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The mathematics behind soccer

Abdullah Zafar studies team movement in soccer using vector fields

The mathematics behind soccer

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.

The Fields Institute launches a new laboratory network

Fields-CQAM aims to bridge academia and industry sectors in mathematics

The Fields Institute launches a new laboratory network

On June 28, U of T’s Fields Institute for Research in Mathematical Sciences officially launched the Centre for Quantitative Analysis and Modelling (Fields-CQAM), which will house 11 new laboratories.

The launch is part of a growing shift for governments and universities alike to initiate and drive academic-industry collaborations. According to Dr. Mona Nemer, Canada’s Science Advisor, doing so requires funding, engagement from industry, and appropriate infrastructure in place to support entrepreneurship.

“Budget 2018 includes $1.3 billion for investments in laboratories, equipment and infrastructure,” wrote Nemer in an email to The Varsity. Budget 2018 will allot $763 million to the Canada Foundation for Innovation and $572.5 million to develop and provide access to big data resources like machine learning. The government’s support of Fields-CQAM attests to Canada’s commitment to drive innovative research that will benefit Ontario in the long-run.

Fields-CQAM will provide the resources and the opportunities to expand mathematical research and its applications in fields such as computer science, medicine, and finance in Ontario. Undergraduate and graduate students alike will also benefit.

“Often new research arises out of the interaction between students and companies, and students are important to building research capacity in both industry and academia,” continued Nemer. “[Student researchers] are directly involved in carrying out research in academic institutions, and their research projects and results are often the basis for developing industrial partnerships.”

Professor Huaxiong Huang, Director of Fields-CQAM, spearheaded the launch event with the opening remarks, and lab directors presented a diverse array of research projects.

Professor Alec Jacobson, a Lab Director from U of T, will use Fields-CQAM’s infrastructure to advance his team’s research in 3D surface geometry used in computer graphics and computer-aided design. These have significant applications in 3D printing, mixed reality systems, and video games.

Jacobson is also a lead supervisor in the 2018 Fields Undergraduate Summer Research Program, an annual program partly sponsored by Fields-CQAM that selects students from across the globe to engage in mathematical research. The program groups four to six undergraduate students together to tackle hypothetical industry challenges that involve mathematics.

Fields-CQAM is also supporting projects in health and medicine. When most people think of cancer diagnosis, math usually does not come to mind.

However, computational research is pivotal in identifying metastasis — the spread of cancer to other regions of the body. Last year, over 80,000 Canadians died of cancer, and 90 per cent of these deaths were due to metastasis. Fields-CQAM Lab Director Nima Maftoon of the University of Waterloo’s computational metastasis lab aims to develop models to better track cancerous cells and target metastatic tumours for optimal drug delivery, halting the spread of cancer.

York University professor Jianhong Wu, Director of the Mathematics for Public Health Laboratory, aims to address Ontario’s public health needs and crises by developing novel procedures with statistical analyses and algorithms to track epidemics, like acute respiratory infections and vector-borne diseases. Wu’s team has partnered with pharmaceutical giant Sanofi Pasteur to advance their research efforts.

Health care aside, Fields-CQAM is also conducting research in finance. Professors Matt Davison, Adam Metzler, and Mark Reesor are lab directors for the Financial Data Analytics Laboratory. Their goal is to provide insights in social media from financial data that would be of use to financial institutions.

Aside from an expansive laboratory network, Fields-CQAM will also host workshops and lectures for graduate students. Such workshops will train graduate students entering the industrial workforce.