before slumping the past two months, smacked 20 home runs in the first half to make the National League All-Star team.

Even so, the family’s best athlete might be younger sister Jacey, who has spent several years playing for U.S. national youth soccer teams. She’s a senior at Palo Alto High and will play next year at UCLA.

Champ also has excelled athletically — he won Special Olympics gold medals in swimming, bowling and basketball, and he’s since become an avid golfer. Now, as Joc’s rise to prominence has given Champ a wider platform, he’s not shy about speaking publicly on behalf of people with disabilities.

The Dodgers, for instance, invited Champ to speak last month at the opening of a handicap-accessible field in Los Angeles. Joc Pederson also is sponsoring a luncheon in October for Best Buddies, an international organization dedicated to helping people with intellectual and developmental disabilities. Champ has been involved with Best Buddies in the Bay Area.

Beyond this, Joc and Champ clearly have a strong connection. Champ joined his brother on the field at the Home Run Derby in Cincinnati in July and also traveled to Los Angeles to spend a week with him during the season.

Joc is the one hitting home runs in the major leagues, but he finds inspiration in Champ.

“It’s just being around him — how happy and passionate he is, his positive attitude and outlook on life,” Joc said in a recent phone interview. “You don’t get to choose the cards you get.”

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The Pederson family home includes a motivational sign above one kitchen door — “Dream Big” — and a batting cage wedged into the cramped backyard.

Baseball always was a central part of Stu and Shelly Pederson’s life together — they went to Mexico on their honeymoon, because that’s where Stu was playing winter-league ball. They also traveled around the U.S. during his 12 seasons in the minors, from Lodi and San Antonio to Albuquerque and Syracuse.

They ultimately returned to Palo Alto, where Stu grew up, to raise their family. Champ is the oldest (he turns 28 on Friday), followed by Tyger (26 in October), Joc (23) and Jacey (17).

Joc Pederson doesn’t remember much about going to occasional Giants games as a kid, aside from the rubber chickens that fans hung on the right-field wall when opposing pitchers walked Barry Bonds. Shelly figures that’s because Joc was more interested in eating licorice and running around the ballpark, like a typical little boy.

Tyger was a better athlete than his younger brother for most of their childhood; he played baseball at the University of the Pacific. Then Joc hit a growth spurt, on his way to 6 feet 1 and 215 pounds, and zoomed into another realm.

All along, both boys (and later Jacey) embraced Champ. Joc coached his basketball team in the Special Olympics, and Tyger was his bowling partner. Champ attended the same schools as his brothers while growing up, taking some special-needs classes in high school.

Champ’s developmental delays with speech put him on a parallel path with Tyger, who is two years younger, and probably brought them closer.

“They kind of fed off each other with some milestones,” Shelly said. “They hung out together, and then Joc came along and tagged along. They’ve always been an intact unit.”

This meant occasionally standing up for Champ when other kids pointed out his differences. It didn’t happen often, but Tyger and Joc vigilantly included Champ in most activities.

The boys’ message, as Stu put it: “This is my brother. If you accept me, you have to accept him. We come as a package. We come as a family.”

As Shelly sees it, part of this comes from outsiders’ tendency to view people with disabilities at face value. If they don’t know or understand Champ, she reasons, then they don’t realize his sharp wit and abundant sense of humor.

These traits were on full display during a recent conversation at the family home. At one point, asked about his relationship with his siblings, Champ offered a sly grin toward nearby Jacey and replied, “I’m really close to my sister. I love her the most.”

On his time in high school with Tyger: “I was the popular one.”

On his Special Olympics success: “I conquered the world, pretty much.”

On his two years in junior college: “I wanted to be a party boy and join a frat.”

And on his interest in golf: “My goal is to win the green jacket at the Masters.”

Good-natured quips aside, Champ is seizing the openings created by Joc’s ascent with the Dodgers.

Last week, New Era — with whom Joc has an endorsement deal — released a special line of baseball caps with “Live Like a Champ” stitched across the front. The company will donate 31 percent of the proceeds (to signify Joc’s uniform number) to Best Buddies.

That organization matches buddies with kids who have disabilities, and also helps adults such as Champ with job placement. He recently had an interview at Facebook, arising from a gentleman he and his parents met at the All-Star Game in July.

Champ works a few part-time jobs for now, including as an usher at Stanford sporting events. But he enjoys nothing more than giving motivational speeches.

Tyger’s baseball teammates at UOP came to understand Champ’s impact in 2013. He spoke to the Tigers before a game, and they won. Then it happened again. Before long, then-coach Ed Sprague (a onetime Stanford star) and his players viewed Champ as their good-luck charm.

He started traveling with the team, rooming with Tyger on the road and encouraging the players as a group before every game. Those talks turned into “The Book of Champ,” a collection of his speeches.

That experience was cool and all, but it didn’t match Champ’s reaction when he met Angels first baseman Albert Pujols in March. They crossed paths at the screening of a movie, “Where Hope Grows,” partly about baseball and mostly about Down syndrome.

Pujols later sent Champ a signed jersey, through Joc. The gesture carried special meaning because Pujols’ daughter, Isabella, also has Down syndrome.

“I know how special and loving those kids are,” Pujols said. “Champ is awesome.”

Still, Champ sometimes struggles to balance brotherly loyalty with his upbringing as a Giants fan. Once last year, in a conversation with Dodgers outfielder Andre Ethier, Champ enthusiastically referred to the Giants as “my team.” Ethier gently reminded Champ his brother plays for the Dodgers.

Shelly Pederson routinely fields Giants-Dodgers questions from friends who can’t seem to separate Joc’s success from the bitter rivalry. Face it, folks: He wears Dodger Blue, and the family will not root against its own.

“All my friends hope I do well and the Giants win,” Joc said. “I’m used to it.”

Those childhood pals will find themselves in that familiar predicament this week at AT&T Park. They will root for Pederson but not the Dodgers.

Peer past these allegiances, though, and a deeper tale emerges: one of a tight-knit family shaped by its oldest child, who marches through life with a smile on his face no matter the challenges.

“Champ was always the glue — he brought the family closer,” Tyger said. “He just shines his light on everybody.”

Ron Kroichick is a San Francisco Chronicle staff writer. E-mail: rkroichick@sfchronicle.com Twitter: @ronkroichick