Months later, having seen the man play and lead on a daily basis, these same players shake their heads and wonder why he never has been given his due.
Why isn't Abreu among the big names in their game?
Chone Figgins, who has teamed with him to provide an unmatched top-of-the-order tandem, has developed a fine appreciation of Abreu's talent, personality and commitment.
"I've learned a lot being around Bobby," Figgins said. "He helped me improve an important part of my game [on-base percentage] with his discipline and approach. He's just a great guy to be around, always in a good mood, always willing to help you out."
Figgins, the Angels' leadoff man, was stunned to learn that the highest Abreu has finished in a Most Valuable Player balloting is 14th. That was in 2005 with the Phillies. Abreu has collected votes five other times, most recently in 2007, when he finished 17th with the Yankees.
"That's crazy," Figgins said. "Bobby's done things only the true elite have done.
"You look at the numbers he's putting up and the names of guys he's grouped with, and you're talking about Hall of Famers: Willie Mays, Barry Bonds, Rickey Henderson. That's the elite of the elite right there, and Bobby's doing things only they did.
"I think he's having a Hall of Fame career, and nobody seems to even notice. I wish I could tell you why, but I have no idea."
With his eighth-inning steal against the Athletics on Friday night, Abreu joined Bonds as the only players in modern history with five seasons combining at least 30 steals and at least 100 RBIs. Honus Wagner and Ty Cobb achieved the milestone in the early 1900s, and Hugh Duffy did it in the late 19th century.
In Philadelphia (after a brief fling in Houston) and the Bronx before landing with the Angels for a $5 million, one-year deal right before Spring Training, Abreu performed the same multiple acts that have convinced manager Mike Scioscia the new guy has been the team's MVP amid a stellar cast.
"It's just the way it is," Abreu said with a shrug and a grin when asked about the relative lack of national acclaim. "I don't know. I just go out and play and try to help my team win."
Scioscia cited "the balance he's brought to the offense" with his dual abilities to get on base and drive in runs, calling him a "swing man."
Abreu takes pride in his dependability. Reaching 150 games for the 12th consecutive season on Friday night against the A's, he joined Mays, Billy Williams, Pete Rose and Cal Ripken Jr. in another impressive club.
"I'm always going to play 156 games," said Abreu, who has visited the disabled list only once, in 1997, with a fractured hamate bone in his right hand. "Just give me one day off a month. That's all I need."
For a dozen seasons, Abreu has gone about his steady business: driving pitchers to distraction with his patience, scoring and driving in runs, running the bases with passion and intelligence, playing solid defense in right field with a powerful, accurate arm.
In his spare time, he's been a teacher, showing young teammates the nuances of the game. His efforts have been reflected in dramatically improved play by a variety of young Angels.
When Scioscia called Abreu the team's MVP, he was really saying something.
Figgins, Kendry Morales and Torii Hunter all have had brilliant seasons, Hunter's marred only by a month-long interruption with a groin injury caused by crashing into walls that don't give.
Hunter has a theory on why Abreu has flown under the radar while joining Mays, Bonds, Henderson, Joe Morgan and Craig Biggio as the only players in history to surpass 250 homers, 2,000 hits, 1,000 runs, 1,000 RBIs and 300 steals.
"Bobby came up in the home run era, with Mark McGwire, Sammy Sosa, Barry," Hunter said. "The big bomb, that's all anybody cared about. Bobby's game is more subtle. He was left out in the cold with his singles, doubles, walks.
"He's quiet but deadly -- a deadly assassin."
Hunter was with the Twins when he became acutely aware of Abreu's penchant for the big hit during his 2 1/2 seasons with the Yankees.
His .361 average this season with runners in scoring position is fourth-best in the American League, and since May 25 he's second in the league in RBIs with 86, reaching triple digits for the seventh year in a row.
"Believe me, nobody wants to face Bobby in clutch situations," Hunter said. "When I was in Minnesota, he was the guy we didn't want to beat us in the clutch.
"You see everything Bobby's done, the kind of teammate he is, he's got to be a Hall of Fame candidate. It's nice to see him start to get the recognition and respect he's deserved all along.
"I know he gets much respect from players. They know who can play. And Bobby's always been one of the best."