But Grich hurt his back and didn't play past June 8 of the ensuing season, and Rudi broke his hand and missed the last three months. So there was Baylor, hitting just .237 through the first four months, watching his team lug through an eventual 74-88 finish and being subject to boos from an Angels fan base that expected more out of its new slugger.
The next year, Baylor turned it around, batting .255 with 34 homers and 99 RBIs.
The year after that, in 1979, he was named the American League's Most Valuable Player and led the Angels to their first postseason appearance.
Thirty-four years later, Baylor is back with the Angels as their hitting coach -- and hoping to walk Hamilton through a similar kind of resurgence.
"I'm looking forward to the challenge," Baylor said during a conference call on Thursday. "The one thing about my style is that we try something for a while, and if that doesn't work, we don't just keep pounding our head against something that doesn't work. He's a real key to the offense. ... We just have to get him on that path to success. He's had it before; he just has to recapture it again, and believe in his swing. We're going to work on that from Day 1 of Spring Training."
Baylor was plucked from the D-backs and signed to a two-year contract to become Mike Scioscia's third hitting coach in the last two years, 17 months after the front office let go of Mickey Hatcher in May 2012 and eight days after Scioscia and general manager Jerry Dipoto agreed on a series of coaching changes -- dismissing hitting coach Jim Eppard and bench coach Rob Picciolo, while promoting third-base coach Dino Ebel to the bench.
Baylor and Scioscia have hit it off over the years, as the Angels' 14-year manager has taken part in his celebrity golf tournament in Southern California.
"I respect him," Baylor said of Scioscia. "There's just a calmness, probably about the both of us."
Baylor is even more familiar with Dipoto, the former reliever he managed with the Rockies from 1997-98 and worked under when Dipoto was an executive in Arizona in 2011.
"It's really interesting negotiating with a general manager that was your closer at one time," Baylor said. "We haven't talked probably since I asked him for a recipe for a cookbook for our church."
And then, of course, there was his ties to the organization. The best years of Baylor's 19-year career as an outfielder and designated hitter were the six he spent in Anaheim, when he batted .262 with 141 homers, 523 RBIs and 89 stolen bases from 1977-82. He's a member of the Angels Hall of Fame. He and his wife, Becky, reside in Riverside County.
And though the D-backs wanted him to return to Kirk Gibson's staff next year, Baylor found it difficult to pass up on an opportunity to come back.
"I haven't been there for a while," Baylor said, "but I still have the same enthusiasm about the organization."
Baylor was the manager of the Rockies from 1993-98 and the Cubs from 2000-02, compiling a 627-689 record and winning the National League's Manager of the Year Award in 1995. He's spent 10 years as a hitting coach in the Majors, with the Brewers (1990-91), Cardinals ('92), Braves ('99), Mariners ('05), Rockies ('09-10) and D-backs ('11-13). In six of those seasons, his offense finished among the top 10 in the Majors in runs scored.
"Not only his knowledge of hitting, but just his presence is going to be something that's very, very important to us," Scioscia said. "I think he's going to be a great sounding board for me, I think he's going to make decisions easier for us moving forward, and I just don't know if there's a guy that has as much respect as Don does walking into a clubhouse or walking into a meeting with hitters, to have everybody stand up and take notice of what he's saying."
Scioscia dismissed the notion that a message carries more weight if it comes from a guy with a baseball-playing resume like Baylor's, saying: "I think that what Don has accomplished outside of playing the game is what's important to us."
But it certainly can't hurt.
Baylor's philosophy is about "putting the ball in play" and "staying in the middle of the field," and he isn't a very big fan of the strikeout -- which will make it interesting to see how he works with the likes of Hamilton and Mark Trumbo, two guys who struck out a combined 342 times last season.
"I don't harp on guys about strikeouts, but that's one thing that I really don't condone," Baylor said. "Guys think it's OK to strike out 100 times, 120 times, 130 times. That bothers me. You can't start runners if guys are strikeout guys. That kills you. My philosophy is going to be try to stay in the middle of the field. A lot of pitchers don't pitch inside anymore, so why not stay in the middle of the field?"