The "Big League Stars" set consists of 18 small hard plastic statuettes of players from both the American & National Leagues(9 players from each league). They were issued in 1956 and are exact replicas of the Dairy Queen/Tasti Freeze series of the same year. The only difference is that the Big League Stars statues are painted gold and the DQ series are white(the pictures above and below are from an error boxes- those are actually DQ statues in the Big League Stars package). 

The Big League Stars were sold in stores two ways. Most collectors are familar with the individual carded packages with one player statue displayed in a plastic bubble. The back side of the package is a baseball card of the player. The packaging pictured above and below are super rare. They contain the full American & National Leagie series.  We've been in the hobby over 30 years and have only seen a handful.