The organization, however, has had Story getting playing time at second base and third base in his Minor League career. The idea is to create versatility so that Story doesn't get blocked in his climb to the big leagues.
Good idea, but … "They have three All-Stars as the positions I play,'' he said with a smile.
On Tuesday, three Rockies will be on the NL roster for the All-Star Game presented by T-Mobile -- second baseman DJ LeMahieu will start in place of injured Dee Gordon of the Marlins, and third baseman Nolan Arenado and shortstop Troy Tulowitzki will be in reserve.
Sunday, however, was about the future.
And the two Rockies selected for the SiriusXM Futures Game made their presence felt in the U.S. Team's 10-1 victory against the World Team at Great American Ball Park.
Dominican-born outfielder Raimel Tapia singled with two out in the third and eventually scored to give the World Team a short-lived 1-0 lead. Tapia finished 2-for-3 for the World Team.
Story, meanwhile, doubled to drive in one run and scored another in the midst of the United States Team's five-run sixth inning.
It is another entry on the resume for Story, a supplemental pick after the first round in the 2011 Draft, who just last week was promoted from Double-A New Britain to Triple-A Albuquerque.
And he could find himself getting some time at first base or even in the outfield, according to general manager Jeff Bridich, who points to the value provided by versatile in-season callup Ben Paulsen, a first baseman who is getting added playing time because of his ability to play left field. Story came into the Futures Game as a defensive replacement at second base.
"At first, I wanted to be a shortstop all the time,'' he said. "I got over that. I am very confident at all three positions.''
LeMahieu has become a model for him. Originally a second baseman when the Cubs signed him out of LSU, LeMahieu initially got playing time at third base in addition to shortstop, and then he auditioned at second base, earning an everyday role and becoming, at 6-foot-4, the tallest full-time second baseman in big league history.
Story's bat is certainly there. He is hitting .275 with 12 home runs between his two stops this year after hitting 18 home runs at low-A Asheville in 2012, 12 at High-A Modesto in 2013, a combined 14 at three stops in 2014.
Same with Tapia, who spent his first two years playing for the Rockies' team in the Dominican Summer League. He came to the mainland in 2013, and hit .357 for short-season Grand Junction, and .326 at low-A Asheville a year ago.
He's hitting .326 at High-A Modesto this year, and already has eight home runs in the pitcher-friendly northern section of the California League, one shy of his total for a year ago.
More importantly he has become more aggressive on the bases, following up the 33 stolen bases with 18 already this year, and has put in extra time in the outfield, showing enough improvement in left field that he is getting some exposure in center field.
"`He is a plus-runner with an above average arm,'' said Freddie Ocasio, the manager at Asheville last year and Modesto this year, and a coach for the World Team on Sunday. "His defense needs to get better, and he continued to work on it.''