The slugging third baseman is not only expected to challenge for rookie of the year honors - there's also a sense that he might already be one of the game's top hitters at his position. After all, the Cubs batted him cleanup in his first three major league games.
''I'm sure things will start to settle in and I will become more of just a guy,'' Bryant said. ''I've never been the type that likes the center of attention. I understand that is part of the job.''
The Cubs kept Bryant in the minors for a short while even after he hit .425 with nine home runs in spring training, and in doing so the team gained an extra year of control before he can hit free agency. Chicago got off to a solid start without him, and the Cubs are currently two games behind NL Central-leading St. Louis.
How much of an impact can a rookie like Bryant have? If he's good enough, the sky really is the limit. In just the last few years, baseball has seen Mike Trout and Jose Fernandez produce two of the best seasons ever by rookies. Trout was second in the American League MVP vote in 2012, and a year later, Fernandez was third in the National League Cy Young Award race.
If Bryant even approaches that level, the Cubs have a shot to return to the playoffs for the first time since 2008.
Amid slightly less fanfare, the Arizona Diamondbacks called up Cuban rookie Yasmany Tomas last week, but they have used him only as a pinch-hitter so far. Tomas singled Sunday for his first major league hit.
Here are a few other developments from the last week:
ODD YEAR TROUBLE?
The San Francisco Giants won the World Series in 2010, 2012 and 2014 while failing to make the playoffs in the intervening seasons. This is an odd-numbered year, and the Giants are off to a 4-10 start. They're already six games out of first place in the NL West.
Yes, that's Houston sitting in first place in the AL West after averaging 104 losses over the last four seasons. The Astros are only 6-6, but they've achieved this decent start with hardly any production yet from power hitters George Springer, Evan Gattis and Chris Carter.
The New York Mets have won eight in a row and are still undefeated at home, but injuries are mounting for the early NL East leaders. Catcher Travis d'Arnaud broke his hand when he was hit by a pitch, and reliever Jerry Blevins had his throwing arm fractured by a line drive. This for a team that already lost right-hander Zack Wheeler to elbow surgery and David Wright to a hamstring problem.
One of the strangest statistical starts this season belongs to Mets outfielder Curtis Granderson, who is hitting .146 with no extra-base hits but has already drawn a major league-leading 12 walks.
As expected, Dee Gordon, Billy Hamilton and Jose Altuve are around the top of the stolen base chart, but some sleeper candidates on the basepaths may be emerging. Desmond Jennings of Tampa Bay already has five steals - he's a third of the way to his total from last season.
Then there's Detroit shortstop Jose Iglesias, who sat out 2014 because of stress fractures in his shins - and therefore missed out on the Tigers' initial transition from manager Jim Leyland to Brad Ausmus. Detroit has been running more under Ausmus, and a now-healthy Iglesias already has four steals this year to go along with his .436 average. He won't hit like that all season, but when he's on base, the Tigers seem willing to turn him loose.
LINE OF THE WEEK
Jorge Soler, Cubs, went 3 for 5 with two home runs and scored the winning run in the 10th inning of a 7-6 victory over Cincinnati last Monday. Amid all the anticipation of Bryant's arrival, the 23-year-old Soler has gotten off to a solid start in the outfield for Chicago.