Math+and+Sports


 * **Mathematics and Sports ** || [[image:http://www.mathgoodies.com/images/mrsglosserlogo3_small.gif width="267" height="44" caption="Math Goodies"]] || **WebQuests  ** ||
 * [[image:http://www.mathgoodies.com/images/tab9x2.gif width="10" height="20"]] ||


 * [[image:http://www.mathgoodies.com/images/Baseball-icon.png width="48" height="48"]] || [[image:http://www.mathgoodies.com/images/Basketball-icon.png width="48" height="48"]] || [[image:http://www.mathgoodies.com/images/American-Football-icon.png width="48" height="48"]] || [[image:http://www.mathgoodies.com/images/Soccer_48x48.png width="48" height="48"]] || [[image:http://www.mathgoodies.com/images/stadion-icon.png width="48" height="48"]] ||
 * [[image:http://www.mathgoodies.com/images/tab9x2.gif width="10" height="10"]] ||

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. > || || **PLAYER** || **AT-BATS** || **HITS** || **BATTING AVERAGE** || > || Ken Griffey, Jr || 600 || 173 ||  || > || Sammy Sosa || 625 || 180 ||  || > || Tony Gwynn || 411 || 139 ||  || ||
 * 1) What is a batting average?
 * 2) How is a batting average calculated?
 * 3) Calculate the batting averages for the following players.
 * 1) Compute the batting averages for 25 players in the 2008 season.
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Find historical player stats for 20 baseball players from the 2009 season.
 * 3) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Compute the batting average for each player.
 * 4) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Create a table for your results.
 * 5) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">How does a batting average measure a player's performance?

<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">**Part II: Earned Run Average**
 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">What is an Earned Run Average?
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">How is an ERA calculated?
 * 3) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Gather pitching stats for Earned Runs (ER) and Number of Innings Pitched (IP).
 * 4) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Calculate the ERA for each pitcher.
 * 5) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Create a table for your results.
 * 6) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">How does an earned run average measure a pitcher's performance?

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;"> WebQuest 2: Win-Loss Percentage
<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">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) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Look at win and loss data for teams in football. For example, the NFL.
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Compute the WL% for five teams in a league, five in a conference and five in a division.
 * 3) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Create a table for your results.
 * 4) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Look at win and loss data for teams in basketball, for example, the NBA.
 * 5) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Compute the WL% for ten teams of your choice.
 * 6) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Create a table for your results.
 * 7) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">What other sports use WL%?
 * 8) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Is WL% always expressed as a percentage? Explain your answer.

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;"> 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". || [[image:http://www.mathgoodies.com/images/tab.gif width="30" height="2"]] || [[image:http://www.mathgoodies.com/images/nba_draft_lottery_image.jpg width="153" height="86"]] ||
 * [[image:http://www.mathgoodies.com/images/tab.gif width="2" height="8"]] ||^  ||^   ||
 * 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) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">What is the formula for the number of possible combinations of //r// objects from a set of //n// objects?
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">How many different committees of 5 people can be chosen from a group of 11?
 * 3) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">How many non-playoff teams participate in the Draft Lottery?
 * 4) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">What kind of balls are used?
 * 5) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">How many numbered balls are placed the lottery machine?
 * 6) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">How many balls are randomly drawn from the lottery machine?
 * 7) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Does the order in which the balls are drawn matter?
 * 8) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">How many combinations are there when the balls are randomly selected from the lot of numbered balls?
 * 9) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">How many combinations are actually used in the NBA Draft?
 * 10) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">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. || [[image:http://www.mathgoodies.com/images/tab.gif width="10" height="8"]] || [[image:http://www.mathgoodies.com/images/nba-draft-lottery_top.gif width="140" height="74"]] ||


 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">One outcome is disregarded: it is given to no team and ignored. How many outcomes are then distributed among the non-playoff teams?
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">From a mathematical standpoint, why do you think is this done?
 * 3) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">What is 14C4? How would you compute this?
 * 4) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Can a team's win-loss record affect their chances of getting the first draft pick?

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;"> WebQuest 4: Graphing Historical Data for a Sport or Event
<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">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. ||^  ||  || <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">The following tasks may require some of the math and sports resources listed near the bottom of this page.
 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">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) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Print the Olympic data you gathered, or save it to your computer.
 * 3) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Decide which type of graph is appropriate] for summarizing your data.
 * 4) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Graph your Olympic data.
 * 5) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Gather historical data from the Super Bowl. For example, [|Super Bowl Game-Time Temperatures] can be summarized in a [|line graph].
 * 6) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Print the Super Bowl data you gathered, or save it to your computer.
 * 7) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Decide which type of graph is appropriate] for summarizing your data.
 * 8) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Graph your Super Bowl data.

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;">Other Topics for Further Exploration

 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Percent change in number of home runs scored by a baseball player.
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Field goal percentage] (FG%) in basketball.
 * 3) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Pythagorean Expectation [ 1 ] [ 2 ] [ 3 ] [ 4 ]
 * 4) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Win Probability (WP) in Football.
 * 5) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Win Expectancy (WE) in baseball.
 * 6) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Advanced NFL Stats] including:
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Super Bowl Probabilities
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Check out the Win Probability graphs and play-by-play of your favorite team's [|biggest comebacks and most exciting games].
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Browse the [|archive] for previous years or the current season by week, for example, [|Week 22].
 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Sabermetrics, the study of baseball statistics [ 1 ] [ 2 ] [ 3 ]
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Simpson's Paradox - correlation does imply causation [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ]

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;">Topics for Lower Grades:

 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Students can look at the basics of football scoring and add whole numbers.
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">The Super Bowl uses Roman Numerals to identify each game. Write these Roman Numerals as numbers in standard form.
 * 3) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">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.

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;">Topics for High School and College:

 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Mathematics in Sports
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Mathematics and Sport Theme Articles]

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;">Sports Resources:

 * || **Batting Average** || [[image:http://www.mathgoodies.com/images/tab.gif width="4" height="1"]] || **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** || [[image:http://www.mathgoodies.com/images/tab.gif width="4" height="1"]] || **Basketball** || [[image:http://www.mathgoodies.com/images/tab.gif width="4" height="1"]] || **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 || ||


 * || **NBA Draft Lottery** ||
 * Countdown to NBA Draft 2010 - 2010 Mock Lottery ||
 * [|As ping pong balls bounce, fates of 14 teams hang in balance] ||
 * [|NBA Draft Lottery Probabilities] (PDF) ||
 * e-How ||
 * PROBABILITY OF GETTING A TOP-THREE PICK || ||


 * || **Olympics** ||
 * The 2010 Winter Olympics ||
 * Olympics Statistics and History ||
 * [|Winter olympic medals by country] ||
 * [|Olympic.org] -Official website of the Olympic Movement ||
 * Olympic Games WikiPedia || ||

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;">Math Lessons from Math Goodies:

 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Reading and Writing Decimals]
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Understanding Percent]
 * 3) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Percent and Proportions]
 * 4) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Fraction-Decimal-Percent Conversions]
 * 5) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Percent Goodies Game]
 * 6) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Probability]
 * 7) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Data and Line Graphs]
 * 8) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Percent Change] (Increase and Decrease)

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;">Math Resources:

 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Bar graph paper] (PDF)
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Line graph paper] (PDF)[[image:http://www.mathgoodies.com/images/newred.gif width="31" height="12"]]
 * 3) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Paper for circle graphs] (PDF)
 * 4) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Create a graph
 * 5) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">[|Comparing Graphs]

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;">Other Resources:

 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Links to selected websites in each webquest above.
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Search engines such as Bing, Google, Yahoo!

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;">Evaluation:

 * 1) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Print or save tables, graphs and other data you gathered in these webquests.
 * 2) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Discuss your findings with a classmate or family member, and a teacher or a sports aficionado.
 * 3) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Name three formulas you learned in these webquests.
 * 4) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Create five original problems from math and sports.
 * 5) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Share your problems in our [|Facebook discussions] (JPG or PNG).
 * 6) <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">Add the graphs you created to our [|Facebook discussions] (JPG or PNG).

<span style="color: #0768ac; font-family: Arial,Helvetica,sans-serif; font-size: 18px; font-weight: bold;">Conclusion:
<span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 14px; font-weight: normal;">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.


 * [|More WebQuests] ||