“Believe me, I know the rivalry,” Cashman said Monday, “because the Dodgers were always on the losing end of it until ’81.”

Cashman was 14 then, growing up in Kentucky among fans of the Cincinnati Reds. He preferred the Dodgers, maybe to be different from his friends, he said Monday, but probably because he just loved their players. The infield of Steve Garvey, Davey Lopes, Bill Russell and Ron Cey played four World Series together in eight years.

The modern Dodgers had hoped similar success would follow their new owners’ spending spree, but the team lugs a 29-39 record into Tuesday’s game with the Yankees. Cashman, as the Yankees’ general manager, surely knows things could be worse.

His team is 38-31, trailing Boston and Baltimore in the American League East but still very much in contention. Cashman’s job is to keep the leaky ship bobbing along, which must be exhausting, even six weeks before the July 31 trading deadline.

“Man, I’ve been active already,” Cashman said. “They’re not really big splashes, but it seems like from midspring on, we’ve been on overdrive, mixing and matching. I’m always open for business.”

The patchwork Yankees led the division through the first eight weeks of the season, which was more than anyone could have expected. They lost their share of the lead on Memorial Day after the first of four consecutive defeats to the Mets, part of a five-game losing streak the Yankees repeated last week in California.

The best the Yankees can say about their recent trip west is that they escaped Oakland before the pipes at the Coliseum pumped untreated sewage into the clubhouse, which happened Sunday after the A’s played the Seattle Mariners. Even so, the stench of a losing streak in Oakland and Anaheim followed the Yankees home.

“A 4-6 record makes it seem better than it felt,” Cashman said, adding later, “We’re glad we’re off the West Coast.”

The Yankees are not quite as creaky as the infrastructure of the Coliseum — and, really, shame on Major League Baseball for refusing to let the A’s move to San Jose — but they are prone to regular breakdowns. They cannot play long without losing a major piece. Out West, it was Kevin Youkilis (back) and Mark Teixeira (wrist) going down again, joining Derek Jeter and Curtis Granderson among the players who just keep getting hurt.

The pitching, as a whole, is fine; heading into Sunday’s game, no team in the majors had more games holding the opposition to four runs or fewer. But the offense is sandwiched between Kansas City and Houston in runs per game near the bottom of the American League. Cashman said Teixeira was likely to be headed for the disabled list, and he sounded especially pessimistic about Youkilis, who is already there.

“Back issues usually don’t get better,” Cashman said. “They can, but they’re very debilitating.”

Youkilis had back trouble last year, but the Yankees signed him anyway, for one year and $12 million. Cashman said he felt comfortable about the deal partly because Youkilis’s old team, the Chicago White Sox, who presumably knew him well, had offered two years. In any case, the Yankees were desperate to replace Alex Rodriguez, whose hip has kept him out all season.

Rodriguez is scheduled to take simulated at-bats in Tampa, Fla., on Tuesday, Cashman reported, adding that Rodriguez took several rounds of batting practice Monday and fielded grounders to both sides. The dream of Rodriguez’s simply fading away may be morphing into something else.

Rodriguez’s production has steadily declined, and of course he is still a target of baseball’s steroids cops. His return is far from certain, but for all his baggage, the Yankees might actually need him again. As Cashman likes to say, Rodriguez still could be better than the average third baseman. For a below-average offensive team, that would help.

The replacements have done their part, and the Yankees cannot ask for more. Vernon Wells, who helped carry the team for weeks, now has the same basic numbers he did with the Angels last season: 56 hits in 243 at-bats, for a .230 average. Last season he had 11 homers and 16 walks; this season, 10 homers and 15 walks.

First baseman Lyle Overbay has also struggled, hitting .194 with no homers since the first day of the Mets series. Now the Yankees must lean on Overbay to replace Teixeira again.

“A lot of these guys were major contributors to us, in some cases in surprising ways, based on recent performance the last few years,” Cashman said. “They were given an opportunity, and in many cases have taken advantage of it. But we all knew, in most of these cases, they were holding the fort for when the regulars came back.”

Cashman used the well-worn metaphor of Sisyphus, forever pushing a boulder up a hill only to have it roll back down. The rock is gaining speed in the wrong direction, but the Yankees, at least, have not yet been crushed. The Dodgers, Cashman’s long-ago dream team, would envy their problems.