By Bruce Levine–

CHICAGO (CBS) — The smart money at the start of the season was that the National League Rookie of the Year frontrunner would be the Chicago Cubs’ Kris Bryant. True to form, the 23-year-old third baseman has had an excellent start to his big league career.

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The Cubs have started four rookies since the addition of Kyle Schwarber. And now just 28 games into Schwarber’s career, it appears the team’s 2014 first-round pick has put himself in the conversation with Bryant for the award.

Most would disagree with the premise that a player could deserve the award over individuals who have competed the whole year in the major leagues. Still, there’s a historical perspective to consider when trying to quantify the number of games in which a player performs and the total impact on a team.

Willie McCovey came up to the San Francisco Giants on July 30, 1959. The 21-year-old first baseman collected four hits off of future Hall of Fame pitcher Robin Roberts that day and never looked back. McCovey hit 13 home runs and batted .354, winning the rookie award while having played in only 52 games.

Projected out, Schwarber could be in the conversation with Bryant and the Giants infielder Matt Duffy at the end of 2015. Through 27 games, Schwarber had six home runs and 21 RBIs while batting .352 — all very McCovey-like.

The 23-year-old Schwarber has plenty of confidence in his ability, without appearing arrogant.

“I am intently reading the pitcher pitch by pitch,” he said Sunday. “I go off of previous pitch or previous at-bat. Staying in my approach of me getting my pitch is what I am going through. I try to keep things simple, but I am staying in the moment.”

I took Schwarber back to his second week in the big leagues, facing Reds closer Aroldis Chapman. After a good at-bat, Chapman struck Schwarber out with a 101-mph fastball. As the young Schwarber made his way back to the dugout, he stared Chapman the whole time. The unspoken message seemed to be: “You got me, but I will get you.”

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“I am always up there thinking I am going to hit the ball hard,” Schwarber said. “I know it won’t always be that way. Still, against him or anyone else I am going to have the mindset to hit the ball hard. When you have a good approach and do your work before the game, you have a pretty good chance to succeed.”

Schwarber’s learning how to catch, play the outfield and hit in the majors after less than a year in the minor leagues.

“My goal is to get better every day,” he said. “It can be talking to (Anthony Rizzo) about hitting or (coach Mike) Borzello about catching. Now, it can be outfield conversation with Davey Martinez. I don’t really allow anything but getting the job done to enter my thinking. I go out there and play a baseball game. I am just trained to think along with the game.”

The impression he has made on his teammates and manager has been significant.

“There are at bats that he is frustrated on,” Cubs first baseman Anthony Rizzo said. “You can hit a lineout like he did (Saturday) and it can spiral you downhill. He and I will talk about those things. He just grinds out at-bats, he comes here early, going over scouting reports. He is looking at pitchers and how they will approach him. He is doing three jobs at once right now. He has been fun to watch.”

Cubs manager Joe Maddon has wasted little time plugging Schwarber into his lineup, near the top of the batting order.

“I see a very confident young major league player,” Maddon said. “He is very confident. Some people may want to attach cocky too that, but I think he handles it well. I think he thinks he is good at the plate. I think the people who watch him feel the same way. He will meet up with some difficulties along the way, and he will work through it.”

The Cubs haven’t had two players finish 1-2 in the rookie of the year vote since 1989 (Jerome Walton and Dwight Smith). They appear to be on the brink of doing it again 26 years later.

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