You’ll find sports just about everywhere… on the field, in the gym, and on TV. But have you ever noticed the connection between math and sports that is about more than just the scoreboard? You can see it in how games are scheduled and how teams are matched up. And even how certain decisions may be made to keep things fair and competitive.

Teachers and students often talk about math in the context of science or engineering. But the world of athletics, from youth leagues to pro teams, depends on math more than most people realize.

The Geometry of the Game Schedule

Let’s start with something every sports team needs: a schedule. Imagine if a school district wanted to run a round-robin basketball tournament where each team plays every other team once. It sounds simple until you try to map it out fairly.

Here’s where graph theory comes in. In his article for Consortium, Joseph Malkevitch used math to show how tournament structures can be built and balanced. Each team becomes a point (called a vertex), and each game is a connection (an edge) between two teams; the result is a simple graph or network.

If you have four teams, you need six games. Rather than dragging the tournament out over six days, graph-based planning can group games into just three time slots, with two games each. That’s efficient! And it keeps teams from waiting too long between games.

Odd numbers? No problem, although the number of days needed will grow as the number of teams increases. With an odd number of teams, one team sits out each round. This built-in “bye” round rotates fairly so that everyone gets equal play.

Using Math and Sports to Model Fairness and Home Advantage

Fairness in sports isn’t only about enforcing the rules. It also matters where the games take place. When one team gets a few more home games than the others, it can throw things out of balance. Malkevitch uses diagrams with arrows (directed graphs) to show who’s hosting each game, which makes it easier to spot when things feel one-sided, really showing the power of math in sports.

When the pattern becomes clear, it’s easier to adjust the schedule so things feel more balanced.

It’s About More Than Just Schedules

Math doesn’t just come into play in the background. It’s actually part of the sport, too. Think about figure skating. Math and sports intersect when skaters plan their routines, for example, when to place the most difficult jumps; they have to weigh being more tired with the scoring bonus that kicks in during the second half of their routine. Or think about a coach mapping out plays based on what’s most likely to succeed. Even something like the shape of a golf club has been improved by applying massive amounts of math. 

In many of these examples, you’re looking at not just modeling but also decision-making strategy. This is where game theory comes in. It helps you think about your options and also anticipate what someone else might do next.

Bringing Math and Sports Into the Classroom

These topics are a great way to bring math modeling discussions into your class. And if you have students interested in participating in a COMAP math modeling contest (like HiMCM®/MidMCM), these are the kinds of challenges students tackle in the contests. Some past contest problems have involved modeling international sports leagues, studying how momentum shifts in tennis matches, and even building new ways to rank Olympic medal counts.

A math modeling mindset allows students to understand that math involves more than merely solving problems; it’s more about optimizing our daily decision-making.