When the young fan inquired as to how much time Rogers, Brandon Morrow, Todd Redmond and Dustin McGowan had spent practicing their sport when they were 10 years old, the 28-year-old right-hander from the Dominican Republic surprised everyone.
"I say 14, but that's the time that I said I didn't want to play other sports, just baseball," Rogers explained. "I played basketball, volleyball and baseball, but I was focused more on basketball before 14.
"The tradition in my family is baseball, but I didn't play too much, because I had to work and help around the house with my mom before that. But ... when I got to 14, I said, 'I don't want any other sport. I just want to focus on baseball.'"
Just three years after starting to take the sport seriously, Rogers was signed by the Colorado Rockies as a free agent out of the Dominican. It wasn't until three years later that he first found his way to a mound.
"I signed when I was 17 years old as a shortstop," Rogers said. "I played three years as a shortstop in the Dominican Summer League, then they told me they were going to put me at pitcher and see what happens. I was [upset], because I liked to hit; I liked to play shortstop.
"But I said to myself that it might be the only reason I could keep playing baseball, because maybe if I said no, they would release me, and I don't even know what I would do after that. So I said I would do everything I could to be a good pitcher, and focus on that."
For many young Latin players, baseball is a pathway to help their families. A teenaged Rogers was no different, looking for a way to give his mother a permanent home and to avoid becoming a truck driver, which was the only other option in his mind.
"[The Rockies] signed me because they thought I could play in the big leagues as a shortstop, and that's what they told me," Rogers said. "I was focused on being able to help my family, because we couldn't even purchase a house. We were renting and we paid every month, and I thought to myself, 'Everything that I get, I am going to give it to my mom to buy a house.'"
After being purchased by Cleveland from Colorado during the 2012 season and then being acquired by the Blue Jays from the Indians for Yan Gomes and Mike Aviles prior to the 2013 season, Rogers now has more than three years of Major League service time under his belt. He avoided arbitration with the Blue Jays on Friday by signing a one-year, $1.85 million contract, and has been able to fulfill the goals he set when he was younger.
Now, his focus is on potentially earning a spot in Toronto's 2014 rotation, after making a solid impression among last season's starting five.
"I'm going to do everything that I can to be [in the rotation]," Rogers said. "That's all I can do. Right now, I know I'm focused a little bit more, because I know what I have to do. I've taken time in Dominican winter ball to worry about my pitches, and especially my changeup, because I have to be more confident with it.
"This is one pitch you have to use in the big leagues to get people out, and control it. I've tried to work with that in the Dominican and tried to be confident with my changeup, and I think it's going to be really good when I come into Spring Training to fight for the spot."
Throughout his time in the Dominican this winter, Rogers has impressed everyone around him. He worked up his inning load with three regular-season starts for the Tigres del Licey before completely dominating the opposition in three playoff starts so far.
Since his very first offseason outing in December, in which the righty allowed three runs, Rogers has thrown 26 scoreless innings through five games, walking just six and striking out 22 over that span. Rogers believes the changes he's made, and tips he's taken from an eight-time All-Star, have helped him find success that will carry over to the Blue Jays' season.
"I talked to Pedro Martinez about my changeup, and Neftali Cruz [the Blue Jays' development coordinator in Santo Domingo]," Rogers said. "Pedro told me just to throw it; don't think about anything different over there. Neftali told me just come into the game to work.
"Right now, everybody is talking about me in the Dominican. I [threw] 26 innings with no score in a row, and I'm 3-0 in  innings in the playoffs, and everything is good right now. [When] I go back, I think I'm going to pitch one game if we make it to the final, and we'll see what's going to happen. I'm just trying to be as ready as I can for Spring Training."