Definition of "bigs"

In the Appalachian League, where Cal Ripken once played in Bluefield, W.Va., a ballplayer's chances of making it to the bigs are less than one in six.

2004 June 23, Michelle Boorstein, “Ballclub^s Pullout Caps Va. Town^s Run of Woes; Struggling Martinsville No Longer Celebrates Its Boys of Summer”, in Washington Post

But he can become just as effective as any of the other bigs passing the ball who get double-teamed.”

2007 January 2, Howard Beck, “Knicks Resolve to Get More Out of Curry in the New Year”, in New York Times‎