A Baseball Paradox
from I Think, Therefore I Laugh by John Allen Paulos
Babe Ruth and Lou Gehrig played baseball for the New York Yankees. Suppose Ruth had a higher batting
average than Gehrig for the first half of the season. Suppose further that during the second half of the
season Ruth had a higher average than Gehrig. Is it possible for Gehrig's batting average for the entire
season to be higher than Ruth's batting average? The answer is yes, but how can that be?
One way that it can be is this:
During the first half of the season,
Ruth hits for an average of .344, getting 55 hits in 160 times at bat.
Gehrig hits for an average of .342, getting 82 hits in 240 times at bat.
During the second half of the season,
Ruth hits for an average of .250, getting 60 hits in 240 times at bat.
Gehrig hits for an average of .238, getting 38 hits in 160 times at bat.
Nevertheless, for the whole season:
Ruth hits for an average of .287, getting 115 hits in 400 times at bat.
Gehrig hits for an average of .300, getting 120 hits in 400 times at bat.