**Question:**Buster Posey had the best batting average in the National League in 2012, 0.336, 178 hits in 530 at bats. Andrew McCutchen had the second best batting average in the league – 0.327, 194 hits in 593 at bats. Had Andrew McCutchen received more walks and made fewer outs he would have had a higher batting average. How many more walks or fewer outs would have resulted in Andrew McCutchen winning the batting title?

**Answer**: A batting average is hits divided by at bats. A walk is not at bat. If Andrew McCutchen had walked more and had fewer at bats his batting average would have been higher.

Andrew
McCutchen had 194 hits. Solve this
problem by using the definition of batting average to solve for the number of
at bats consistent with 194 hits and a 0.336 average.

0.336=(194/AB)

Or

AB=194/0.336

Or

AB=577.38

577.38 is
the breakeven point. However, there is
no such thing as a fractional at bat. At
AB=577, Andrew McCutchen has a higher batting average than Buster Posey.

Andrew
McCutchen actually had 593 at bats. An
additional 16 walks (593-577) would have given Andrew McCutchen the batting
title.

This problem
could also be solved with algebra.

X is the
number of additional walks

593-X is the
number of at bats after X additional walks

From the
batting average definition:

0.336=194/(593-X)

or

193=0.336*593-0.336*X

Or

0.336*X=0.336*593-194

or

X=(199.248-194)/0.336

X=15.6

Again, there
is no such thing as a fractional walk
Had Andrew McCutchen walked an additional 16 times he would have won the
batting title.

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