U of T student Abdullah Zafar studies the intersection of math and movement. COURTESY OF FARZAD YOUSEFIAN

Third-year U of T math and physics student Abdullah Zafar is collaborating with Sport Performance Analytics Inc. to study the mathematics behind team movements in soccer.

Zafar, a soccer player himself, presented his research at the ASSU Undergraduate Research Conference in January, in a presentation entitled “Weaving the Fabric of Football: How Vector Fields and Fractal Dynamics Structure Patterns in Team Movement and Performance.”

This project was brought to life after Zafar and Farzad Yousefian, founder and president of Sport Performance Analytics Inc, noticed a gap in how sports models were approached and analyzed. The pair sought to understand the underlying mechanics behind group movement and team dynamics on the field.

To achieve this, the research team collected data from the Canadian women’s soccer team at the Summer Universiade. Zafar analyzed the overall patterns of individual player movements and explored their relation to player performance measures.

While each player’s movement is individually determined, their overall movement on the field is influenced by other players’ positions. Zafar quantified movements of the latter type and analyzed them as a single unit.

Using vector fields, Zafar measured team movement and found a correlation to physical metrics like player heart rate and distance played. He characterized these patterns of team movement as Brownian motion.

Zafar’s findings could be used to assess efficiency and performance on the field, and develop strategies to impact the tactical side of team sports with practical training protocols.

In an interview with The Varsity, Zafar explained that quantifying group movements by collecting variables such as speed, directionality, and steps per minute was the easier part of the process. However, painting a group picture in terms of a complete analysis was a challenge.

The project has come a long way since last summer, and is being presented at various conferences.

Moving forward, data collection will still be a major barrier, considering that performance data is like personal property to teams, and Zafar notes that getting access to it can be difficult. Were the research team to have access to league information, the sports teams need not worry about competition between them. In the long run, access to more information would allow the data to be more generalizable.

Zafar said that this initial report serves only as a pilot study a proof of principle that demonstrates that this field of research can be pursued.

Currently, the team is breaking the project into more concise research questions that can address specific aspects of sports performance, including tactical and physiological perspectives.

According to Zafar, another challenge is obtaining funding. Compared to health and wellness, sports performance analysis receives less funding. Shifting the perspective of the research to one of clinical importance could be the key to accessing funding in the future.

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