Mathematics and Sports

Many people have some sort of experience with sports, which could be anything from watching a sporting event on T.V. to playing on a sports team, but they are not always aware of the vital role that math plays in sports. You have been choosen to explore the numerous connections between math and the world of sports.

WebQuest #1 - Baseball

Complete the following questions. You may need to visit the websites provided at the bottom of the page to assist you. 

Batting Averages

1. What is a batting average?
2. How is a batting average calculated?
3. Calculate the batting averages for the following players.

4. Create your dream team of 25 players and compute their batting avergaes for the 2016 season.
5. Find historical player stats for 10 baseball players from a season at least 10 years ago.
6. Calculate the batting average for the 10 players choosen in question 6.
7. Create a table for your results.
8. How does a batting average measure a player’s preformance?

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 10 of your favourtie pitchers.
5. Create a table for your results.
6. How does an earned run average measure a pitcher’s performance

Baseball 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

Historical Baseball Stats

WebQuest 2 – Win-Loss Percentage

Win-Loss Percentage is provides important data for any team. WL% can be computed for baseball teams, but it is also used in many other sports.

1. Look at win and loss data for football teams in the CFL
2. Compute the WL% for five teams in the league.
3. Create a table for your results.
4. Look at win and loss data for basketball teams in the NBA
5. Comupte 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 - NBA Draft Lottery

The NBA Draft Lottery is an event that is held annually by the National Basketball Association. Teams who missed the playoffs in the previous season participate in a lottery process to determine the draft order. The draft lottery uses a lot of mathematics, including combinatoris and probability. To understand how the lottery works, you will need to understand factorials, combinations and outcomes.

Try the following practice lessons to develop a better understanding of combinatorics and probabiliity:

Intro to Probabilitiy

Sample Spaces

Addition Rules for Probability

Independent Events

Dependent Events

1. What is the formula for the number of possible combination of r objects from a set of n objects?
2. How many different committee 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 in the lottery machine?
6. How many balls are randomly drawn from the lottery machine?
7. Does the order in which the balss 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?

In the draft lottery, the numbered balls are drawn to the top of the machine to deteremine the combination. The team assigned to that combination will receive the number one pick. Non-playoff teams are then ranked in reverse order of their regular season record, and assigned chances (click here for more details). The team with the worst record gets the largest number of outcomes. The second worst team would receive the second largest number of outcomes, and so on for each of the teams in the lottery. The team with the winning outcome is assigned the first pick in the NBA Draft. That means, the NBA Draft is weighted in favour of the worst lottery teams based on their record for the season.

10. One outcome is disregarded: it is given to no team and ignored. How many outcomes are then distributed among the non-playoff teams?
11. From a mathemactical standpoint, why do you think this is done?
12. What is 14C4? How would you compute this?
13. 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

To summarize sportss statisitcs, tables and graphs are often used. Standings for teams and leagues are summarized in tables, and historical data about a sport or event is often represented by graphs. 

The 2010 Winter Olympics were held in Vancouver, B.C, Canada. The first of the modern Summer Games opened on Sunday, March 24, 1896, in Athens, Greece. Historical data about these events have been tracked for years. Take a look at the following resources to see some of the data that has been collected:

Historical Data

Winter Olympic Medals by Country

1. Gather historical data from the Olympics.
2. Print the data you have gathered, or save it to your computer.
3. Decided which type of graph is appropriate for summarizing your data.
4. Graph your Olympic data.
5. Gather historical data from a sport of your own choice.
6. Print the data you have collected or save it to your computer.
7. Decided which type of graph is appropriate for summarizing your data.
8. Graph your sports data. 

1.  Print or save tables, graphs and other data you have gathered in webquests.
2. Discuss your findings with a partner(s).
3. Identify three different formulas you have learned from the webquests.
4. Create 3 of your own problems involving math and sports.
5. Share your problems with at least one other person. 

Congratulations, you have completed the Mathematics and Sports webquest activities! This webquest should provide you with a better understanding of how mathematics is applied to sports. Next time you watch or take part in a sporting event you will have a more enhanced knowledge of where and how mathematics is applied.