fantasy baseball math activity

8/2/2019 Fantasy Baseball Math Activity

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The Middle School Math Project

http://www.pbs.org/mathline Page 1

Fantasy BaseballPart I

(Number and Number Relations)

Objective

Students will study a thematic unit based on the game of baseball to investigatenumber and number relations.

Overview of the Lesson

The following is an overview of the unit Fantasy Baseball - Parts I and II:

Students play a few innings of baseball as an introductory activity to this thematicunit based on the game of baseball. The unit is centered around the analysis of the

statistical data contained on professional baseball trading cards. These cards are firstused to familiarize students with some of the basic terminology associated with thegame. Next, students are directed to focus their attention on the actual statisticaldata included on the card and how to utilize this statistical data to determine theoverall rating of a players past performance. Additionally, students form work withdecimals and ratios to obtain key statistical data. This key statistical data, such as thenumber of home runs to the number of cumulative times at bat, are essential to thenext phase of the unit: building a nine-player baseball team.

Student pairs act as co-managers of a baseball team. Each pair receives a pack ofbaseball cards. They compute and analyze the key statistical data of the given players,make decisions on who they want to keep and who they want to trade, arrange theirlineups, and play simulated games. Students use the key statistical data to constructindividual player spinners, determine the line up, and play a simulated baseballgame. The ultimate goal is to be the manager of the winning team of the FantasyBaseball World Series.


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PBS MATHLINE

MSMP Fantasy Baseball-Part 1: Lesson Guide http://www.pbs.org/mathline Page 2

Materials

Per Student

Fantasy Baseball Pre-Assessment Worksheet

Baseball Card Glossary

Player Guidelines

Copy of Baseball Statistics or Baseball Cards for 2 players (Robin Ventura isincluded in materials)

Player Comparison Chart Worksheet

Calculator

Cutout tag board bases labeled Home, 1st, 2nd. and 3rd

Procedure

Describe the Fantasy Baseball unit to the students:During this unit, you will become managers of your very own baseball team. Youwill learn how to use decimals and ratios to analyze key statistical data, draft players,make trades, construct a lineup, and play simulated games, all the way to theFantasy Baseball World Series. All of this will occur as we study the mathematics ofbaseball. Baseball trading cards will be used as our source of information.

Note: A copy of a Fantasy Baseball Pre-assessment is included. If used, studentsshould complete this activity prior to the beginning the unit.

It is important that all students have a general knowledge of how the game ofbaseball is played before they study this unit. Therefore, as an introduction, havestudents play a few innings of baseball. If this is not possible, show a video clip of afew innings of a baseball game and discuss some of the plays and players.

Place the four tag board bases around the room. Each student should receive a copyof the Robin Ventura baseball card (or a baseball card of a player of your choosing )and a copy of the Baseball Card Glossary. Point out that the terminology in theglossary matches the terminology on the baseball card. Have students demonstratetheir understanding of the definitions of the terms in the glossary by playing asimulated game. These terms include: hit (H), double (2B), triple (T), homerun(HR), runs batted in (RBI), base on balls (BB), strikeout (SO), and stolen base (SB).The other terms which are included in the glossary should also be discussed at thistime. These additional terms will probably be very easy for students to understand


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PBS MATHLINE


and master. They include year (YR), TEAM, games (G) and official at bats (AB).Average (AVG) will be discussed later.

Place students in small groups where they further discuss the glossary terms. Havethem closely scrutinize the data of the sample player based on the definitions ofthese terms. This should strengthen their familiarity with some of the baseballterminology, while at the same time making them keenly aware of how anunderstanding of decimals, ratios, and statistics enable them to make decisions basedon mathematics.

To prepare students to be able to make informed decisions about trades, line-ups etc.,it is essential to have them focus on some comparative relationships which arecalled key statistics. To begin this process, review ratios and proportions. Followingthis review, distribute the Player Comparison Chart and Player Guidelines. ThePlayer Guidelines should be used to assist students in the evaluation anddiscrimination of players based on their interpretation of the data.

Systematically discuss and compute the following key statistics. Make sure thatstudents understand why these statistics are so important and the theoreticalimplications embedded in their values.

Batting Average (AVG) HAB

On-Base Percentage (OB%) (H + BB)(AB + BB)

Cumulative at Bats (CUM. AB) AB + BB

HR : CUM. AB (unit ) Ratio HR = 1AB + BB x

SO : CUM. AB (unit) Ratio SO = 1AB + BB x

Note: TheHR : CUM. AB and the SO : CUM. AB are computed to represent unitratios so that there is a clearer picture of what is happening in the homerun andstrikeout categories. Therefore, if the unit ratio is known, the manager will havesome theoretical idea of what performances to expect from a player based on his past

performances.

To assess students interpretation of these ratios, have them determine the mostfavorable performances of this player and why. When assessing the HR: CUM. AB(unit) Ratio, is it more favorable to have the unit compared to a larger number orsmaller number? Likewise, when assessing the SO : CUM. AB (unit) Ratio, is itmore favorable to compare the unit to a larger number or smaller number?


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PBS MATHLINE


For practice, provide students with the data for a another baseball player. Again,students should go through the process of computing the key statistical data. Theresults should be analyzed to determine the possible benefits or handicaps in havingthis player on their team.

ResourcesScheidt, Tim. Fantasy Baseball, 1994. Giant Step Press. Solvang, California


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PBS MATHLINE


Ideas for Online Discussion

(Some ideas may apply to more than one standard of the NCTM Professional Standards for TeachingMathematics.)

Standard 1: Worthwhile Mathematical Tasks

The teacher of mathematics should pose tasks that are based on knowledge ofstudents understandings, interests, and experiences. (p. 25) A unit that buildsaround a theme, is different from one that is structured around a mathematicaltopic. Comment on any strengths or concerns you might have about each way oforganizing.

The knowledge of so many mathematical skills is needed to successfullycomplete this unit. Do you feel that the skills should be taught in advance andthen applied to the situation or should the skill be taught in the context of theapplication?

Standard 4: Tools for Enhancing Discourse

In this thematic unit, students played and dramatized a game, used real datafrom baseball cards, chose when to use a calculator and computer, andconstructed spinners to simulate a game. When planning a unit, how do youinsure that a variety of tools for enhancing discourse are used?

Standard 6: Analysis of Teaching and Learning

It is essential for teachers to make plans, both short- and long-range. (p. 63)Using thematic units as an integral part of the instructional program providesthe environment for both. What affect has the use of thematic units had onyour students and on you?


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FANTASY BASEBALL

Player Comparison Chart

T e a m N a m e _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _

M an age r s __________________________ _ __ __ __ __ __ __ __ __ __ __ __ __ __ __

Complete the chart below for each of the eligible players you have received. Be sure to calculate the battingaverage and on-base percentage to the nearest thousandth and record the HR: Cum. AB ratio and SO: Cum.AB ratio as unit ratios rounded to the nearest whole number.

Pos./YR Name AB Cum.

ABAvg. OB% HR:

Cum.AB

SO:

Cum.AB

PBS MATHLINE MSMP Fantasy Baseball-Part 1: Activity Sheet


8/18

Name _ _ _ _ _ __ _ _ _ _ __ _ _ _ _ __ _ _ _ _

Date _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _

Period _ _ _ _ _ _ _ _ _ _ _ _ _ _

Fantasy Baseball

Pre-Assessment -- New Kids In Town

Imagine that two new kids have just moved into your neighborhood and arelooking to play on a local baseball or softball team. You have been told by yourcoach that one of these students will be joining your team. Below are the statisticsthat they accumulated for their previous teams. Analyze these statistics to help youdetermine which player your would like to have on your team. On a separate sheetof paper, explain who you would select, Player A or Player B. Be sure to supportyour selection with the statistics that are given.

Player A

AB H 2B 3B HR BB SO37 13 4 0 5 3 9

Player B

AB H 2B 3B HR BB SO61 24 8 3 2 9 7

PBS MATHLINE MSMP Fantasy Baseball Part 1: Activity Sheet


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BASEBALL CARD GLOSSARY

YR the year the player played for a given team.

TEAM the team played for during the year. Major League teams arerepresented by the team name (Tigers, Giants, etc.). Minor Leagueteams are represented by the city in which the tram resides (Nashville,Eugene, etc.)

AVG this number represents the player's batting average. This average is thedecimal equivalent of the ratio of hits to official at bats.

G the number of games the player appeared in for the team.

AB this represents the number of official at bats the player had during theseason. Official at bats (AB) do not include walks (BB) or sacrifice hits(bunts, sacrifice files). Sacrifice hits do not count as at bats because theplayer makes an expected out in order to advance the runner(s).

R the number of runs the player scored (times he crossed home plate).

H the number of hits a player got during the season. This numberrepresents the total singles, doubles, triples and home runs the playeraccumulated during the season.

2B the number of doubles or times the player reached second base safelydue to a hit.

3B the number of triples or times the player reached third base safely dueto a hit.

HR the number of home runs the player hit during the season.

RBI the number or runs batted in that the player was credited with duringthe season. This means that other players scored runs due to theplayer's hitting performance.

BB the number of walks (also known as bases on balls) the player receivedduring the season.

SO the number of strikeouts the player had during the season.

SB the number of stolen bases the player had during the season.

PBS MATHLINE MSMP Fantasy Baseball Part 1: Activity Sheet


10/18

Fantasy Baseball

Player Guidelines

Use the following guidelines to help you determine whether or not you would liketo keep certain players for your team. Although these guidelines do not representeverything you should consider, they'll be helpful when you receive your initialdraft of players.

BATTING AVERAGE

below .220 weak hitter: you won't want to keep unless their other statistics(OB%, HR : Cum., AB ratio, SO : Cum. AB ratio) are consideredfavorable.

.220 - .250 low average to average hitter: again, check their other statisticsand weigh your choices.

.250 - .300 good, solid hitter; more than likely you will want to keep aplayer of this caliber unless other statistics are unfavorable oryou are able to trade for a player with better overall statistics.

.300 & up excellent hitter: this could be your superstar. Look over theother statistics but expect to keep this player.

ON-BASE PERCENTAGEThe opinion of a group of student experts:

"We like to see a player that has an on-base percentage that is 60 to 100points higher than their batting average. We also feel that this percentageshould be .340 or higher: The higher the percentage, the better!"

HR : CUM. AB (UNIT) RATIOThe guidelines for this statistic generated by the same group of students experts:

"We consider a HR : Cum. AB ratio of 1:30 to be very good. We feel that

this ratio or one that has a smaller number deserves strong consideration.The smaller the number, the better!"

SO : CUM. AB (UNIT) RATIOThe guidelines for this statistic, also generated by the group of students experts:

"We consider a SO : Cum. AB ratio of 1:8 to be very good. We feel that thisratio or one that has a larger number deserves strong consideration. Inthis case, the larger the number, the better!"

PBS MATHLINE MSMP Fantasy Baseball Part-1: Activity Sheet


11/18

The Middle School Math Project

http://www.pbs.org/mathline Page 1

Fantasy BaseballPart II

(Number and Number Relations)

Objective

Students will study a thematic unit based on the game of baseball to investigatenumber and number relations.

Overview of the Lesson

Following is the overview of Fantasy Baseball - Parts I and II:

Students play a few innings of baseball as an introductory activity to a thematic unitbased on the game of baseball. The unit is centered around the analysis of thestatistical data contained on professional baseball trading cards. These cards are firstused to familiarize students with some of the basic terminology associated with thegame. Next, students are directed to focus their attention on the actual statisticaldata included on the card and how to evaluate these statistics to determine theoverall rating of a players past performance. Additionally, students form ratiosusing selected data to obtain key statistical data. This key statistical data, such as thenumber of home runs to the number of cumulative times at bat (unit ratio), areessential to the next phase of the unit: building a nine-player baseball team.

Student pairs act as co-managers of a baseball team. Each pair receives a pack ofbaseball cards. They compute and analyze the key statistical data of the given players,

make decisions on who they want to keep and who they want to trade, arrange theirlineups, and play simulated games. The simulated games are played using playerspinners which are configured based on the statistical data of each player. Theultimate goal is to be the manager of the winning team of the Fantasy BaseballWorld Series.


12/18

PBS MATHLINE

MSMP Fantasy Baseball-Part 2 Lesson Guide http://www.pbs.org/mathline Page 2

Materials

Each Pair

Pack of Baseball Trading Cards

Baseball Card Glossary (from Part I)

Player Guidelines (from Part I)

Statistical Guide (from Part I)

Player Comparison Chart (from Part I)

Player Analysis Charts ( 2 worksheets )

How to Make A Player Wheel (Written Directions & Pictorial Model)

Calculator

Player Wheel materials: card stock scissors, markers, spinners (spinners can be

made by spinning a bobby pin around the pencil point)

Procedure

For the remainder of the unit, students should work in pairs, as co-managers of abaseball team. Distribute a set of professional baseball trading cards to each of theteams. Each team will need a name, so first have the co-managers decide on namesfor their teams.

Once the names have been selected and recorded, the co-managers are to use the

data from each of the baseball cards in their pack to complete the Player ComparisonChart. Instruct them to evaluate this information and based on these evaluationsdecide which players they want to keep and which players they want to trade.Remind them that they must have a player for each of the nine positions on theteam: pitcher, catcher, first baseman, second baseman, third baseman, shortstop,right fielder, center fielder and left fielder.

When all of the co-managers have completed this evaluation process and havemade the decisions on who they want to trade, allocate appropriate time for thetrade talks. At this time co-managers make the necessary deals to obtain the playersthey need/want to complete their nine player teams.

The next phase involves the completion of the Player Analysis Charts. One chartshould be completed for each player on the team. (There are 5 per page, so co-managers will need 2 pages.) Specific instructions for computing the additional dataare included on the Statistical Guide sheet.

The co-managers first use this information to decide on the batting order for theirplayers. Suggest that they should think carefully about how to strategically position


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PBS MATHLINE


their players in the line-up, particularly their top hitters, to maximize the potentialfor scoring runs.

Secondly, this information is used as the source of data for the player wheels. Aplayer wheel must be constructed for each player. Its construction is based on theprobabilistic outcome of a players performance each time he comes up to bat.Generally when a player is at bat one of the following occurs: He either hits a single,double, triple, home run, or he walks, strikes out, flies out or grounds out. The player wheel is therefore divided into those eight sections. Based on the playersrecord last season, the number of times each one of these events occurred iscompared to the total number of times the player came up to bat. These ratios arerenamed to their decimal equivalents and are then converted to degrees. A circle isthen divided into the eight sections based on the number of degrees in each section.Using a spinning device, theplayer wheel becomes a tool to be used when studentsplay the Fantasy Baseball games. (Instructions for constructing the player wheel areprovided on the "How to Make a Player Wheel" sheet. A pictorial model is alsoprovided.)

Students are finally ready to begin the Fantasy Baseball tournament. Provide amodel baseball diamond and four chips for each game. Co-managers will spin eachwheel in the order of their line-up and move their players (chips) around the basesbased on the label in the section where the spinner lands. During the games, theymust keep a record of the number of outs and the number of runs. Because of thelimiting features of playing a simulated game of baseball, stolen bases and certainplays such as an on-base player advancing two bases from his teammates single, willnot be allowed

Depending on the amount of time you can devote to the tournament, you may

have to limit games to 2 or 3 innings. You may also want to divide the teams into 2leagues where each team plays every team in its league. The team with the mostwins in each league will play each other in the Fantasy Baseball World Series.

Extensions & Connections

Have students investigate the role that mathematics plays in other sports such asbasketball, soccer, tennis and football.

If there are 20 baseball teams and every team played each other, and all of thewinners played each other, and these winners played each other, in total how many

games will have been played to determine the winner?


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PBS MATHLINE


Resources

Scheidt, Tim. Fantasy Baseball , 1994. Giant Step Press. Solvang, California.

Ideas for Online Discussion

(Some ideas may apply to more than one standard of the NCTMProfessional Standards for TeachingMathematics.)

Standard 1: Worthwhile Mathematical Tasks

Provide a brief overview of a thematic unit that you have used with yourstudents.

From your experience, does the thematic unit concept provide the missing

structure needed to enhance the learning of the content?

Standard 3: Students Role in Discourse

Fantasy Baseball provided numerous opportunities for students to try toconvince themselves, and one another of the validity of particularrepresentations, solutions, conjectures, and answers. (p. 45) Describe howpromoting and encouraging discussion and debate can enhance the studentlearning and increase the level comprehension.

Standard 6: Analysis of Teaching and Learning

How would you assess students knowledge of the mathematical content at theconclusion of this unit?


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FANTASY BASEBALL

Player Analysis Chart(Examples)

Year 1991

Name Cum.AB H IB 2B 3B HR BB SO OtherOuts FO GO

Robin Ventura 686 172 123 25 1 23 80 67 367 183 184

RATIO123686

25686

1686

23686

80686

67686

183686

184686

DECIMAL EQUIVALENT .1793 .0364 .0014 .0335 .1166 .0976 .2667 .2682

DEGREES 65 13 0 12 42 35 96 97

YEAR 1985

NameCum.

AB H IB 2B 3B HR BB SOOther

Outs FO GO

Willie McGee 646 216 162 26 18 10 34 86 310 155 155

RATIO162646

26646

18646

10646

34646

86646

155646

155646


DEGREES 90 14 10 6 19 48 86 86PBS MATHLINE MSMP Fantasy Baseball-Part 2: Activity Sheet


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Player Analysis Chart

NameCum.AB H IB 2B 3B HR BB SO

OtherOuts FO GO

RATIO

DECIMAL EQUIVALENT

DEGREES


OtherOuts FO GO

RATIO

DECIMAL EQUIVALENTDEGREES


OtherOuts FO GO

RATIO

DECIMAL EQUIVALENT

DEGREES


OtherOuts FO GO

RATIO

DECIMAL EQUIVALENT

DEGREES


OtherOuts FO GO

RATIO

DECIMAL EQUIVALENT

DEGREESPBS MATHLINE MSMP Fanatasy Baseball-Part 2: Activity Sheet


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FANTASY BASEBALL

How to Make A Player Wheel

Year 1991


OtherOuts FO GO

Robin Ventura 686 172 123 25 1 23 80 67 367 183 184

RATIO123686

25686

1686

23686

80686

67686

183686

184686


DEGREES 65 13 0 12 42 35 96 97

A. Use a copy of the Player Wheel master or construct two (2) circles, 41/2" in diameter, on cardstock. Clearly mark the center point on thecircle.

B. Using your protractor as a straight edge, draw a radius anywhere inyour wheel.

C. Get out your completed Player Analysis Charts. Determine yourpreferred order of placement for each statistical category. Using yourfirst category, construct the appropriate angle and draw another radius.

Label this section of your wheel with the correct statistical abbreviation.

D. Continue Step C until all of the angles have been measured and thestatistical abbreviations recorded on the wheel.

E. Write the player's full name on the back of the wheel.

F. Cut out the player wheel.



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FANTASY BASEBALLHow to Make a Player Wheel

(Pictorial model)

A B

1B

C D E and F

2B GO

1B

SOBB

2B

GO

1B

SOBB

G H and I

C

H

I

C

A

G

O

W

H

I

TE

S

O

X

Robin Ventura

Avg. 284

HR

RobinVentura

HR


fantasy baseball math activity

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