"There's a lot of other guys around the American League that have thrown the ball better than I have," Price said, "so I shouldn't be an All-Star, I don't think so."
Still, every team is required to have at least one player in the All-Star Game, and the consensus seems to be that it will be either Price or reliever Jake McGee.
The case for McGee rests on prolonged consistency. Price's is based on a strong reputation and a strikeout-to-walk ratio that is threatening the single-season record. Exactly midway through the season, Price's strikeout-to-walk ratio is 10.29. Only Bret Saberhagen's 11.00 ratio in 1994 was better.
With that in mind, Tampa Bay manager Joe Maddon says people should ignore Price's sub-.500 record and pedestrian ERA.
"If you break it down, the higher ERA's been based on a couple bad innings," Maddon said. "For the most part, he's done a wonderful job. The walk-to-strikeout ratio is pretty spectacular. And moving forward, I believe it's going to continue to be as good if not better."
But Maddon is even more forward with his support of McGee.
He has said that he thinks McGee should be an All-Star and he echoed that sentiment after the reliever notched his second save of the season in Game 1 of a doubleheader at Oriole Park at Camden Yards on Friday.
If Price doesn't think that he deserves to be an All-Star, then McGee's chances get even better to play in the game for the first time.
"Nice and calm, fixes his necklace and throws the next pitch," Maddon said of McGee. "And I dig that."
Fans can cast their votes for starters at MLB.com -- online or on a mobile device -- using the 2014 All-Star Game MLB.com Ballot Sponsored by Experian until Thursday, July 3, at 11:59 p.m. ET. The 2014 All-Star Game will be played at Target Field on Tuesday, July 15 on FOX.
David Wilson is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.