Told that he's one of the youngest in the AFL -- only the Rangers' Luis Sardinas is younger -- Baez just shrugs.
"I've heard that," Baez said. "If you do good here, you have to keep working hard. They just tell me to do my job every time, play hard, do everything right."
Baez flashed some of his defensive skills as well with a diving stop, and he nearly threw the runner out. Replay might have backed up Baez. What's impressed McLeod and others are the shortstop's instincts for the game.
"When you watch him play defense and watch him on the bases, he plays like a veteran who has been in the Major Leagues for a long time and at a very young age," McLeod said. "That was the most pleasant surprise for me, and it's really fun to watch him on defense. It's like he sees things before it happens."
Baez knows he still has things to work on.
"When I have pressure on me, I have to learn how to slow down and slow my body down -- both ways [offense and defense]," Baez said.
That will come with experience. Baez began the year in extended Spring Training, then was assigned to Class A Peoria, where he batted .333 in 57 games. In early August, he was promoted to Class A Daytona. He batted .188 in 23 games, but finished 7-for-24 in his final seven games, hitting two home runs in the final game of the season.
Was there a big difference between Peoria and Daytona?
"I guess they knew I was going pretty good [at Peoria], and [the Florida State League pitchers] made me chase a lot," Baez said. "At the end, I was doing pretty good."
Tom Beyers, the Cubs' Minor League hitting coordinator, called Baez's first year in pro ball a "huge success." What helped, Beyers said, was that the Cubs eased Baez into the day to day routine of the game.
"The biggest thing for him, and what really helped was starting him in extended [Spring Training]," Beyers said. "It slowed everything down and he got used to how to take care of himself not only on the field but off the field."
Extended spring is a lot like instructional league, which is wrapping up this week for the Cubs top prospects, including Albert Almora and Jorge Soler.
"It's a great time for us as coaches to get guys when they're in their first year of pro ball, whether it's a young high school kid or a Latin kid in the U.S. for the first time," Beyers said. "That was huge for Javy. He showed he was ready for a challenge."
Baez grew up in Bayamon, Puerto Rico. He idolized Alex Rodriguez. Seven years ago, his family moved to the U.S. because his sister -- who is one year younger -- has special needs, and they wanted better medical treatment.
"I wanted to stay in Puerto Rico," Baez said. "I knew it would be different over here. But baseball is the same."
The Cubs benefited. They selected Baez in the first round of the 2011 First-Year Player Draft, ninth overall, out of Arlington Country Day High School in Jacksonville, Fla. He is one of seven first-round picks from 2011 playing in the AFL.
Baez has only played shortstop, and he's been on a mission to get to the big leagues.
"That was my dream since I started playing baseball and watching it on TV," Baez said. "I was like, 'I want to be there.'"
He's well aware the Cubs have a shortstop in Starlin Castro. Baez will move if needed.
"It doesn't matter," Baez said.
"He's got tons of talent and it's not just hitting, it's his overall game," Beyers said. "One of his biggest strengths is aptitude. I was very impressed with how he took instruction and applied it right away in a ballgame. Some guys, that process takes longer than others. His is pretty quick, and the knowledge he has of how the game is played, he always seems to be a step ahead."
When asked if he has a timetable for when he'll get to the big leagues, Baez gives the standard answer.
"I'll let the coach pick that," Baez said. "I just want to do my job every time."
One of these days, someone will say they want to be in the big leagues tomorrow. Baez smiled.
"If I can be there tomorrow, I will," Baez said.
He's on the right track.