In modern times, a season batting average higher than .300 is considered to be excellent, and an average higher than .400 a nearly unachievable goal. The last player to do so, with enough plate appearances to qualify for the batting championship, was Ted Williams of the Boston Red Sox, who hit .406 in 1941, though the best modern players either threaten to or actually do achieve it occasionally, if only for brief periods of time.
Spring 2007. Three papers submitted. One paper accepted. My batting average: 0.333. Not much worse than Babe Ruth, so I'm feeling okay.