Mathematics and Sports		WebQuests

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 how math is used to compute, summarize and analyze this data.

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. Links are included in each webquest to help you explore. In some cases, you may also need to browse the sports and the math resources listed at the bottom of this page. As you embark on your web explorations, keep in mind that most of the links on this page target a new browser window. You might not be able to do all four webquests at once. 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.

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.

1. What is a batting average?
2. How is a batting average calculated?
3. 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

4. Compute the batting averages for 25 players in the 2008 season.
5. Find historical player stats for 20 baseball players from the 2009 season.
6. Compute the batting average for each player.
7. Create a table for your results.
8. How does a batting average measure a player's performance?
   

Part II:  Earned Run Average

1. What is an Earned Run Average?
2. How is an ERA calculated?
3. Gather pitching stats for Earned Runs (ER) and Number of Innings Pitched (IP).
4. Calculate the ERA for each pitcher.
5. Create a table for your results.
6. 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.

1. Look at win and loss data for teams in football. For example, the NFL.
2. Compute the WL% for five teams in a league, five in a conference and five in a division.
3. Create a table for your results.
4. Look at win and loss data for teams in basketball, for example, the NBA.
5. Compute the WL% for ten teams of your choice.
6. Create a table for your results.
7. What other sports use WL%?
8. 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 (NBA) 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.

1. What is the formula for the number of possible combinations of r objects from a set of n objects?
2. How many different committees of 5 people can be chosen from a group of 11?
3. How many non-playoff teams participate in the Draft Lottery?
4. What kind of balls are used?
5. How many numbered balls are placed the lottery machine?
6. How many balls are randomly drawn from the lottery machine?
7. Does the order in which the balls are drawn matter?
8. How many combinations are there when the balls are randomly selected from the lot of numbered balls?
9. How many combinations are actually used in the NBA Draft?
10. What is wrong with the numbered balls shown in this image taken from this page?

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.

11. One outcome is disregarded: it is given to no team and ignored. How many outcomes are then distributed among the non-playoff teams?
12. From a mathematical standpoint, why do you think is this done?
13. What is ₁₄C₄? How would you compute this?
14. Can a team's win-loss record affect their chances of getting the first draft pick?
    

WebQuest 4:  Graphing Historical 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.

1. 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.
2. Print the Olympic data you gathered, or save it to your computer.
3. Decide which type of graph is appropriate for summarizing your data.
4. Graph your Olympic data.
5. Gather historical data from the Super Bowl. For example, Super Bowl Game-Time Temperatures can be summarized in a line graph.
6. Print the Super Bowl data you gathered, or save it to your computer.
7. Decide which type of graph is appropriate for summarizing your data.
8. Graph your Super Bowl data.

Other Topics for Further Exploration

1. Percent change in number of home runs scored by a baseball player.
2. Field goal percentage (FG%) in basketball.
3. Pythagorean Expectation [ 1 ]  [ 2 ]  [ 3 ]  [ 4 ]
4. Win Probability (WP) in Football.
5. Win Expectancy (WE) in baseball.
6. 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.
• Browse the archive for previous years or the current season by week, for example, Week 22.

7. Sabermetrics, the study of baseball statistics [ 1 ]  [ 2 ]  [ 3 ]
8. Simpson's Paradox - correlation does imply causation [ 1 ]  [ 2 ]  [ 3 ]  [ 4 ]  [ 5 ]

Topics for Lower Grades:

1. Students can look at the basics of football scoring and add whole numbers.
2. The Super Bowl uses Roman Numerals to identify each game. Write these Roman Numerals as numbers in standard form.
3. 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:

1. Mathematics in Sports
2. Mathematics and Sport Theme Articles

Sports Resources:

Batting Average Earned Run Average Wikipedia e-How Buddy Project Urban Dictionary Figure This! Math Home Run Web MLB Historical Player Stats MLB Baseball Pitching Statistics and League Leaders

Baseball Basketball Football Baseball Stats 101 NBA at ESPN NFL Standings Baseball-Reference.com NBA.com Statistics Index Super Bowl Historical Player Stats (PDF) databaseBasketball.com Super Bowl History

Math Lessons from Math Goodies: 

1. Reading and Writing Decimals
2. Understanding Percent
3. Percent and Proportions
4. Fraction-Decimal-Percent Conversions
5. Percent Goodies Game
6. Probability
7. Data and Line Graphs
8. Percent Change (Increase and Decrease)

Math Resources: 

1. Bar graph paper (PDF)
2. Line graph paper (PDF)
3. Paper for circle graphs (PDF)
4. Create a graph
5. Comparing Graphs

Other Resources:

1. Links to selected websites in each webquest above.
2. Search engines such as Bing, Google, Yahoo!

Evaluation:

1. Print or save tables, graphs and other data you gathered in these webquests.
2. Discuss your findings with a classmate or family member, and a teacher or a sports aficionado.
3. Name three formulas you learned in these webquests.
4. Create five original problems from math and sports.
5. Share your problems in our Facebook discussions (JPG or PNG).
6. Add the graphs you created to our Facebook discussions (JPG or PNG).

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 sports, probability and statistics.

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