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.
The most recent champions are Miguel Cabrera, at .338 in the AL, and Dee Gordon, at .333 in the NL. The closest finish in a batting race came in 1945 when Snuffy Stirnweiss batted .309, topping Tony Cuccinello 's .308 average for the American League title by .00008. George Kell beat out Williams in 1949 by .00015.