— Burt Kaliski Jr. (@modulomathy) August 22, 2013
Clearly, if the baseball player had exactly 1000 at-bats, he or she could achieve a batting average of exactly .233 with exactly 233 hits. But this would not be part of a typical seven-game series by any means. The most at-bats any Major League Baseball player has had in an entire season is 716.
We need a smaller number of at-bats, something more consistent with the typical 4 to 5 per game, or 28 to 35 for a seven-game series.
Within this constraint, the best match is 7/30, which is off from the .233 average by just over .0003.
There are only five other fractions with denominators less than 100 that have a decimal value rounding to .233: 17/73; 14/60 and 21/90 (which are equivalent to 7/30); and 10/43 and the equivalent 20/86. None would be a typical performance for a seven-game series. The fraction with the smallest denominator among these alternatives would require more than six at-bats per game on average, which would be unusual for a seven-game series. Even in the celebrated Red Sox-Yankees 2004 ALCS with its two extra-inning games, the most at-bats any player had was 36.