Batting Averages and More (PBS Mathline)

  “Batting Averages and More” is a classic real-world educational lesson plan originally produced by PBS MATHLINE. The curriculum uses the framework of sports analytics to teach middle and high school students core mathematical concepts like ratios, fractions, decimals, and data organization.

The Core Math: How Batting Average Works

In baseball, a batting average is simply a ratio converted into a decimal.

\(\text{Batting\ Average\ (BA)}=\frac{\text{Total\ Hits\ (H)}}{\text{Official\ At-Bats\ (AB)}}\)

To calculate it like the PBS lesson plans require, students follow a strict multi-step mathematical process:

1. Calculate Official At-Bats: Students learn that total plate appearances do not equal official “at-bats”. They must subtract exclusions like walks (BB), hit-by-pitches (HBP), and sacrifice flies/bunts (SF/SH) from the total times a player steps up to the plate.

2. Perform Long Division: Divide the total number of hits by those official at-bats. For example, if a player has 6 hits in 20 official at-bats, the fraction is \(\frac{6}{20}\).

3. Convert and Round to the Thousandths Place: \(\frac{6}{20}\) equals 0.300. In baseball culture, this decimal is written without the leading zero and read as a whole number (e.g., “batting .300”). If a calculation results in a repeating decimal like 0.3333…, students practice rounding up or down to exactly three decimal places.

Beyond Batting Average: “And More”

The “and more” portion of the PBS curriculum expands into richer data analysis and probability modeling:

• Decimal Comparison: Students use a place-value grid to compare which decimals are larger (e.g., comparing a .335 hitter to a .319 hitter by looking closely at the hundredths and thousandths columns).

• Advanced Ratios (OBP and Slugging): Introducing On-Base Percentage (OBP) and Slugging Percentage (SLG), where weighted values are assigned (a double counts as 2 bases, a triple as 3, and a home run as 4) to teach advanced weighted averages.

• Probability Simulations: Using tools like dice rolls or coin flips to simulate a player’s season-long performance based on their average. For example, rolling a 6-sided die where a 1 or 2 represents a “hit” simulates a .333 batting average.