Mantle: June 23 .392
Williams: May 8 .474
As late as June 5 Williams BA was .401. In 1956 Mantle was at .400 on June 8.
At the end of April Williams led .426 to .306. By June 5: Williams .401, Mantle .362. June 16 they were tied at .379. June 29 Mantle had his biggest lead, 34 points: .389 to .355. Lead changes:
Date Mantle, Williams
Williams didn't play September 2-16.
Mantle played his last game September 22.
Final game for Williams:
So Ted Williams never took a serious run at .400 in 1957 but instead battled Mickey Mantle for the second consecutive year and won. Mantle had led almost all the way in 1956 only to have Williams to take the lead September 14-21.
1956 BA race: Mantle v. Williams. Tuesday, November 22, 2016
Their game 1957 logs:
This link has that data combined, which is how the graph was created. The first two date columns have the dates when they played. Column three has all dates during the regular season. For dates when they played doubleheaders, the BA after game two is shown. For dates when they did not play, the BA of the most recent game is carried forward.
Williams had the highest BA six times: 1941, 1942, 1947, 1948, 1957, 1958. Mantle led once, 1956.