
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 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
webbased 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 
ATBATS 
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  WinLoss Percentage
WinLoss 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
 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 nonplayoff 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?
 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.
Nonplayoff 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. 


 One outcome is disregarded: it is given to no team and ignored. How many
outcomes are then distributed among the nonplayoff 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 winloss 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
1221. 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 GameTime 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
] [ 3
]
[ 4
]
 Win Probability (WP)
in Football.
 Win Expectancy (WE)
in baseball.
 Advanced NFL Stats including:
 Sabermetrics, the study of baseball statistics [ 1
] [ 2
] [ 3
]
 Simpson's Paradox  correlation does imply causation [ 1
] [ 2
] [ 3
] [ 4
] [ 5
]
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 threedigit number; however,
it is actually a decimal rounded to the nearest thousandth.

Topics for High School and College:
 Mathematics in Sports
 Mathematics and Sport Theme Articles
Resources
Sports Resources
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
 Links to selected websites in each webquest above.
 Search engines
such as Bing,
Google,
Yahoo!
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.
 Share your problems on
Facebook.
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. 
