Calculating Baseball Statistics

Tell the students, “We are going to learn about all of the math that is involved in the game of baseball.” Pass out the baseball unit pre-test to the students. Say, “We are going to take this pre-test to see what you already know about baseball because in order to do the math we have to know some things about the game.” Encourage the students to complete each question even if they do not know the answer. After allowing the students to complete the pre-test either individually or with a partner, review the answers.

Remind the students that these mathematical concepts (Mean or Average) are not just limited to baseball, but can be found in a variety of areas. In football many averages are calculated such as completion percentage, field goal percentage, and average points scored per game. In basketball, free throw percentage and 3-point percentage are common averages. In hockey goals against average is calculated to determine the success of a goalie. Nascar also calculates the average speed of a driver for a specific race.

H:\Thinkfinity\pretest.doc

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* As an alternative introduction, the following trivia game can be used to introduce the lesson.

https://www.readwritethink.org/parent-afterschool-resources/activities-projects/play-ball-read-write-30149.html

* Another introduction or hook can be done by putting the following website on a smartboard.

https://www.exploratorium.edu/baseball/reactiontime.html

Have a few students come to the board and test their reaction time. Record the reaction time of 8-10 students. Have the students rank the reaction times of their classmates from greatest to least. The students will then conclude why they believe a particular student in their class had the fastest reaction time.

Then have the students express why they think it would be important for a major league baseball player (or professional athlete in general) to have a fast reaction time.

Display the baseball statistic pages on the overhead and have the students do a “think-pair-share” discussing the abbreviations found on the statistical page.

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H:\Thinkfinity\StatPageKey2.PDF

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For a larger class the pages could be printed and handed out to the students. They are to identify what each of the abbreviations represent. After four to five minutes, ask for answers and have the students put the correct terms next to their abbreviations on their baseball notes sheet.

H:\Thinkfinity\IntroductionNotes.doc

H:\Thinkfinity\IntroductionNotesKey.PDF

Using the same statistical sheet show the students how to find where the year (Y-Axis) meets the specific abbreviated column (X-Axis) to find a specific statistic. Do the following two examples on the board as a whole class.

How many triples did Ken Griffey Jr. have in 2008? Answer: 1

In what year did Curtis Granderson have 52 walks? Answer: 2007

Have the students in their groups complete the five practice problems. Review answers as a whole group.

Display a picture of Joe Mauer on the board. “Does anyone know who this baseball player is?” Pause for responses. Tell the students it is Joe Mauer, catcher for the Minnesota Twins. “He is considered one of the best offensive players in baseball.” “Does anyone know what I mean by offensive player?” After listening to suggestions, tell the students that offensive means when a player is at-bat. Tell the students that the two main ways baseball players are judged on their offensive ability is by their batting average and slugging percentage. To illustrate the importance of batting average, tell the students that Joe Mauer just signed a new contract this year, primarily because he led the American League in batting average last year. He will be paid $184,000,000 over the next 8 years. Have the students try and figure out how much he will be paid each year ($23,000,000). Tell the students that they will learn the statistics involved with and how to calculate both batting average and slugging percentage.

Ask the students if anyone knows the difference between batting average and slugging percentage. After the suggestions have been given, have the students read the batting average and slugging percentage documents on the overhead.

H:\Thinkfinity\BattingAverage.doc

H:\Thinkfinity\Slugging_Percentage.doc

As a ticket out the door, have the students write one difference between batting average and slugging percentage without using their notes or looking on the board.

Day 2

Using the baseball statistical pages from the previous day, ask the students to identify the categories that they think they would need in order to calculate a player's batting average. After suggestions have been given highlight the hits category and the at-bats category. Show the students the following formula for calculating batting average:

H / AB

The quotient is rounded to the nearest thousandth. Remind the students that the quotient is the answer to a division problem.

Remind the students that the thousandths place is the third place to the right of the decimal. They should have known it was to the right of the decimal by its ending (ths).

Do the following example as a whole class:

Curtis Granderson 2009

Hits=157

At-Bats= 631

157/631 = 0.24881141

The first 8 is in the thousandths place and the second 8 is the digit to the right. The 8 tells us to round up, so the 8 in the thousandths place becomes a 9. So Curtis Granderson's batting average for 2009 is 0.249

To check for comprehension, have the students complete the first batting average example on their dry erase boards. When they have an answer, have them hold up their boards to show the teacher. If their answers are correct have the students continue and complete the remaining four batting average problems. If their answers are not correct, have those students come to the front of the room and rework the problem in a small group setting under the supervision of the teacher or instructional aide. If you need more examples use the statistical information from the lesson listed below. The statistical information can also be used for additional slugging percentage examples.

http://illuminations.nctm.org/LessonDetail.aspx?ID=L257

H:\Thinkfinity\battingaveragepractice.doc

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Put the batting average and slugging percentage information pages back on the overhead. Have the students recall the differences between slugging percentage and batting average. Tell the students they are now going to learn how to calculate slugging percentage. Using the same two baseball statistical pages of Ken Griffey Jr. and Curtis Granderson begin a “numbered pairs” activity. Have the one's show the two's where the hits category is and have the two's show the one's where the at-bats category is located. Tell the students they will be using many more statistical categories than they did for calculating batting average. Unlike batting average where only hits and at-bats were used, slugging percentage uses those categories as well as doubles, triples, and home runs.

Have the students find the practice problem chart on their calculating slugging percentage paper. Tell the students that some of the information will be copied directly from the baseball statistical page, but some of the categories will need to be calculated. Have the students fill in all of the information that they can about Ken Griffey Jr. (year 2009) on their chart using the statistical page. (They will only be able to fill in, hits, doubles, triples, homeruns, and at-bats)

H:\Thinkfinity\sluggingpractice.doc

H:\Thinkfinity\SluggingKey1.PDF

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Calculate the slugging percentage for Ken Griffey Jr. in 2009 with the students. Complete the chart on the board as the students complete charts at their seats. The first category that needs to be calculated will be singles (1B). Singles are never their own category on any statistical page or baseball card. To find singles it is the difference of Hits and XBH or Extra Base Hits. Remind the students that difference is the answer to a subtraction problem. Extra base hits are the sum of all of your doubles, triples, and homeruns. Remind the students that sum is the answer to an addition problem. For example, Ken Griffey Jr. in 2009 had 19 doubles, 0 triples, and 19 homeruns. His XBH would be 19 + 0 + 19 or 38. To find his singles it would be Hits (83) minus XBH (38). Ken Griffey Jr. had 45 singles (1B) in 2009. Once all of the singles, doubles, triples, and homeruns are recorded, you need to calculate the value of each. Singles are worth one base, so you find the product of singles and 1. Remind the students that product is the answer to a multiplication problem. Doubles are worth two bases so you calculate the product of doubles and 2. Triples are worth three bases so you calculate the product of triples and 3 and homeruns are worth four so you calculate the product of homeruns and 4. For example, Ken Griffey Jr. in 2009 had 19 doubles. 19 times 2 (because a double is worth two bases) would give you 38. The base value for doubles would be 38. Once you have the base value for singles, doubles, triples, and homeruns you are now ready to calculate total bases. Total bases (TB) are found by adding up the base values for singles, doubles, triples, and homeruns. For example, Ken Griffey Jr. in 2009 had a singles base value of 45, doubles value of 38, triples value of 0, and homeruns value of 76. 45 + 38 + 0 + 76 = 159. Ken Griffey Jr. in 2009 had 159 total bases (TB). The final step is the same as calculating batting average, except hits divided by at-bats, it is now total bases divided by at-bats rounded to the nearest thousandth. For example Ken Griffey Jr. in 2009 had 159 total bases and 387 at-bats. 159/387 = 0.410852713. His slugging percentage for that year would be 0.411.

To check for understanding, have the students complete the first slugging percentage example on their dry erase boards. When they have an answer, have them hold up their boards to show the teacher. If their answers are correct have the students continue and complete the remaining slugging percentage problems. If their answers are not correct, have those students come to the front of the room and rework the problem in a small group setting under the supervision of the teacher or instructional aide. Remind the students they are to use the information from their Ken Griffey Jr. and Curtis Granderson statistical data sheets. As a ticket out the door, have the students write the formula for calculating singles (H- XBH or Hits minus Extra Base Hits) without using their notes.

Summative Assessment and Homework

As a summative assessment, have the students complete the following batting average and slugging percentage activity. This assessment can be completed in a variety of ways, from graded homework assignment to a traditional quiz. The formulas needed can either be provided for learning support students or for more advanced students the formulas must be memorized.

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H:\Thinkfinity\BA&SLGkey1.PDF

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As a homework assignment have the students complete the following writing activity on batting average and slugging percentage.

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Interventions/Extension/ Higher Order Thinking

Interventions

As listed above in the procedures, have students who have difficulty calculating data or rounding numbers use the batting average and slugging percentage generators. They still must be able to identify the correct data from the chart and enter it into the generator.

Higher Order Thinking/Extension

Have the students go to the following website:

http://www.funbrain.com/math/index.html

The students will play the following math baseball game and calculate their own "math" batting average and slugging percentage. The type of problems (addition, subtraction, multiplication, division, all of the above) can be determined by the teacher and the level of difficulty (easy, medium, hard, super brain) can be adjusted for the varying levels of student abilities. The students will get 20 at-bats where they need to record the result (single, double, triple, homerun, or out) of each at bat. They should also record the number of runs they scored after those 20 at-bats. When they are finished they will calculate their own batting average and slugging percentage using the statistics they just collected.

After all of the batting average and slugging percentages have been calculated, have the students put their calculations on the board along with the number of runs they scored. Have the students draw comparisons and create connections between the batting averages and slugging percentages and the number of runs scored.

Finally, have the students select which student they feel had the best overall performance by looking at the three statistical numbers (batting average, slugging percentage, and runs scored). They need to justify why they feel this student had the best performance. (Answers will vary, as some students will select the student with the highest batting average, some will select the student with the highest slugging percentage, and some will select the student with the most runs scored.)

The focus of this lesson is to incorporate the real world (baseball) into the math classroom. It would be beneficial if the students were familiar with the concepts (rounding, problem solving, finding data from a chart) before this lesson. This lesson is better served as a reinforcement of concepts as opposed to an introduction of concepts.

Formative Assessment

Formative Assessments

Ongoing formal assessments can be done during small group or partner work. It can also be done by evaluating work done in class and the students' interaction with each other.

After the batting average and slugging percentage problems are completed, the students will complete their first independent problem on dry erase boards. Their answers can be shown directly to the teacher, if correct they can complete the remaining problems independently. If incorrect they can be pulled into a small group format for further instruction and clarification.

As the students are working independently the teacher can monitor student work and progress.

Related Materials & Resources

Materials and Resources for the Lesson

Fun with baseball stats. (n.d.). Retrieved from http://illuminations.nctm.org/LessonDetail.aspx?ID=L257

Play ball! read and write sports trivia. (n.d.). Retrieved from https://www.readwritethink.org/parent-afterschool-resources/activities-projects/play-ball-read-write-30149.html

http://www.funbrain.com/math/index.html

References

Nightengale, B. (2010, March 21). Minnesota Twins, Joe Mauer agree to eight-year contract extension. USA Today,

Player search. (n.d.). Retrieved from http://mlb.mlb.com/mlb/players/

Author

Date Published

March 01, 2010

Calculating Baseball Statistics