Questions: Major League Baseball general managers are depending more and more on specialized mathematical formulas known as "analytics" to evaluate players and make personnel decisions. One such formula is known as BABIP, or "Batting Average on Balls in Play." The formula is defined as BABIP = (H-HR)/(AB-K-HR+SF), where H= hits, HR= home runs, AB= at bats, K= strikeouts, and SF= sacrifice flies. The stats of two players are shown below. Determine each player's BABIP. At Bats Hits Home Runs Strikeouts Sacrifice Flies --------------- 1st player 566 169 16 111 3 2nd player 554 170 26 171 2 Find the 1st player's BABIP. BABIP = 346 (Simplify your answer. Round to three decimal places as needed.) Find the 2nd player's BABIP. BABIP = (Simplify your answer. Round to three decimal places as needed.)

Major League Baseball general managers are depending more and more on specialized mathematical formulas known as "analytics" to evaluate players and make personnel decisions. One such formula is known as BABIP, or "Batting Average on Balls in Play." The formula is defined as BABIP = (H-HR)/(AB-K-HR+SF), where H= hits, HR= home runs, AB= at bats, K= strikeouts, and SF= sacrifice flies. The stats of two players are shown below. Determine each player's BABIP.

At Bats Hits Home Runs Strikeouts Sacrifice Flies
---------------
1st player 566 169 16 111 3
2nd player 554 170 26 171 2

Find the 1st player's BABIP.
BABIP = 346 (Simplify your answer. Round to three decimal places as needed.)
Find the 2nd player's BABIP.
BABIP = (Simplify your answer. Round to three decimal places as needed.)

Transcript text: Major League Baseball general managers are depending more and more on specialized mathematical formulas known as "analytics" to evaluate players and make personnel decisions. One such formula is known as BABIP, or "Batting Average on Balls in Play." The formula is defined as BABIP $=\frac{H-H R}{A B-K-H R+S F}$, where $H=$ hits, $H R=$ home runs, $\mathrm{AB}=$ at bats, $\mathrm{K}=$ strikeouts, and $\mathrm{SF}=$ sacrifice flies. The stats of two players are shown below. Determine each player's BABIP. \begin{tabular}{|l|c|c|c|c|c|} \hline & At Bats & Hits & Home Runs & Strikeouts & Sacrifice Flies \\ \hline 1st player & 566 & 169 & 16 & 111 & 3 \\ \hline 2nd player & 554 & 170 & 26 & 171 & 2 \\ \hline \end{tabular} Find the 1st player's BABIP. BABIP $=346$ (Simplify your answer. Round to three decimal places as needed.) Find the 2nd player's BABIP. $\mathrm{BABIP}=\square$ $\square$ (Simplify your answer. Round to three decimal places as needed.)

Solution

Solution Steps

To determine each player's BABIP, we will use the given formula: \[ \text{BABIP} = \frac{H - HR}{AB - K - HR + SF} \] We will plug in the respective values for each player and compute the BABIP, rounding the result to three decimal places.

Step 1: Define the BABIP Formula

The formula for Batting Average on Balls in Play (BABIP) is given by: \[ \text{BABIP} = \frac{H - HR}{AB - K - HR + SF} \] where:

$ H $ = Hits
$ HR $ = Home Runs
$ AB $ = At Bats
$ K $ = Strikeouts
$ SF $ = Sacrifice Flies

Step 2: Calculate the 1st Player's BABIP

For the 1st player:

$ H = 169 $
$ HR = 16 $
$ AB = 566 $
$ K = 111 $
$ SF = 3 $

Substitute these values into the formula: \[ \text{BABIP}_1 = \frac{169 - 16}{566 - 111 - 16 + 3} \] \[ \text{BABIP}_1 = \frac{153}{442} \] \[ \text{BABIP}_1 \approx 0.346 \]

Step 3: Calculate the 2nd Player's BABIP

For the 2nd player:

$ H = 170 $
$ HR = 26 $
$ AB = 554 $
$ K = 171 $
$ SF = 2 $

Substitute these values into the formula: \[ \text{BABIP}_2 = \frac{170 - 26}{554 - 171 - 26 + 2} \] \[ \text{BABIP}_2 = \frac{144}{359} \] \[ \text{BABIP}_2 \approx 0.401 \]