The latest example of that desire was standing right next to him in the form of Zack Greinke, who agreed Saturday to a six-year, $147 million contract with the team many expected him to end up with when his free-agent process began.
Greinke badly wants to win, too. And until his three-hour November meeting with Dodgers president Stan Kasten, general manager Ned Colletti and skipper Don Mattingly, the 29-year-old right-hander didn't realize just how much winning he can do here.
Then they all went through the roster together.
"When I wrote all the lineups down and the pitching staffs down on paper, it made me realize how good the Dodgers actually are," Greinke said. "When I was here earlier this year, the team was a lot different."
That was on May 31, when Greinke was still pitching for the Brewers and Guggenheim Baseball Management was only a month into its $2 billion purchase of the Dodgers.
Since then, the Dodgers took on more than a quarter of a billion dollars while acquiring Adrian Gonzalez, Carl Crawford and Josh Beckett from the Red Sox. They traded for former Marlins shortstop Hanley Ramirez. They gave Andre Ethier an $85 million extension. They signed Brandon League to a three-year, $22.5 million contract. And, on Monday, they introduced Korean starter Hyun-Jin Ryu after paying more than $60 million for his services.
Now there's Greinke, who gives the Dodgers eight quality starting pitchers and slides right behind fellow Cy Young Award winner Clayton Kershaw, giving Los Angeles a younger version of the Randy Johnson-Curt Schilling duo that helped the D-backs win the World Series in 2001.
Over the last four years, starting with his Cy Young season in '09, Greinke has gone 57-33 with a 3.37 ERA while averaging 208 innings and 206 strikeouts per season. Few would say he's worthy of being baseball's highest-paid right-hander, but the starting pitching market was thin and the Dodgers seemingly have money to burn.
But money, Greinke stresses, wasn't the greatest motivator in choosing Los Angeles.
"Besides that," he said, "it was the fact that they can be good for every year of my contract. So there's no rebuilding, which is nice. At this stage of my career, winning's the No.1 thing, and this place probably has as good a chance as anyone to win."
Greinke went 15-5 with a 3.48 ERA in 2012, topping 200 innings for the fourth time in five years and reaching 200 strikeouts for the second straight season. He began it with the Brewers, was acquired by the Angels just before the non-waiver Trade Deadline and posted a 2.04 ERA in his last eight starts.
The Angels wanted to bring him back, but they went in another direction on the first day of the Winter Meetings, when Greinke's agent, Casey Close, told GM Jerry Dipoto the kind of contract his client sought. Other teams flirted with the idea, too, Greinke mentioned.
Down the stretch, though, it came down to the Rangers and Dodgers.
"At one point, I was favoring Texas," Greinke admitted. "But that changed at the end."
Money, of course, was a factor.
"That's what it gets to at the end," Greinke added, "but I don't want to get too deep into it and say that's the only reason I came here."
It also didn't hurt that he's admittedly a fly-ball pitcher and Rangers Ballpark is very hitter-friendly. Greinke, about as analytical as they come, had 10 priorities in his offseason search, all with varying degrees of importance. And the Dodgers, he said, hit on almost everything.
"The only thing it didn't is that I live in Florida and L.A. is all the way out here, so it makes the travel a little bit tougher," said Greinke, whose offseason home is in Orlando. "But everything else was a positive for playing out here."
Greinke got that sense when he came here in November, showing up with his wife, Emily, and nobody else -- no friends, no agent, no entourage. Colletti called it "probably the best free-agent meeting I've ever had in decades doing this." In some weird way, perhaps it quelled any questions about Greinke handling a big market.
"When he left that day," Colletti recalled, "we all looked at each other and said, 'We need to figure out a way to get this kid here."
And these days, the Dodgers get what they want.