# Math and...

## Math and Sports


### Learning Objectives

After completing this section, you should be able to:
1. Describe why data analytics (statistics) is crucial to advance a team’s success.
2. Describe single round-robin method of tournaments.
3. Describe single-elimination method of tournaments.
4. Explore math in baseball, fantasy football, hockey, and soccer (projects at the end of the section).
Sports are big business and entertainment around the world. In the United States alone, the revenue from professional sports is projected to bring in over $77 billion, which includes admission ticket costs, merchandise, media coverage access rights, and advertising. So, whether or not you enjoy watching professional sports, you probably know someone who does. Some celebrities compete to be part of half-time shows and large companies vie for commercial spots that are costly but reach a staggering number of viewers, some who only watch the half-time shows and advertisements.

### Data Analytics (Statistics) Is Crucial to Advance a Team’s Success

Analyzing the vast data that today’s world has amassed to find patterns and to make predictions for future results has created a degree field for data analytics at many colleges, which is in high demand in places that might surprise you. One such place is in sports, where being able to analyze the available data on your team’s players, potential recruits, opposing team strategies, and opposing players can be paramount to your team’s success.
Hollywood turned the notion of using data analytics into a major motion picture back in 2011 with the release of Moneyball, starring Brad Pitt, which grossed over $110 million. The critically acclaimed movie, based on a true story as shared in a book by Michael Lewis, follows the story of a general manager for the Oakland Athletics who used data analytics to take a team comprised of relatively unheard of players to ultimately win the American League West title in a year’s time. The win caught the eye of other team managers and owners, which started an avalanche of other teams digging into the data of players and teams.
In today’s world of sports, a team has multiple positions utilizing data analytics from road scouts who evaluate a potential recruit’s skills and potential to the ultimate position of general manager who is typically the highest-paid (non-player) employee with the exception of the coaches. Being able to understand and evaluate the available data is big business and is a highly sought after skill set. In college and professional sports, it is no longer sufficient to have a strong playbook and great players. The science to winning is in understanding the math of the data and using it to propel your team to excelling.

### Single Round-Robin Tournaments

A common tournament style is single round-robin tournaments (), where each team or opponent plays every other team or opponent, and the champion is determined by the team that wins the most games. Ties are possible and are resolved based on league rules.
An advantage of the round-robin tournament style is that no one team has the advantage of seeding, which eliminates some teams from playing against each other based on rank of their prior performance. Rather, each team plays every other team, providing equal opportunity to triumph over each team. In this sense, round-robin tournaments are deemed the fairest tournament style.
One hindrance to employing a round-robin-style tournament is the potential for the number of games involved in tournament play to determine a winner. Determining the number of games can be found easily using a formula which, as we will see, can quickly grow in the number of games required for a single round-robin tournament.
As the examples show, single round-robin tournament play can quickly grow in the number of games required to determine a champion. As such, some tournaments elect to employ variations of single round-robin tournament play as well as other tournament styles such as elimination tournaments.

### Single-Elimination Tournaments

When desiring a more efficient tournament style to determine a champion, one option is single-elimination tournaments (), where teams are paired up and the winner advances to the next round of play. The losing team is defeated from tournament play and does not advance in the tournament, although some leagues offer consolation matches.
A single-elimination tournament offers an advantage over single round-robin tournament style of play in the number of games needed to complete the tournament. As you can see, in comparing the number of games in a single round-robin tournament in  with the number of games in single-elimination tournament as shown in , the number of games required for single round-robin can quickly become unmanageable to schedule.
There are modifications to both the round-robin and elimination tournament styles such as double round-robin and double-elimination tournaments. Next time you observe a college or professional sporting event, see if you can determine the tournament style of play.

### Check Your Understanding


### Key Terms

1. data analytics
2. seeding

### Key Concepts

1. Describe how a round-robin tournament is organized.
2. Compute the number of games played in a round-robin tournament.
3. Describe how a single-elimination tournament is organized.
4. Compute the number of games played in a single-elimination tournament.

### Formulas

Number of games in a single round-robin tournament with  teams is .
Number of games in a single-elimination tournament with  teams is .

### project


### Lucas Sequence and Fibonacci Sequence

The Lucas numbers bear some similarity to the Fibonacci numbers and exhibit a stronger link to the golden ratio. Edouard Lucas is credited with naming the Fibonacci numbers and the Lucas numbers were so named in his honor. The Lucas numbers play a role in finding prime numbers that are utilized in encrypting data for actions such as using your debit card to obtain money at a cash machine or when making a credit card purchase for point of sale as well as when shopping online.
Complete the following questions to explore numbers in the Lucas sequence as well as their relationships to the numbers in the Fibonacci sequence.
    
    

### Solar Array for a Residence

One of the first steps in adding solar to a residence is determining the size of a system to achieve the desired output. In this project, we will explore the solar needs of a residence and estimate needs of a solar array to supply electrical output to meet various percentages of electrical need.
Step 1: Obtain an electric bill from your apartment/home. Find the average monthly or yearly usage if listed or call the electric company to inquire. If an electric bill is not available, use the Internet to find an average monthly or yearly electric usage for your area.
Step 2: Determine a daily and hourly usage. Divide the average monthly usage by 30 or the yearly average by 365. Divide again by 24 to calculate an average hourly electric usage, which will yield the average kilowatt-hours for how much electrical power your is being utilized in an hour.
Step 3: Multiply your average hourly use (kilowatts) by 1,000 to convert to watts.
Step 4: Use the Internet to determine the average daily peak hours of sunlight where you live.
Step 5: Divide your average hourly watts (Step 3) by the average daily peak hours (Step 4) to calculate the average energy needed for a solar array to produce every hour.
Step 6: Determine the average energy needed in a solar array per hour to meet each of the following:
    
    
Step 7: Using the values computed in Step 6, compute the residential savings based on an average cost of 12 cents per watt.

### Vaccine Validation

Validation of vaccines is a topic that exploded in the news when the Covid-19 pandemic spread across the world. As governments and organizations looked for a vaccine to curb the spread and minimize the severity of infection, concern was expressed by some for what appeared to be a quick discovery for a Covid-19 vaccine.
Conduct an Internet search to explore the following questions. Pay special attention to the sources you select to ensure that they are credible sources.
    
    

### Frequency and Ultrasonic Sounds

Ultrasonic sounds have been utilized for a variety of reasons, from purportedly repelling rodents and other animals as well as a variety of other applications. Using an Internet search, complete the following questions to explore some of these applications and examine the validity of various claims.

### Repelling Insects, Rodents, and Small Animals

Some radio stations purport to play a high pitch sound dually with their music to aid in deterring insects and other annoying bugs to aid in providing a bug-reduced listening environment. To deter small rodents, some products claim to emit ultrasonic sounds that drive away mice and other similar pests.
    
    

### Disbursing Teenagers

Some business owners and communities have turned to products such as the “mosquito” sonic deterrent device to discourage groups of teenagers from loitering around storefronts and community landmarks, citing a public nuisance issue and public safety concerns.
    
    

### Jewelry Cleaner

Use of pastes and liquid chemicals to clean jewelry can be harsh on stones as well as metals. So how can we safely obtain the sparkling clean look at home that jewelry stores provide? Some would say the answer is to use an ultrasonic jewelry cleaner, but do these really work?
    
    

### Specialized Ringtones

As the use of cell phones has become commonplace and families grow towards each member having their own cell phone, specialized ringtones have become popular and can aid in identifying who is calling just by the ringtone.
Ever hear of ringtones that can be heard by teens but often not their teachers? The banning of cell phone use by K–12 students during class time as been implemented across a wide array of schools and some students have purportedly found ways to get around teachers hearing a cell phone ring through the use of ultrasonic ringtones.
    
    

### Streaming Services and Math

With the ability to stream music virtually anywhere you are, it is not surprising that Google Play Music, Apple Music, and a slew of other companies such as Spotify, Amazon Music, YouTube Music, Sound Cloud, Pandora, Deezer Music, Tidal, Napster, and Bandcamp have invested heavily to bring streaming service to users worldwide. Streaming services have expanded to offer virtually every genre of music with vast libraries to meet diverse user requests.
Considering all of the choices available for streaming music, there is a wide array of options for subscribing. Conduct an Internet research to review your current streaming choices, if any, and evaluate competitors’ products.
    
    

### Math and Baseball

Baseball is known to have one of the largest pools of statistics related to the game and its players. Managers, coaches, and pitchers study the statistics of the players on opposing teams to give their team an edge by knowing what pitches to throw for the best probability to be missed by a batter. In similar fashion, batters study pitchers’ statistics to learn a pitcher’s strength and how to predict what a pitcher will throw and how to best hit against a pitcher.
The three primary baseball statistics are batting average, home runs, and runs batted in (RBIs), which are the components of the title of Triple Crown winner that is awarded to players who dominate in these three areas. However, there is a wealth of other statistics to evaluate when studying the performance of a player.
Conduct an Internet search to research statistics and how they are calculated in the following categories:

### Batting Statistics

1. There are about 30 batting statistics. Select a minimum of 10 batting statistics. Compose an organized list including the name of the statistic, abbreviation, explanation of what it represents, as well as how it is calculated.
    As an example: AB/HR represents at bats per home run and is calculated by the number of times a player is at bat divided by home runs.

### Pitching Statistics

1. There are about 40 pitching statistics. Select a minimum of 10 pitching statistics. Compose an organized list including the name of the statistic, abbreviation, explanation of what it represents, as well as how it is calculated.
    As an example: K/9 represents strikeouts per nine innings and is calculated by the number of strikeouts times nine divided by the number of innings pitched.

### Fielding Statistics

1. There are around 10 fielding statistics. Select a minimum of five fielding statistics. Compose an organized list including the name of the statistic, abbreviation, explanation of what it represents, as well as how it is calculated.
    As an example: FP represents fielding percentage is calculated by the number of total plays divided by the number of total chances.

### Overall

1. Select a player from recent years to evaluate. The player can be one that you have followed, one from a favorite team, or any current player. Find the statistics shared in Questions 1–3 to use in evaluating the potential strengths and weaknesses of the player. Write a short paragraph analyzing your selected player, supported by the statistics from the answers to Questions 1–3.

### Math and Fantasy Football

Fantasy football offers spectators an added dimension to football season with a competitive math-based game where the active components are real-life players in the current season. For clarity in this exercise, the actual fantasy football players will be denoted as FFP and actual professional team members will be denoted as players.
While some fantasy football leagues have slightly different setups or scoring systems, most share some common elements.
Often using a lottery system to determine who picks first, second, and so on, FFPs select 15 current players to comprise their personal fantasy football team. The players selected can be from any professional teams and a FFP can utilize any team recognized by their league. FFPs can elect to keep the same players on their team for the whole league play or trade for any player not selected by another FFP in their league.
At the start of each week during football season, each fantasy football player selects their roster of actual players to comprise their roster of starting players. Typically, a starting roster consists of the following players: 
    
    
As actual professional games are played, points are tallied based on your league’s scoring system. The points the team members on your starting roster make during the week are computed and whichever FFP has the highest score for the week wins that week.
The FFPs with the best records of wins versus losses enters fantasy football playoffs to determine the ultimate league champion and collects the pot.
The above overview of fantasy football describes the basic game play. The fun comes in understanding and analyzing the math behind the scoring.
    
    

### Math and Hockey

Hockey is full of math from obvious components such as scoring and statistics to the shape of the rink and the angles involved in puck movement.
Collegiate and professional hockey games are 60 minutes long and are divided into three periods of 20 (60/3) minutes each. At any one time, there are five players and one goalie on the ice for each team. If a player is called on a penalty and is placed in the penalty box, that team now has four players, which is 20% less players on the ice competing against five opponents. In some instances, a team may have two players in the penalty box at one time, resulting in three players, or 40% less players on the ice compared to a full team. Being one player down for a 2-minute penalty or potentially 5 minutes for a major penalty leads to an imbalance on the ice and calls for a quick change of offense and defense strategy.

### Rink Composition—North American

An ice rink is comprised of various geometrical shapes, each with precise dimensions.
    
    

### Statistics

Using an Internet search, select two top hockey players from the same league to answer the following questions:
1. Write a paragraph sharing a minimum of five statistics for each player you have selected. Describe how each of the statistics are calculated and what each statistic means.
2. Write a paragraph comparing the two players and determine who you believe is the better player. Support your choice.

### Scoring

The basics of scoring in ice hockey is simple, the team with the most goals is the winner. But, how to score the most goals involves much math!
    
    

### Math and Soccer

As the world’s most popular sport, you’ll be excited to confirm that soccer is full of mathematics ranging from scoring and statistics to footwork, angles, and field shape.
Soccer requires understanding of mathematical concepts and equations as well as skill, fitness, and game knowledge. One such example is angles, which you all will remember from your geometry class. While players are not carrying protractors and measuring angles during play, mental calculation of angles is a constant in any successful player’s thinking. A goalie is not physically able to cover the entire open net region and a player must calculate an angle to kick the ball consistent with the net opening while predicting the ability of the goalie to stop the ball from entering the net.
    
    
Using an Internet search, select two top soccer players from the same league to answer the following questions:
    
    

### Chapter Review


### Section 13.1 Math and Art


### Section 13.2 Math and the Environment


### Section 13.3 Math and Medicine


### Section 13.4 Math and Music


### Section 13.5 Math and Sports


### Chapter Test
