# Algebra Project

PLAY BALL A Game of Statistics

SUMMARY � You have been hired by the Major League

Baseball Commissioner to explain the mathematics of baseball so more people can appreciate the game.

� Your job is to analyze a variety of statistics related to baseball and then use what you have learned to publish an explanation of some aspect of baseball statistics. That way people can get greater enjoyment from the game.

STEP 1: BACKGROUND Write what you know about baseball and the statistics of the game

STEP 1: BACKGROUND 1. In a document write everything you know about

baseball  Include as many words, phrases, and ideas as that you

can associate with baseball  Give historical background if you can  Write why you think statistics is an important feature of

the game

STEP 1: BACKGROUND 2. Look at the back of a few baseball cards

 Go to this website or look at your own cards Vintage Baseball Card Blog: http://www.goldenagebaseballcards.com/back-of-the-cards- Mar2010.htm

 Write what you know about some of the statistics shown  You may research definitions of some of the statistics

Baseball Almanac: http://www.baseball-almanac.com/bstatmen.shtml

� You will submit this to the project dropbox later

STEP 2: INVESTIGATE STATISTICS Analyze some important baseball statistics 1. Batting average 2. On-base percentage 3. Earned run average

STEP 2: INVESTIGATE STATISTICS � In a second document you will write your

analysis of three baseball statistics 1. Batting average 2. On-base percentage 3. Earned run average

STEP 2: INVESTIGATE STATISTICS o Include all of your data tables, charts, and

calculations � Your charts should have

o A title at the top o Labels and units for each axis o A legend or key as appropriate

� You will submit this to the project dropbox later

A list of charting tools is at the end of this presentation

STEP 2: INVESTIGATE STATISTICS BATTING AVERAGE � Batting average lets us know the likelihood that

a batter will reach first base

1. Using the batting averages table below  Create a scatter graph or line graph in a charting tool  Show how the averages change over time

Player/Years 1998 1999 2000 2001 2002 2003 2004

Sammy Sosa 0.308 0.288 0.320 0.328 0.288 0.279 0.253

Ken Griffey 0.284 0.285 0.271 0.286 0.264 0.247 0.253

Derek Jeter 0.324 0.349 0.339 0.311 0.297 0.324 0.292

Roberto Alomar 0.282 0.323 0.310 0.336 0.266 0.258 0.263

Data source: www.baseball-reference.com*

STEP 2: INVESTIGATE STATISTICS BATTING AVERAGE 2. Analyze your graph to determine the relative

value of the players. Specifically answer these questions:

A. What can you say about the players’ batting consistency over time?

B. Rank the players then explain and defend your choices

C. Define batting average in your own words and describe how it is calculated

D. Show the equation used to calculate it

STEP 2: INVESTIGATE STATISTICS BATTING AVERAGE 2. (More questions)

E. What limitations does this statistic have? What doesn’t it tell you about a player?

F. Why is the batting average designated as an “average”?

G. Why is information often presented in graphs instead of just in a list or table?

H. How do you choose the appropriate graphical representation for the data you’re working with

STEP 2: INVESTIGATE STATISTICS ON-BASE PERCENTAGE � The on-base percentage shows the percent of time

a player can be expected to reach base safely by either a hit or a walk

� Use the player comparison table below and the following formula for on-base percentage

Player Games AB H 2B 3B HR BB SO A 118 377 83 11 5 0 28 40 B 112 433 128 5 1 2 40 16

STEP 2: INVESTIGATE STATISTICS ON-BASE PERCENTAGE 1. Calculate the on-base percentage for each player 2. Recommend the best player for your team

 Make sure to defend your point of view with data

STEP 2: INVESTIGATE STATISTICS EARNED RUN AVERAGE � Earned run average (ERA), is a measure of

pitching ability � Using the formula for ERA below and the table

on the next slide 1. Compute each pitcher’s ERA 2. Create a bar graph to compare the pitchers

ERA is calculated by multiplying 9 innings by the number of earned runs. That value is then divided by the number of innings pitched.

STEP 2: INVESTIGATE STATISTICS EARNED RUN AVERAGE � All time winning pitchers (active players)

Pitcher Team Wins Losses Innings Pitched

Earned Runs

ERA Strike Outs

Greg Maddux Los Angeles 333 203 4616 1574 3169

Kenny Rogers Detroit 207 139 3066 1427 1850

Roger Clemens Houston 348 178 4817 1661 4604

Randy Johnson New York 280 147 3798 1357 4544

Tom Glavine New York 290 191 4149 1596 2481

Mike Mussina New York 239 134 3210 1296 2572

David Wells Boston 230 148 3281 1483 2119

Jamie Moyer Philadelphia 216 166 3351 1551 1992

John Smoltz Atlanta 193 137 3161 1150 2778

Curt Schilling Boston 207 138 3110 1188 3015

STEP 2: INVESTIGATE STATISTICS EARNED RUN AVERAGE 3. Use your bar graph to answer these questions

A. Who among these players is the best pitcher? B. Justify your response with data C. Which factors should be taken into account when

determining the best pitcher? D. Why is ERA an “average”?

STEP 3: PRESENTATION You will create a movie, slideshow or other visual display of baseball math

STEP 3: PRESENTATION � You will prepare a visual presentation that will help

your audience appreciate the math of baseball � Your presentation should have these parts

1. An introduction of how statistics help us understand the game of baseball

2. Pose one question that can be answered by using statistics

3. The statistics you evaluated to answer the question

4. Your findings backed up with a data table and a graph

5. Your conclusion 6. Citation of sources

that you used

Note that you will not actually do an oral presentation to the class nor to the teacher

STEP 3: PRESENTATION � You choose the topic. Some suggestions are:

 Compare player statistics and salaries  Compare the performance of two players during any year  Evaluate the greatest hitters of all time  Compare and contrast a group of players’ individual

statistics  Highlight a recent game’s statistics

� Your visual display will be one of the these formats  A digital poster  A slideshow  A short movie  Other (your choice)

� With teacher approval

� See an example of a student’s slideshow  Example-Baseball-SlideShow.pdf

� Note that this example answers three questions that are answered with statistics

� You only need to pose and answer one question

STEP 3: PRESENTATION

A list of presentation tools appears at the end of these slides

STEP 3: PRESENTATION � For citing your sources you may

 List them at the end of your slideshow or movie, or  List them in a separate document that you submit to

the dropbox

SUBMIT YOUR WORK This section describes how to submit your work for this project

SUBMIT YOUR WORK (4 PARTS) 1. Submit your baseball background document to

the project dropbox (from step 1) 2. Submit your statistics investigation document

to the same project dropbox (from step 2)

3. For your presentation (step 3)  If it located on a website

� Submit the URL to the comment area of the project dropbox � Make sure that the URL works by loading the page into a

browser  If it is a document (such as PowerPoint), submit the

file to the project dropbox

 If it is in a separate document submit the file to the project dropbox

 Otherwise, it is embedded in your presentation so you don’t have to do anything else

SCORING RUBRIC (PART 1 OF 3) � You must submit all four required items before

� This project is worth 30 points � However your score will be scaled as needed for

the gradebook  Suppose you earned: 24/30 (80% B-)  But the gradebook shows 60 points for the project  Your score would be scaled to: 48/60 (still 80%)

SCORING RUBRIC (PART 2 OF 3) Criteria 1 2 3 4 5 Points

1. Background info

Describes 1 aspects of baseball. Describes 1 statistics

Describes 2 aspects of baseball. Describes 2 statistics

Describes 3 aspects of baseball. Describes 3 statistics

Describes 4 aspects of baseball. Describes 4 statistics

Describes 5 or more aspects of baseball. Describes 5 or more statistics

5

2. Batting average

Graph is very incomplete

Graph is missing some parts such as title or labels

Graph is correct and complete. Answers to six questions are reasonable.

Graph is correct and complete. Answers to seven questions are reasonable.

Graph is correct and complete. Answers to all eight questions are reasonable.

5

3. On-base percentage

Calculations contain two mistakes

Calculations contain one mistake

Calculations are correct; no recommend ation is made

Calculations are correct; recommend ation does not make sense

Calculations are correct; recommendati on is reasonable

5

SCORING RUBRIC (PART 3 OF 3) Criteria 1 2 3 4 5 Points

3. Earned run average

Graph is very incomplete

Graph is missing some parts such as title or labels

Graph is correct and complete. Answers to some questions don’t make sense.

Graph is correct and complete. Answers to all questions are reasonable but not backed with data.

Graph is correct and complete. Answers to all questions are reasonable and backed with data.

5

4. Presentation

Has two missing or incorrect parts (2 points)

Has one missing or incorrect part (4 points)

Is complete and correct with all 6 parts, and has only a basic visual design (6 points)

Is complete and correct with all 6 parts, and shows nice visual design (8 points)

Is complete and correct with all 6 parts, and has a visually appealing design (10 points)

10

that you may use (if you want to)  Project-PlayBall-Background.doc

� For your statistical analysis  Project-PlayBall-Sources.doc

� To list the resources you used for your presentation

CHARTING TOOLS � You may use any spreadsheet program such as Excel � Or you may use any free web-based charting tool

such as these:  Chart Tool: http://www.onlinecharttool.com/graph.php  ChartGo: http://www.chartgo.com/en/chartline.jsp

VISUAL PRESENTATION FORMATS This is a list of free presentation tools that you may use. Otherwise feel free to use any other tool that you like more.

� Digital poster  Glogster: http://www.glogster.com

� Slideshow or Movie  Animoto: http://animoto.com  Prezi: http://prezi.com  One True Media: http://www.onetruemedia.com

MATH STANDARDS – ALGEBRA

� Use statistics to compare center (mean) (6.ID.2)

� Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers (6.SP.1)

� Recognize that a measure of center for a numerical data set summarizes all of its values with a single number (6.SP.3)

� Display numerical data in plots on a number line, including dot plots and histograms (6.SP.4)

� Summarize numerical data sets in relation to their context, such as by:  Describing the nature of the

attribute under investigation, including how it was measured and its units of measurement (6.SP.5b)

 Giving quantitative measures of center (6.SP.5c)

� Summarize categorical data for two categories in two- way frequency tables. Recognize possible associations and trends in the data (6.SP.5)

� Represent data in two quantitative variables on a scatter plot (6.SP.6)

You will be using these math skills for this project:

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