The tension between sports and academics has persisted for generations. 

Some may argue that participating in sports may be one reason for our country’s lagging academic performance. On the other side are those who point to studies that suggest sports participation can elevate academic skills, as well as improve confidence and social interactions.

Regardless of your feelings on the issue, it’s tough to deny that students generally like sports. The fact is playing sports, whether at school or in the community, is fun. A 28-year study found 57% of students participated in at least one sport during their high school career. Conversely, only 46% of students say they “love” or “really like” math. 

Taking these statistics to their logical conclusion, it seems more students would rather play sports on the field than crunch numbers in the classroom. 

The Intersection of Sports and Mathematics

When it comes to math and sports specifically, there really shouldn’t be any conflict between the two. In fact, there’s a very good argument that math is an integral part of all modern sports, including baseball, football, soccer, and more. 

Ask a student-athlete to provide some statistics about their favorite sport or player, and they are likely to spout off data that include batting averages (baseball), three-point conversions (basketball), and even DVOA (a football statistic that stands for “defense-adjusted value over average”). In many cases, these statistics are provided to them, but if you ask these students what they mean and how they are calculated, many will have no trouble explaining the concepts.

They can relay this information because these statistics are important to them and practically applied to their lives and interests. It’s one of the reasons sports analytics has become such an important and lucrative field over the last few decades. Researchers apply these statistics to help fans understand the games better and create detailed mathematical models that help athletes improve performance, help coaches identify problems, and help teams select players for recruitment.

The Role of Math in Sports

Sports are games where wins and losses are the sole quantifications of success. They are, therefore, subject to all kinds of important mathematical questions:

• How frequently does a team or individual win or lose?
• How many points is a team likely to score under certain specific conditions?
• What strategy translates to wins or losses most regularly?
• How should we rank teams and players? By their average scores? Their win/loss records? Their effectiveness?

Researchers use these questions to create mathematical models for optimizing sports strategies and improving training regimens. For example, a coach might measure each player’s VO2 Max score during training and then try different training methods to see which approach optimizes benefits for the team or athlete. They might even use game theory to craft a strategy for players on the field.

Players can use an intuitive understanding of geometry to make better shots and perfect their techniques in games ranging from basketball to billiards. Throwing a basketball, for example, requires an implicit knowledge of angles and distances, even if they aren’t being measured precisely in real time. Billiards relies heavily on geometry but also involves a basic understanding of physics, of which math is a key component. 

Analytics can help improve sports performance for both teams and individuals. For team sports, whole team and individual player outcomes can be combined to yield insights, such as when individual players repeatedly struggle to work together.

Mathematical Models in Sports Analysis

Mathematical models are used to analyze various aspects of sports, including what has already occurred and projecting what may occur. The most common models are predictive analytics and statistical analysis. 

Predictive Analytics predict outcomes and trends in sports and events. This field aims to form a model of how the future relates to the present. Based on the data, a researcher might be able to show how game scores and player performance are determined by variables like training regimens, diet, and even weather. Athletes and coaches can use this information to better prepare themselves for games or matches.

Statistical Analysis, however, is less concerned with the relationship between past, present, and future and more concerned with finding statistical regularities of any kind. For example, statistical analysis might conclude that two team players tend to perform poorly together. Coaches can use this information to determine the genesis of the problem and identify a solution. 

The Mathematics Behind Sports Equipment

Besides athletic performance, physics also plays a role in the development and effectiveness of sports equipment. As physical objects, sports equipment must adhere to the laws of physics. Since these physical laws are fundamentally expressed through mathematical equations, we can conclude that mathematical principles govern the performance and durability of sports equipment.

One good example of this is the uniform an athlete wears during competition. Sports uniforms need to be lightweight to reduce mass. They also need to be aerodynamic to minimize wind resistance. Swimmers’ uniforms also need to be optimized for aqueous environments. In every case, there are curves defined by differential equations, which will optimize performance for the wearer.

Similar calculations are made for balls, shoes, rackets, bats, and other equipment. For example, statistical analysis might conclude that two team players tend to perform poorly together.

Mathematical modeling also improves sports equipment performance and drives design innovation. Equipment designers across all sports continually refine their models to gain even the smallest advantage that might give players a winning edge. 

Data Analytics in Sports

When it comes to player performance and even team performance, data are everything. Thanks to the rise of cheap, high-speed computing, data analytics is a more powerful and widespread discipline than ever.

Researchers use mathematical models, refined with data, to identify strengths, weaknesses, and trends in sports. The goal is to remove problems and exploit strengths.

The information researchers feed into their models comes from various sources, including innumerable data points. Some of the most popular include: 

• Number of points scored
• Batting averages
• Frequency of fouls
• Timing of points
• Age of players
• Weather

Data analytics also informs scouting and recruitment decisions well before players are on a team. Mathematical models for talent evaluation use data from a player’s previous history to determine where their talents might fit into a new team. Researchers consider their overall skill level and where a player might add the most value to a team.

The use of data analytics was memorialized in the 2011 film, Moneyball, starring Brad Pitt and Jonah Hill. The film told the story of Billy Beane, general manager of the 2002 Oakland Athletics, who used analytics to overcome the divide between a longstanding losing record and a tight budget. Using data analytics, Beane’s under-the-radar team won 20 consecutive games (a franchise record and the fourth-longest winning streak in baseball) and wound up making it to the American League division playoffs.

Math: The Reigning MVP of Modern Sports

Mathematics is everywhere in sports. If your student prefers playing sports to studying numbers, show them math’s important role in their favorite sport. If they are interested in a career as an athlete, help them understand how a strong command of math will increase their odds of successful recruitment.  

For even casual football or baseball fans, fantasy sports require a keen understanding of applied mathematics. Understanding touchdown-to-interception ratios or on-base percentages can help fantasy sports “general managers” pick players in the draft and make meaningful trades throughout the season. 

Researchers use sports data to identify statistical patterns and forecast wins and losses. This information is invaluable for players, coaches, and managers trying to gain an advantage over their competitors. Likewise, equipment designers develop complex computer models to create designs that are faster, lighter, and stronger.

From fantasy sports to strategic analysis to equipment design, mathematics is the silent powerhouse driving success in modern sports, both on and off the field.

Download our printable Olympic math activities for some practical applications to the mathematical aspects of sports.