# Mathematics and Sports

### Introduction

Most people are familiar with sports rules and terminology; however, they are not always aware of the important role that math plays in sports. A myriad of data on players, teams, divisions and leagues is provided by the media and the sports world. You have been selected to explore the numerous connections between math and sports.

### The Tasks

You are probably familiar with professional sports and stay abreast of scores and standing for your favorite teams. In each webquest below, you will engage in web-based inquiry to answer the questions presented and to perform the tasks required. These tasks will require a computer, access to the web, graph paper (see the math resources below), paper, pencil and a ruler. Access to a printer is helpful, but not required. Links are included for each quest to help you explore. In addition, there are links to sports and math resources at the bottom of this page. It’s time to “play ball!”

**WebQuest 1 – Baseball Stats**

**Part I: Batting Average**

The following tasks may require some of the sports resources listed near the bottom of this page. Try our Lessons on Decimals, then do the following:

- What is a batting average?
- How is a batting average calculated?
- Calculate the batting averages for the following players.

PLAYER |
AT-BATS |
HITS |
BATTING AVERAGE |

Ken Griffey, Jr | 600 | 173 | |

Sammy Sosa | 625 | 180 | |

Tony Gwynn | 411 | 139 |

- Order the batting averages in tem 3 from least to greatest.
- Compute the batting averages for 25 players in the 2008 season.
- Find historical player stats for 20 baseball players from the 2009 season.
- Compute the batting average for each player.
- Create a table for your results.
- How does a batting average measure a player’s performance?

**Part II: Earned Run Average**

- What is an Earned Run Average?
- How is an ERA calculated?
- Gather pitching stats for Earned Runs (ER) and Number of Innings Pitched (IP).
- Calculate the ERA for each pitcher.
- Create a table for your results.
- How does an earned run average measure a pitcher’s performance?

**WebQuest 2 – Win-Loss Percentage**

Win-Loss Percentage is important data for any team. For example, WL% can be computed for a baseball team. However, WL% is also used in other sports. Try our Lessons on Understanding Percent, then do the following:

- Look at win and loss data for teams in football. For example, the NFL.
- Compute the WL% for five teams in a league, five in a conference and five in a division.
- Create a table for your results.
- Look at win and loss data for teams in basketball, for example, the NBA.
- Compute the WL% for ten teams of your choice.
- Create a table for your results.
- What other sports use WL%?
- Is WL% always expressed as a percentage? Explain your answer.

**WebQuest 3 – The NBA Draft Lottery**

The NBA Draft Lottery is an annual event held by the National Basketball Association in which the teams who had missed the playoffs in the previous season participate in a lottery process to determine the draft order in the NBA Draft. The lottery is normally held during the fourth week of May. The non-playoff teams are often called “lottery teams”.

The NBA draft lottery uses a lot of mathematics, including combinatorics and probability. To better understand how the lottery works, you need to understand factorials, combinations and outcomes. Try our Lessons on Probability, then do the following.

- What is the formula for the number of possible combinations of
*r*objects from a set of*n*objects? - How many different committees of 5 people can be chosen from a group of 11?
- How many non-playoff teams participate in the Draft Lottery?
- What kind of balls are used?
- How many numbered balls are placed the lottery machine?
- How many balls are randomly drawn from the lottery machine?
- Does the order in which the balls are drawn matter?
- How many combinations are there when the balls are randomly selected from the lot of numbered balls?
- How many combinations are actually used in the NBA Draft?

In the draft lottery, numbered balls are drawn to the top of the machine to determine a combination. The team that has been assigned that combination will receive the number one pick. Non-playoff teams are then ranked in reverse order of their regular season record, and are assigned chances, as shown here. The largest number of outcomes is assigned to the team with the worst record. The team with the second worst record gets the second largest number of outcomes, and so on for each of the 14 teams in the lottery. The experiment is conducted, and the team to which the winning outcome was assigned receives the first pick in the NBA Draft. Therefore, the NBA Draft is weighted in favor of the worst lottery teams based on their season record.

10. One outcome is disregarded: it is given to no team and ignored. How many outcomes are then distributed among the non-playoff teams?

- From a mathematical standpoint, why do you think is this done?
- What is
_{14}C_{4}? How would you compute this? - Can a team’s win-loss record affect their chances of getting the first draft pick?

**WebQuest 4 – Graphing Data for a Sport or Event**

Tables and graphs are commonly used to summarize sports statistics. Standings for teams and leagues are often summarized in tables, and historical data about a sport or event is often summarized in graphs.

**The 2010 Winter Olympics** in Vancouver, British Columbia, Canada ended on February 28, and the accompanying Paralympics are being held March 12-21. The first of the modern Summer Games opened on Sunday, March 24, 1896, in Athens, Greece. The first IOC Games was hosted in the Panathenaic stadium in Athens in 1896. The Winter Games were added in 1924. Historical data about this event has been tracked for years! For example, view a bar graph of Winter Olympic medals by country.

The **Super Bowl** is the championship game of the National Football League (NFL), the premier association of professional American football. It was first played on January 15, 1967. The Super Bowl is a very popular football event. A great deal of historical data about the Super Bowl is available, including Super Bowl Standings.

The following tasks may require some of the math and sports resources listed near the bottom of this page. Try our Lessons on Data and Graphs, then do the following.

- Gather historical data from the Olympics. For example, choose a country and look at the data. If you chose the United States, then you would see a table for number of participants, men, women, sport, and medal.
- Print the Olympic data you gathered, or save it to your computer.
- Decide which type of graph is appropriate for summarizing your data.
- Graph your Olympic data.
- Gather historical data from the Super Bowl. For example, Super Bowl Game-Time Temperatures can be summarized in a line graph.
- Print the Super Bowl data you gathered, or save it to your computer.
- Decide which type of graph is appropriate for summarizing your data.
- Graph your Super Bowl data.

**Other Topics for Further Exploration**

- Percent change in number of home runs scored by a baseball player.
- Field goal percentage (FG%) in basketball.
- Pythagorean Expectation [ 1 ] [ 2 ]
- Win Probability (WP) in Football.
- Win Expectancy (WE) in baseball.
- Advanced NFL Stats including:

- Super Bowl Probabilities
- Check out the Win Probability graphs and play-by-play of your favorite team’s biggest comebacks and most exciting games.

**Topics for Elementary Students:**

- Students can look at the basics of football scoring and add whole numbers.
- The Super Bowl uses Roman Numerals to identify each game. Write these Roman Numerals as numbers in standard form.
- Have students compare and order decimals by looking at batting averages of their favorite baseball players. They can find real data for players at websites such as ESPN.com. They should be reminded that a batting average is stated as a three-digit number; however, it is actually a decimal rounded to the nearest thousandth.

**Topics for High School and College:**

**Resources**

**Sports Resources**

**Batting Average**

**Earned Run Average**

MLB Baseball Pitching Statistics and League Leaders

**Baseball**

Historical Player Stats (PDF)

**Basketball**

NBA at ESPN

**Football**

**NBA Draft Lottery**

Countdown to NBA Draft– Mock Lottery

NBA Draft Lottery Probabilities

**Olympics**

Olympics Statistics and History

Winter olympic medals by country

Olympic.org -Official website of the Olympic Movement

**Instructional Math Units**

- Decimal Part I
- Decimals Part II
- Understanding Percent
- Percent Applications
- Probability Theory
- Data and Line Graphs

**Math Resources**

- Bar graph paper (PDF)
- Line graph paper (PDF)
- Paper for circle graphs (PDF)
- Create a graph

**Other Resources**

**Evaluation**

- Print or save tables, graphs and other data you gathered in these webquests.
- Discuss your findings with a classmate or family member, and a teacher or a sports aficionado.
- Name three formulas you learned in these webquests.
- Create five original problems from math and sports.

**Conclusion**

Congratulations! You have explored the important role that math plays in the world of sports. These explorations should give you a better understanding of the numerous connections between sports, probability and statistics, and other areas of mathematics.