There has been a persistent theory brewing within the Dodgers organization over the past few seasons, a theory about their Southern California rivals that originated two Octobers ago and has played out in a thrilling divisional battle this year.

When the Dodgers play the San Diego Padres, it seems like they usually get the Padres’ best players.

And when the rivalry heats up, the intensity is typically at its highest for the Padres.

That was certainly the case in the 2022 playoffs, when the underdog Padres won four games in the National League Division Series over the Dodgers, a team with 111 victories to their name.

This manifested itself more subtly last year, when the Dodgers were forced to win a number of close games despite finishing well above the Padres in the standings.

And that has been abundantly clear so far this season, with the Padres winning seven of the 10 games they have faced and cutting the Dodgers’ nine-game division lead to just three heading into the final week of the season.

“So far they’ve let us do what we want,” manager Dave Roberts said Sunday.

So ahead of a crucial three-game series against the Padres this week at Dodger Stadium, which starts Tuesday night, Roberts not only emphasized the dynamic but also challenged his team to respond to it.

“I think it’s pretty easy to see that when we played them, I think 10 times this year, they were more intense than we were,” Roberts said. “And that has to change. I expect it to change. Having those guys play — in really, really meaningful games, that’s going to bring out the best in us.”

Roberts can only hope so.

Significant may be an understatement for what’s at stake this week.

If the Dodgers win the series, they would clinch their third consecutive NL West title, their 11th in the last 12 years, and likely secure a vital first-round bye.

By winning one of the three games, the Dodgers would still control their own destiny going into the final weekend of the season. However, they would still have some work to do with a magic number of two for their final series against the Colorado Rockies.

And if the Dodgers get swept by the Padres, they’ll suddenly find themselves on the back foot: Technically, they’re tied for the division lead with three games remaining, but they know they’ve lost the tiebreaker for the division title at the end of the season because San Diego already leads the head-to-head series (the first time they’ve done that against the Dodgers since 2010).

“Obviously they play us and they played well,” Roberts said of the Padres earlier this season.

And how can the Dodgers fare this week?

“For us, I just want the mindset to be: Keep attacking,” Roberts said. “We’re not chasing anybody. And you can’t go into cautious defense mode.”

According to Roberts, that mentality didn’t always manifest itself during the Dodgers’ previous meeting with the Padres this season.

After beating San Diego 5-2 on the opening day of an international trip to Seoul, South Korea, the Dodgers lost the return game 15-11, a defeat overshadowed by Yoshinobu Yamamoto’s disastrous MLB debut.

A few weeks later, the Padres came to Los Angeles and won only their third series at Chavez Ravine in the last five years.

Two subsequent visits to San Diego didn’t fare much better for the Dodgers. In May, they were ejected and lost the entire series at Petco Park, but in late July they were defeated in two games.

“I think the chaser always seems to have a little bit of extra motivation, so I think that’s part of it,” Roberts said of the intensity gap he’s sometimes seen between the clubs. “But the talent is the same, so there’s no reason why our fighting spirit, our intensity, our focus shouldn’t match or exceed theirs.”

While the Dodgers haven’t pitched great against the Padres (they had a team ERA of 4.62 against San Diego this season), the club’s biggest problem this year has been at bat.

The Dodgers’ .602 OPS against Padres pitching is their lowest mark against a team this season. And on several occasions this year, Roberts and others have hinted at the idea that the Padres aren’t intimidated by the Dodgers’ star-studded lineup, and that they’re comfortable enough with it to know how to avoid danger and rack up outs.

“We’ve got to be proactive and keep attacking,” Roberts said Sunday afternoon of the team’s overall mindset heading into the final stages of the season. “So that’s kind of my message.”

The fact that this week’s series matters at all to the standings is due to San Diego’s second-half revival, which saw it post baseball’s best record (40-17) since the All-Star break.

As a result, the pressure is on the Dodgers to hold them off now and avoid the added complications that would come with squandering the division title and taking the long route through the playoffs — especially for a team already short on pitching.

“It’s going to be fun, a lot of energy,” outfielder Mookie Betts said. “I’m sure there’s going to be a lot of emotions and stuff. These are the games we dream about.”

And if they lose, it could lead to a nightmare scenario at this point.

“Those guys are playing great,” Roberts said. “But … I think we can still stay aggressive and go out there and try to win a series.”