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 an innovative textbook that explains the mathematical underpinnings of baseball so that students can understand the world of statistics and probability - The Johns Hopkins University Press

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Teaching Tips

I have taught the course called Baseball and Statistics at Quinnipiac University every semester from 2008 to the present day. The book was developed during this period of time. The book has been used by over 400 students who gave valuable comments which improved the book enormously.

Teaching with Sandlot Stats
In what follows, I present some ideas on providing a one semester course using my book, “Sandlot Stats

With the help of a calculator, a student will perform each of the statistical processes in the book. By doing so, they will gain an understanding and an appreciation of statistical concepts.

They will also use Microsoft Excel as a statistical software package. It is not the strongest statistical package, but it is available on almost all computers and has enough statistical features to handle the tasks in this book.

The following five websites serve as major sources for baseball data; these sites are used throughout this book, and you will need to become familiar with them:

As an additional book to read along with “Sandlot Stats” I choose either the book “Moneyball” by Michael Lewis or the book “56: The Last Magic Number in Sports” by Kostya Kennedy. These are best-selling books that provide background and relate to the course.

I also sprinkle into the course the history of the game of baseball to show the role of our national pasttime in the history of the United States using the interseting facts that I compiled over my years of research.

There are weekly quizes on the interesting facts, as well as the supplemental best seller and the statistics in Sandlot Stats.

In the first week of the course, I give the students their project for the semester. I pick a topic that parallels the chapters in my book. I want the student to use both descriptive and inferential statistics in their project.

The software tools they need are all included in Microsoft Office. These tools include Word, Excel, and PowerPoint.

At the end of the course each student, or if they are paired each pair of students, give an oral presentation using PowerPoint.

I, also, ask them to provide a written summary of their conclusions.

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Sample Project

One project I used is described in the next paragraphs. Of course, there are many other possible projects that would serve the same purpose. Since many of the chapters in my book compare Henry Aaron to Barry Bonds, I felt that the project should have a comparison theme. In the next paragraph, I describe one of my best projects.

Each student is asked to choose two Major League players. The first player must already be a Hall of Famer. The second player is not a member of the Hall of Fame; however, the student should believe that this player may deserve induction. The website www.baseballhalloffame.org contains all the Hall of Fame players.

In selecting the two players, the following guidelines can be followed:

• The careers of the two players either overlap or are close to overlapping.
• The two players must have played most of their careers at the same position. The possible positions are catcher (C), first baseman (1B), second baseman (2B), shortstop (SS), third baseman (3B), corner outfielder, or center fielder.
• The player not in the Hall of Fame must have played at least 10 years in the Major Leagues

Of course, these guidelines are just guidelines, and an instructor may change some of them.

Beginning in Chapter 4, students will be asked to apply the same statistical methods used to compare the batting performance of Henry Aaron with the batting performance of Barry Bonds to compare the batting performances of their two chosen players. This process of comparing batting performances will continue in subsequent chapters.

The students will create a physical model in the form of a spinner.

The spinner can be assembled by physically making a cardboard disk with a spinning pointer for each of the chosen players or, more easily, by using one of the many available online spinners. A reliable online spinner is available from the National Council of Teachers of Mathematics on the Illuminations website .

The purpose of the spinner disk is to mimic a player’s batting performance and introduce the concept of a simulation. The disk is composed of sectors. Each sector corresponds to an outcome of a plate appearance. The area of each of the sectors corresponds to the probability of that player having that outcome. Spinning the pointer will correspond to a plate appearance (the disk is similar to that found in the classic game All Star Baseball by Cadaco).

At the end of Chapter 10, the students will be asked to give a preliminary argument on whether their potential Hall of Fame player should be admitted to the Hall of Fame. This argument will be based on the descriptive statistics covered in Chapters 1-10.

At the end of Chapter 18, the students will again be asked to answer the same question. They may or may not choose to change their mind, based on the new statistical techniques learned in Chapters 11-18.
Throughout the chapters of this book, the following baseball questions will be addressed:

• What is the difference between a player’s batting performance and batting ability?
• How can a player’s batting performance be used to estimate a player’s batting ability?
• How can statistics be used to compare two or more baseball players?
• Which baseball statistics are most important in assessing the batting ability of a baseball player?
• Which hitting feat will be the hardest to duplicate now and in the future?
• Which baseball statistics are the best indicators for determining the number of runs a player contributes to his team?
• What properties must a player have to duplicate Joe DiMaggio’s 56-game hitting streak?
• Will we ever have another .400 hitter?
• What are the greatest hitting feats of all time?
• Who are the top 10 hitters of all time?

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Completed Student Projects
Based on the sample project described above, here are 3 completed examples by students in my Baseball & Statistics class.

A Suggested Course Outline
Unless you have a class of math majors or a small honors class, it can be difficult to completely cover all the chapters in this book. For Liberal Arts students and non-math majors a suggested course outline can consist of the following:

Note: For a course in just descriptive statistics, use just the first 12 chapters.

 Chapter(s) Approximate Time Allotment Topics 1 -10 5-6 hours Completely cover descriptive statistics 11 2 hours Introduces discrete probability distributions including the binomial and geometric distributions. These distributions are used to calculate probabilities. Examples from baseball are provided. 12 2 hours Introduces continuous distributions and uses the normal distribution function to calculate probabilities. Examples from baseball are provided. Note: After Chapter 12 you can skip to chapters 16, 17, and 18. Many important parts of these three chapters require only the first 12 chapters. Of course, you can show what a confidence interval is and what hypothesis testing is used for. 13 1 hour Sampling distributions for sample means and sample proportions are defined. 14 2 hours Confidence intervals for both the population mean and population proportion are defined. The concepts of level of significance, reliability coefficient, standard error of the mean, and the margin of error are explained. Baseball examples are provided. 15 2 hours Hypothesis testing is explained using our jury trial process. The two hypotheses (null and alternate are introduced). The concepts of statistical significance and the alpha error are explained. A true .300 hitter is defined using hypothesis testing. Finally, the p-value is defined and compared to the alpha error 16 &17 optional 1 hour Any one or any part of the next two chapters can be used. These two chapters are called the research chapters. They introduce the student to mathematical research. The only background needed by the student is supplied in the first 15 chapters 18 1 hour This chapter is called the post-season. It has a research component and a review component in it. The research component involves finding the ten greatest hitters of all time. The review component provides chapter problems which include topics from many of the prior chapters. Appendix A Contains hypothesis testing for two population proportions Appendix B Introduces the chi-square distribution. If time permits you may want to look at the test for independence.

Sandlot Stats: Learning Statistics with Baseball by Stanley Rothman is published by The Johns Hopkins University Press