By Bruce Levine–

CHICAGO (CBS) — The most spectacular baseball plays made on a regular basis in Chicago seem to be the highlight reel clips authored by Cubs infielder Javier Baez.

On Monday night, it Baez who was in the middle of a great relay throw from outfielder Jason Heyward that he then fired to third baseman Kris Bryant to cut down a would-be triple by Marlins second baseman Derek Dietrich.

“Addison (Russell) was yelling ‘three, three, three,'” Baez said. “I just took the ball, did not look and threw it. I just play my game at each position. It is all great fun.”

The 23-year-old Baez has shown perhaps the most growth of any of the young players Cubs player from their first year to the next. This isn’t just an outside observation. Over the weekend, the Cubs engaged in trade discussions with the Rays centered around left-hander Matt Moore but balked when Tampa Bay requested Baez, outfielder Albert Almora and another young pitching prospect, a source said. The Cubs highly value Baez.

Tampa Bay’s request was an understandable one. The Rays later coaxed the Giants into paying a stiff price for Moore in the hours before Monday afternoon’s non-waiver trade deadline, as Tampa received infielder Matt Duffy, who finished second in the 2015 Rookie of the Year voting, and shortstop prospect Lucius Fox, whom San Francisco signed with a $6 million bonus in summer 2015.

Baez has shown great improvement this season. In his two-month debut stint in the majors in 2014, he struck out in 41.4 percent of his plate appearances. Throughout spring training in 2015, manager Joe Maddon pushed Cubs management to include Baez on the big league roster to open the season. Instead, he was sent to Triple-A Iowa — and rightfully so, as he had hitting adjustments to work on and needed to mature.

The mission was accomplished, as Baez showed up a more polished player in late 2015. In limited playing time in the big leagues last season, Baez’s strikeout rate dropped to 30 percent. It sits at 23.7 percent this season, in which he’s hitting .283 with 11 homers, 40 RBIs and a .779 OPS in 89 games. Baez also garnered valuable playoff experience in the playoffs, taking over after shortstop Addison Russell was injured in the NLDS.

In 2016, the versatile Baez has forced his way into the everyday lineup with terrific defensive play at all four infield spots and a more consistent bat. And when he found his name thrown in trade rumors ahead of Monday’s deadline, he kept perspective.

“There will always be rumors about players,” Baez said. “I can’t do anything about that. All I can do is play my game and help our guys win. I just have to stay focused and not let any of that stuff get in my head.”

Baez has great flair to his game and some of the quickest hands in baseball with the bat and the glove. Those reflexes can be a plus or a minus, depending on whether the mental part of the game matches the physical prowess.

Those skill sets are matching up nowadays for Baez.

“I look at the sky being the only limit to my game,” Baez said. “I learned that no matter how good you think you are, you can be better. I see that with my teammates and how hard they work. That motivates me to get better. Like (recently) when I missed a ball from the catcher, I tried to rush a tag. I have to learn to control my skills and take advantage of them at the same time.

“I play my game and have fun out there.”

Bruce Levine covers the Cubs and White Sox for 670 The Score and CBSChicago.com. Follow him on Twitter @MLBBruceLevine.