Batting Averages

Batting Averages


In this topic, you will apply your knowledge of percentages and mean to baseball.

Example 1:
In 530 at bats, a baseball player has a batting average of 0.241. In the next game, he has 4 at bats. What is the most likely number of hits he will get?
Suppose he hits 3 of those swings. What is his new batting average to three places?
Part 1: Most likely number of hits
The baseball player has a batting average of 0.241 after 530 at bats. This means that he has a 24.1% chance of getting a hit whenever he swings at a ball.
1. The most likely number of hits is the number of hits × batting average.
So for the next 4 hits, the most likely number of hits is 4 × 0.241 = 0.964
2. We then round to the nearest whole number of hits.
0.964 hits rounds to 1 hit
Part 2: New batting average
Batting average =
We calculate the new batting average using the fact that after his 530 at bats, the baseball player made 3 more hits from 4 more swings.
New batting average =
=


Original number of hits = original batting average × original number of swings
= 0.241 × 530
= 127.73 which rounds to 128

New batting average =
=
= 0.245

Most likely number of hits: 1
New batting average: 0.245

Sample Problems For Batting Averages
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Complexity=0
Answer the following questions about batting averages.

1. In 171 at bats, a baseball player has a batting average of 0.391. In the next game, he has 2 at bats. What is the most likely number of hits he will get?
Suppose he hits 1 of those swings. What is his new batting average to three places?
2. In 303 at bats, a baseball player has a batting average of 0.354. In the next game, he has 5 at bats. What is the most likely number of hits he will get?
Suppose he hits 0 of those swings. What is his new batting average to three places?
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Complexity=1
Answer the following questions about batting averages.

1. In 126 at bats, a baseball player has a batting average of 0.301. In the next game, he has 2 at bats. What is the most likely number of hits he will get?
Suppose he hits 1 of those swings. What is his new batting average to three places?
2. In 272 at bats, a baseball player has a batting average of 0.363. In the next game, he has 3 at bats. What is the most likely number of hits he will get?
Suppose he hits 0 of those swings. What is his new batting average to three places?
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Complexity=2
Answer the following questions about batting averages.

1. In 415 at bats, a baseball player has a batting average of 0.202. In the next game, he has 2 at bats. What is the most likely number of hits he will get?
Suppose he hits 2 of those swings. What is his new batting average to three places?
2. In 381 at bats, a baseball player has a batting average of 0.316. In the next game, he has 4 at bats. What is the most likely number of hits he will get?
Suppose he hits 4 of those swings. What is his new batting average to three places?


Answers
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Complexity=0

Solution
The player's batting average is 0.391 and the number of swings is 2.
0.391 × 2 = 0.782 which rounds to 1.
Original total number of hits = batting average * total swings = 0.391 × 171 = 67.
New total number of hits = original number of hits + number of hits at next game = 67 + 1 = 68.
New total number of swings = original number of swings + number of swings at next game = 171 + 2 = 173.
New batting average = new total number of hits / new total number of swings = 68 / 173 = 0.393.

Solution
The player's batting average is 0.354 and the number of swings is 5.
0.354 × 5 = 1.77 which rounds to 2.
Original total number of hits = batting average * total swings = 0.354 × 303 = 107.
New total number of hits = original number of hits + number of hits at next game = 107 + 0 = 107.
New total number of swings = original number of swings + number of swings at next game = 303 + 5 = 308.
New batting average = new total number of hits / new total number of swings = 107 / 308 = 0.347.

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Complexity=1
Solution
The player's batting average is 0.301 and the number of swings is 2.
0.301 × 2 = 0.602 which rounds to 1.
Original total number of hits = batting average * total swings = 0.301 × 126 = 38.
New total number of hits = original number of hits + number of hits at next game = 38 + 1 = 39.
New total number of swings = original number of swings + number of swings at next game = 126 + 2 = 128.
New batting average = new total number of hits / new total number of swings = 39 / 128 = 0.305.

Solution
The player's batting average is 0.363 and the number of swings is 3.
0.363 × 3 = 1.089 which rounds to 1.
Original total number of hits = batting average * total swings = 0.363 × 272 = 99.
New total number of hits = original number of hits + number of hits at next game = 99 + 0 = 99.
New total number of swings = original number of swings + number of swings at next game = 272 + 3 = 275.
New batting average = new total number of hits / new total number of swings = 99 / 275 = 0.360.

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Complexity=2

Solution
The player's batting average is 0.202 and the number of swings is 2.
0.202 × 2 = 0.404 which rounds to 0.
Original total number of hits = batting average * total swings = 0.202 × 415 = 84.
New total number of hits = original number of hits + number of hits at next game = 84 + 2 = 86.
New total number of swings = original number of swings + number of swings at next game = 415 + 2 = 417.
New batting average = new total number of hits / new total number of swings = 86 / 417 = 0.206.

Solution
The player's batting average is 0.316 and the number of swings is 4.
0.316 × 4 = 1.264 which rounds to 1.
Original total number of hits = batting average * total swings = 0.316 × 381 = 120.
New total number of hits = original number of hits + number of hits at next game = 120 + 4 = 124.
New total number of swings = original number of swings + number of swings at next game = 381 + 4 = 385.
New batting average = new total number of hits / new total number of swings = 124 / 385 = 0.322.