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.
When I walk down the street and meet people, Ted Williams once said, I just want them to think 'There goes the greatest hitter who ever lived.' . Judging by his .344 career average and his 521 home runs, the most ever by a Red Sox player, Williams accomplished his goal.