Question: What is the winning batting average for the Major League Baseball batting champion of the team whose overall win-loss record is 9,346-9,191 ( a winning percentage of .504 )

text: List of Major League Baseball batting champions
American League
Nap Lajoie led the American League in its inaugural season with a .426 batting average , one of just 13 seasons of a .400+ average in the 20th century . In addition , Lajoie was a part of two separate contested batting average races in 1902 and 1910 . Ted Williams won six AL batting titles . He hit .406 in 1941 , and that is the last time a player has hit over .400 . Rod Carew won seven AL batting titles between 1969 and 1978 . George Brett 's .390 batting average in 1980 is the second-highest since 1941 . Ichiro Suzuki won AL batting titles in 2001 and 2004 . Joe Mauer won the 2006 , 2008 , and 2009 batting titles , becoming the first catcher to win three batting titles and the only catcher ever to win in the AL .
In baseball, batting average (AVG) is a measure of a batter's success rate in achieving a hit during an at bat. In Major League Baseball (MLB), it is calculated by dividing a player's hits by his at bats (AB). In MLB, a player in each league[L] 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. Under current rules, a player must have 3.1 plate appearances (PA) per team game (for a total of 502 over the current 162-game season) to qualify for the batting title. However, if a player's lead in AVG is sufficiently large that enough hitless at bats can be added to reach this requirement and the player still would have the highest batting average, he wins the title. Tony Gwynn, for example, had 159 hits in 451 ABs in 1996 (.353 average) but only 498 PAs. Gwynn's batting average would have dropped to .349 (159 hits in 455 ABs) with four hitless ABs added to reach the 502 PA requirement, but this would still have been higher than the next-highest eligible player (.344 average), so he was awarded the 1996 NL batting title. The first batting average champion in the NL was Ross Barnes; in the league's inaugural 1876 season, Barnes batted .429 for the Chicago White Stockings. The AL was established in 1901, and Hall of Fame second baseman Nap Lajoie led that league with a .426 average for the Philadelphia Athletics. Ty Cobb of the Detroit Tigers, who also holds the highest career batting average of .366, led the AL in average in 11 (or 12) seasons. Honus Wagner and Gwynn are tied for the second-most titles, with eight apiece in the NL.
Year Winner AVG Team ( s ) Runner-up 2nd AVG
1901 Nap Lajoie .426 Philadelphia Athletics Mike Donlin .340
1902 Ed Delahanty .376 Washington Senators Charlie Hickman .361
1903 Nap Lajoie .344 Cleveland Naps Sam Crawford .335
1904 Nap Lajoie .376 Cleveland Naps Willie Keeler .343
1905 Elmer Flick .308 Cleveland Naps Willie Keeler .302
1906 George Stone .358 St. Louis Browns Nap Lajoie .355
1907 Ty Cobb .350 Detroit Tigers Sam Crawford .323
1908 Ty Cobb .324 Detroit Tigers Sam Crawford .311
1909 Ty Cobb .377 Detroit Tigers Eddie Collins .347
1910 Ty Cobb .385 Detroit Tigers Nap Lajoie .384
1911 Ty Cobb .420 Detroit Tigers Shoeless Joe Jackson .408
1912 Ty Cobb .409 Detroit Tigers Shoeless Joe Jackson .395
1913 Ty Cobb .390 Detroit Tigers Shoeless Joe Jackson .373
1914 Ty Cobb .368 Detroit Tigers Eddie Collins .344
1915 Ty Cobb .369 Detroit Tigers Eddie Collins .332
1916 Tris Speaker .386 Cleveland Indians Ty Cobb .371
1917 Ty Cobb .383 Detroit Tigers George Sisler .353
1918 Ty Cobb .382 Detroit Tigers George Burns .352
1919 Ty Cobb .384 Detroit Tigers Bobby Veach .355
1920 George Sisler .407 St. Louis Browns Tris Speaker .388