A quarter is another way of saying one fourth, in this setting, one fourth of a year = three months. Quarterly means something that happens every 3 months. Edit
Outfielder Ty Cobb, whose career ended in 1928, has the highest batting average in Major League Baseball (MLB) history. He batted .366 over 24 seasons, mostly with the Detroit Tigers. In addition, he won a record 11 batting titles for leading the American League in BA over the course of an entire season.
In MLB, a player in each league wins the batting title each season for having the highest batting average that year. The American League (AL) winner is known as the Rod Carew American League Batting Champion, while the National League (NL) leader is designated the Tony Gwynn National League Batting Champion.