Travis Shaw knows Dodger Stadium very well

This might be hard to believe for the newest wave of Dodgers fans, but there was a time, not too long ago, where the team did not win the National League West in any year, let alone in every year.

They once went eight years without winning the division. Those were dark days for kids to grow up and believe in the Dodgers, unless you were a kid who grew up at Dodger Stadium.

For that kid, Dodger Stadium was nirvana. It was “Take Your Kid to Work” day, every day.

That kid’s father, Jeff Shaw, was the closer for the Dodgers from 1998-2001, trying to get the team into the playoffs.

That kid, Travis Shaw, is an infielder for the Milwaukee Brewers. He returns to Dodger Stadium on Monday, trying to knock the Dodgers out of the playoffs.

“It’s pretty cool,” Travis said. “I remember everything about that place.”

“He was a park rat,” Jeff said. “He would just come and hang around.”

Jeff retired after his final season with the Dodgers. Travis was 11, and for those four years in Los Angeles, his parents agreed that he could be home-schooled for half the year so he would not have to miss out on his Daddy-Dodger time.

Travis shagged fly balls during batting practice, watched the Dodgers hitters take their swings in the indoor batting cage, took a few swings of his own when the hitters were done.

The Dodgers provided a play room for the sons and daughters of their players. Travis liked to hang out with Cade Kreuter, the son of Dodgers catcher Chad Kreuter, who let the boys use his seats.

“They would sit behind home plate, because there they could eat what they wanted,” Jeff said. “Then they would go back to the play room. They would be up and down. They would be all over the place.”

Travis said that, among the Dodgers players who were not his father, he was closest to Kreuter, pitcher Kevin Brown and infielder Alex Cora. That would be the same Alex Cora who now manages the Boston Red Sox, whom the Brewers could play in the World Series.

In 1999, when the Shaws were in Los Angeles, the Dodgers briefly employed an infielder named Craig Counsell.

Counsell now manages the Brewers, Travis included.

“I remember his dad very well,” Counsell said. “I don’t remember Travis. I’m sure I ran across him and patted him on the head.”

For father and son, the most indelible memories of their time with the Dodgers came in Seattle, where Jeff represented the Dodgers in the 2001 All-Star Game, in his farewell season.

Travis remembers shagging fly balls during the home run derby, and making out like a king in the memorabilia department.

“I have a game ball, signed by all the guys that were there that year,” he said. “I got a [Mark] McGwire signed jersey. And I got an Ichiro bat too. So I got three pretty good ones.”

Jeff remembers Travis on the field during batting practice, throwing baseballs to fans, over and over. Jeff did not much care, until Travis pointed out that he was in business.

The fans were wadding up $20 bills and tossing them at that cute young boy, so that he would throw them a ball.

“I’m going to keep throwing them up,” Travis told his father, “because I’m getting paid.”

Jeff and his wife made the trip from their Ohio home to Miller Park for the first two games of the National League Championship Series, attired in Brewers gear.

The Shaws will not attend the games at Dodger Stadium because they are in the process of moving. All three kids are out of the house now, so the time has come to downsize to a condominium.

Whether in person or on television, Jeff admitted, he gets nervous watching his son play.

“More nervous than in any game I ever played in,” he said.

Jeff said he pushed Travis to follow in his footsteps as a pitcher. Travis rebelled, so successfully that he made it to the major leagues as an infielder – as the Brewers’ regular third baseman for most of the season, as more of a second baseman and first baseman after the team acquired Mike Moustakas in July.

“I’d like to see him play against lefties a little more, but his numbers are just not dictating that right now,” Jeff said. “Counsell has been making all the right moves. Everything he has done so far has been spot on.”

Travis has been delighted to get congratulatory messages from some of his dad’s old Dodgers teammates, including catcher Paul Lo Duca and pitcher Terry Adams. He has marveled at his chance to pitch against one of his dad’s old Dodgers teammates, third baseman Adrian Beltre.

And, even though the Dodgers clubhouse he grew up in has long since been demolished and replaced with a new and improved version, his memories live on.

“It’s something,” he said, “that I will never forget.”

bill.shaikin@latimes.com

Follow Bill Shaikin on Twitter @BillShaikin