This season has been no exception. In fact, they're running even more with the arrival of Bobby Abreu, who feels reborn on the West Coast, and an emerging cast of young speed merchants led by Erick Aybar.
For Abreu, signed to a $5 million one-year free-agent contract on the eve of Spring Training, the Angels turned out to be a heavenly destination.
"I love it here," Abreu said. "The style of game they play is perfect for me. Scioscia is a manager who lets you play. He wants you to be aggressive on the bases. He doesn't get mad if you try to take the extra base. He only gets upset if you don't."
Celebrating his newfound freedom in the form of a green light, Abreu amped it up to 30 steals this season, becoming only the fifth player in history with 30 steals and 100 RBIs in five seasons.
Leadoff catalyst Chone Figgins, in a career year, raised his steals total from 34 to 42, largely because he was on base more often in raising his on-base percentage from .367 to .395.
Torii Hunter stole 18 bases despite missing a month with a groin injury. Erick Aybar delivered 14 thefts, and Maicer Izturis (13) and Howard Kendrick (11) also reached double figures despite spending most of the season sharing second base.
"This is our most athletic team," said Figgins, one of three players left from the 2002 championship club along with John Lackey and Scot Shields.
"With Bobby, Aybar, Izzy, Torii, Kendrick, bringing Junior [Gary Matthews Jr.] off the bench ... we've got a lot of athletes, man. [Former Angels outfielder] Garret [Anderson] is a great athlete, and he'd go first to third, but Bobby steals bases.
"The big difference this year is that we're healthy. We haven't been this healthy the past few years."
As a team, the Angels improved from 129 steals last season to 148, leading the Majors in going first to third on singles 119 times.
Setting a franchise record with 883 runs scored, the club led the Majors by batting .285 and with runners in scoring position at .295 -- up from .279 last season.
Aybar led the club with his .312 average, with Kendry Morales at .306 while leading the team with 34 homers and 108 RBIs. Hunter missed his first .300 season by one hit, settling for a career-best .299. Figgins, at .298, also was on the threshold of .300.
No player was as transformed as Aybar, who was unable to get a squeeze bunt down in the ninth inning of Game 4 of the 2008 American League Division Series in Boston. The call by Scioscia was debated for weeks after the Red Sox ended the Angels' season with a run in the bottom half of the inning.
"We play the game aggressively," Figgins said. "It's who we are."
Crestfallen that night in Boston, Aybar handled the adversity in a manner reflecting high character.
Working diligently to improve his skills during winter ball and in Spring Training, Aybar led the Majors this season with 18 bunt singles and tied for third in sacrifices with 13. With blinding speed, he tied for third with nine triples, leading the Majors in hitting in July with a .411 average.
"Aybar was a lot more confident this year -- all our young guys were," Figgins said. "I think you have to give Bobby a lot of credit for that. Those guys really responded to him."
There is no way to measure Abreu's total impact in numbers. Perhaps his biggest influence -- even more important than his 103 RBIs, 96 runs, 30 steals and 165 hits -- has been on athletes such as Aybar, Morales, Izturis and Kendrick, who have used the right fielder wisely as a mentor.
"He's always there when you need him," Izturis said. "Bobby knows the game and likes to help you with anything you want to ask him."
Scioscia watched his offense take flight in June and roll through August with impressive offensive numbers across the board. With Figgins and Abreu kicking into high gear at the top of the order, they averaged 5.7 runs per game in June, 7.1 in July and 6.2 in August.
A September swoon created some concerns, but the offense emerged from the slump with a late flurry -- averaging 6.3 runs over the last nine games -- and looks to be back in prime operating order for the Red Sox.
"Our guys on the basepaths have done a tremendous job," Scioscia said. "All our guys have gotten good secondary leads and made good reads out there. And the added batter's box offense has made a difference.
"Bobby's fit right into what we do. I talked to Bobby when we were trying to sign him and said, 'We really want to push you, to get after it on the bases.' He said, 'Hey, that's my style, my game.' He's been a great contributor to our running game."
Born to run, Abreu came to the right place.