But if it's possible to be a three-time All-Star and underrated, Crawford is.
Or was. His Q rating might just take a considerable leap in the wake of his performance Tuesday night at Busch Stadium in the 80th edition of the Midsummer Classic.
Having singled off Dodgers ace Chad Billingsley as a pinch-hitter in the fifth inning to start a rally that helped the American League tie the game, Crawford stayed in to play left field and robbed Brad Hawpe of the Rockies by snatching what would have been a tiebreaking home run.
Instead, the AL scored the go-ahead run in the top of the eighth and went on to win, 4-3, making Crawford the game's MVP and cementing his catch in All-Star lore.
"Oh, man, Carl would be on every billboard in the city if he played in New York," said Rays shortstop Jason Bartlett. "Nobody has the tools he has."
Added Tampa Bay first baseman Carlos Pena: "He'd be a super-duper megastar."
Bartlett, Pena, utility man Ben Zobrist and third baseman Evan Longoria didn't have much of an impact on Tuesday's game. Bartlett went 0-for-1 after entering the game at shortstop in the sixth inning; Zobrist struck out as a pinch-hitter in the top of the eighth and stayed in the game at second base; Pena didn't play; and Longoria was removed from the roster early Tuesday because of an infected right ring finger.
That didn't stop anybody from gushing about the All-Star experience, which included Pena's participation in Monday's State Farm Home Run Derby.
"It was unbelievable -- better than I thought," said Pena, who lost a swingoff to hometown favorite Albert Pujols after the first round of the Derby. "I had a blast. We all did. ... Did I want to play? Of course. Does it bother me that I didn't? No. Not at all. I knew I was here to be a pinch-hitter, and the right spot didn't come up.
"We're here to win a baseball game, and we won. And I had a blast. How could I possibly be anything less than thrilled?"
There were two significant thrills for Zobrist.
"Just running out onto the field was an amazing experience," he said. "To go out on the field and look around, it's a pretty humbling experience."
No. 2? Catching Miguel Tejada's popup for the final out of the game, securing the save for Yankees legend Mariano Rivera.
Zobrist said he still had the ball, but he wouldn't say where.
"Let's just say it's in a very safe place," Zobrist said.
Asked if he planned to give it to Rivera, he smiled.
"I have to talk to him about it," Zobrist said. "Did he have an All-Star save [before Tuesday]? Maybe we'll have to make a deal."
Relayed Zobrist's proposal, Rivera, who set a record with his fourth All-Star save, also smiled.
"Oh, OK," Rivera said. "Then yes, I will [talk to Zobrist]. I will."
All of the Rays got to talk to President Obama, who visited both clubhouses before throwing out the ceremonial first pitch.
"That was very cool," Pena said. "He's a cool guy. Very nice to everyone, said hello. He's an impressive man."
Bartlett agreed, adding that the meeting with the leader of the free world was one of many experiences that he's not quite sure he completely soaked in. All the more reason, he added, to work for a return trip.
"There were a lot of nerves," Bartlett said. "When I went into the game, I felt like I was at my first big league Spring Training, when all the young guys go out there in the sixth inning. Butterflies, big-time, and it was like that most of the time here. I felt like I was going through the motions a lot of the time, trying to take it all in but not really able to.
"I just want to come back. I want to come back, not be nervous and have more fun."