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Numerical Computations

Practice working with probability in story problems

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Credit: Tom Thai
Source: http://www.flickr.com/photos/eviltomthai/3632652999/
License: CC BY-NC 3.0

Have you ever heard anyone talk about baseball statistics? Many fans would say that the great players can "bat at least three hundred." It can be hard to understand the numbers that describe a baseball player if you don’t know where they come from. Knowing how to calculate a batting average can help you evaluate the performance of your favorite MLB athletes.

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In 2012, the San Francisco Giants defeated the Detroit Tigers to win the World Series. The catcher, Buster Posey, who ended the season with a .336 batting average, earned the title of National League Batting Champion. A batting average is calculated by taking the total number of hits and dividing by the total number of "at-bats," or batting opportunities. If you look at a batting average as a probability calculation, it’s like dividing the number of favorable outcomes by the number of total possible outcomes to get the probability of an event.

Credit: Don DeBold
Source: http://www.flickr.com/photos/28156071@N00/9396887523
License: CC BY-NC 3.0

So when people say that Buster Posey was “batting three-thirty-six” in 2012, they’re saying that he was getting an average of 0.336 hits per at-bat. This is the same as saying he got 336 hits per 1000 at-bats, or that he got hits 33.6% of the time. That's pretty good! Next time you read a baseball article or listen to the announcers in a game, pay attention to the players' batting averages, and think about whether or not they need to improve their number of favorable outcomes.

See for yourself: http://sports.espn.go.com/espn/wire?section=mlb&id=8459345

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In his 2012 season, Posey had a total of 530 at-bats and 178 hits while the Pittsburgh Pirates' Andrew McCutchen had 593 at-bats and 194 hits. Who had the higher batting average? Does getting more hits always mean your average will be higher?

Image Attributions

  1. [1]^ Credit: Tom Thai; Source: http://www.flickr.com/photos/eviltomthai/3632652999/; License: CC BY-NC 3.0
  2. [2]^ Credit: Don DeBold; Source: http://www.flickr.com/photos/28156071@N00/9396887523; License: CC BY-NC 3.0

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