Start with the premise that a team spending roughly $300 million on baseball players ought to finish in first place. That figure, unequaled in baseball history, is so striking that it underscores everything about the Los Angeles Dodgers. Yet to focus too much on it is to miss the beauty of the pursuit. Nothing is preordained.

“It never means you’re going to win,” Jimmy Rollins, the veteran shortstop, said. “That’s false wisdom — or just dumb thinking. Money doesn’t guarantee you anything but money, that’s it.”

Almost all of the Dodgers, including some no longer here, are very wealthy. But who really cared about that — who could even think about it — on Sept. 2 at Dodger Stadium? Clayton Kershaw, the best and richest pitcher of his time, personified effort and will in a virtuoso performance.

The Dodgers had used their closer, Kenley Jansen, two days in a row. The other relievers, in general, have been unreliable. Kershaw gave them all a night off. He threw 132 pitches, matching a career high, and struck out every San Francisco player in the starting lineup.

With two outs in the ninth inning, Kershaw allowed two singles. Manager Don Mattingly strode onto the grass, and when he did not signal for a reliever, Kershaw said, he knew he would have a chance to finish the game. He told Mattingly he felt fine, and then struck out Marlon Byrd on a slider in the dirt.

Kershaw raised his fist — just a little, up by the shoulders — and smiled. It was a 2-1 victory over the Giants and, very likely, a third consecutive division title.

“He’s a monster,” Mattingly said after the crowd had filed out of his postgame news conference. “He’s like the guy on the other side, Bumgarner. He’s a pro. This guy works so hard to be good.”

Mattingly was leaving the room as he said this, and then he turned and added a final thought: “That’s one of those guys where you say, ‘If anyone’s worth it, he is.’”

Kershaw is in the second season of a seven-year, $215 million contract, the top of the Dodgers’ payroll pyramid. He does not have a reputation for rising in October, like Madison Bumgarner of the Giants. But he is, again, the most dominant pitcher in the majors. His 251 strikeouts this season are the most by a Dodger since Sandy Koufax fanned 317 in 1966.

Soon Kershaw and his fellow ace Zack Greinke will embark on their third postseason journey together. The first ended in the 2013 NL championship series, the second in 2014 in a division series, both against the St. Louis Cardinals. If the standings hold, this year will bring a first-round date with the New York Mets.

The Dodgers won three pennants in the 1940s, five in the 1950s, three in the 1960s, three in the 1970s and two in the 1980s. Considering all that, it is a point of pride to Stan Kasten, the Dodgers’ president, that the team will soon do something unprecedented.

“This franchise, Los Angeles Dodgers or Brooklyn Dodgers, has never been to the postseason three years in a row — ever,” Kasten told a visitor this week. “You didn’t know that? I didn’t know that. Ever! How about that?”

The feat is worth celebrating, largely because it comes in a period of transition for the franchise.

A group led by Mark Walter, Magic Johnson and Kasten bought the team for $2.15 billion in 2012 from Frank McCourt, who had driven it to bankruptcy. Last fall, Kasten hired Andrew Friedman to run the Dodgers’ baseball operations, luring him from Tampa Bay, where his analytical skills had built a contender on a tight budget.

Friedman, who got a five-year, $35 million contract, is working to integrate his philosophies into the front office. He is having fun, he said, but he is not quite there.

“We’re still evolving on a number of fronts,” he said. “Some of it is building up our team and our systems. We’ll be significantly further ahead at this time next year than we are now, because in a lot of respects we were starting from scratch. I’m not patient by nature, but it takes time.”

In August, Friedman added second baseman Chase Utley — Rollins’ old double-play partner with the Philadelphia Phillies — and Justin Ruggiano, an outfielder he brought to the majors with Tampa Bay. At the nonwaiver trading deadline, in July, the Dodgers’ biggest move was a complicated three-team deal with Atlanta and Miami involving 13 players, a draft pick and a significant sunken cost.

The Dodgers had paid $62.5 million in May for Hector Olivera, a Cuban infielder. Before he even played a game for them, they sent him to the Braves and absorbed his $28 million signing bonus. They traded other players, too, and received a package that included four healthy pitchers (Luis Avilan, Jim Johnson, Mat Latos and Alex Wood), one injured pitcher (Bronson Arroyo) and a young infielder, Jose Peraza.

Better starters and relievers changed teams at the deadline, and the Dodgers have been criticized for not making sturdier upgrades. They still do not run the bases especially well — although Utley helps — and getting the game to Jansen can be an adventure. Yet they retained the jewels of a farm system rated by Bleacher Report as the best in the majors, post-trading deadline.

“Listen, at the deadline we had long talks,” Kasten said. “You know the names — the big guys out there. And those deals, if we had done them, would have taken three, four, five of our better people. We were tempted, and we kicked it around a lot. At the end we decided there were some things we would do and some things we would not do, having evaluated everything. But there was discipline, there was real scouting expertise plus real analytical expertise in the mix."

He continued: “We’ll find out if those decisions are good, but we won’t find out in one year, because this is not a one-year project. That’s the mistake writers make: When you look at a payroll this year and you look at a number like 300, you’re just examining one column in one year, and that’s not the way businesses work. That number has a lot of components to it. Many don’t relate to this year; they relate to expenses for next year, and the year after, and the year after that.”

To get a leaner payroll for the future, and a younger team, the Dodgers were willing to spend more in 2015 because their luxury-tax rate is lower than it will be next season. They are paying $18 million to Matt Kemp, who was traded to the San Diego Padres last winter, but got a young catcher, Yasmani Grandal, in return. Grandal earns less than $700,000 and made his first All-Star team this season.

The roster is changing. Grandal’s arrival bumped the incumbent catcher, A.J. Ellis, to a part-time role. Greinke, who leads the majors with a 1.59 ERA but has fewer innings and strikeouts than Kershaw, can opt out of his contract after the season. Prospects like shortstop Corey Seager and pitchers Julio Urias and Jose DeLeon may soon join center fielder Joc Pederson, who is showing signs of emerging from a second-half slump, as future centerpieces.

“For a lot of us that have been here, the window is definitely on the way to closing,” Ellis said. “You don’t know what’s going to happen with this group of guys. There is a sense of urgency to deliver on all the promise and all the talent that we’ve had and how close we’ve been.”

Ellis continued: “The last two postseasons have been completely devastating because we felt like we were the best team each time, and we basically got out-teamed by the Cardinals. They were able to beat us with their toughness and their resiliency, and we weren’t able to match that. Hopefully we’re battle-tested enough that we can get back in there and have a chance.”

A third division title, alone, would do little to satisfy the veterans, or a fan base that is tired of waiting. The Dodgers display novelty championship rings in the plaza beyond right field, about the size of a bumper car; fans can hop in and pose for photos. The last ring is from 1988. Every Dodger knows this.

Kershaw was born that year. His career postseason ERA, in 11 games, is 5.12. His paycheck, and his team’s payroll, would seem to imply more opportunities.