Finalist Award in the 2020 ICM

• Full paper: Riding on the Green: On Perfecting Huskies' Teamwork

• Certificate of Achievement: Finalist Award in the 2020 Interdisciplinary Contest In Modeling

2020 ICM Background

During this year's contest, teams of three students researched, modeled, and wrote a solution to an open-ended interdisciplinary modeling problem. ICM teams should choose one of the following three problems (see the official website for detailed descriptions):

1. The D Problem involved analyzing and quantifying team dynamics. Using the data provided, students developed and analyzed a passing network for a football (soccer) team in order to better understand how overall team performance. Based on their analyses, teams recommended strategies to the coach to improve team success next year.

2. The E Problem asked teams to create a global solution to the plastic waste problem. They needed to determine a plastic waste level that could be mitigated in an environmentally safe way, while simultaneously identifying factors that limit the ability to reach this safe level and ways to more equitably distribute causes and effects.

3. The F Problem asked students to create an international policy that would address the resettlement needs of environmentally displaced persons (those whose homelands are lost to climate change) while also preserving the cultural heritage of those peoples. This problem required students to evaluate cultural significance as well as understand geopolitical issues surrounding refugees.

All three problems required data analysis, creative modeling, and scientific methodology, along with effective writing and visualization to communicate teams' results in a 20-page report. Due to the multi-disciplinary nature of the problems, teams need to use a variety of methods and tools to solve those problems. This allowed teams to showcase their strengths in many diverse areas including climate science, cooperative systems, cultural preservation, data science, ecology, environmental science, international relations, networks, operations research, policy, political science, sports analytics, statistics, and sustainability.

Problem Statement

We chose problem D which required us to mathematically optimize the performance of a soccer team, Huskies, based on the provided data detailing information from last season. The data includes all 38 games they played against their 19 opponents (they played each opposing team twice), covering 23,429 passes between 366 players (30 Huskies players, and 336 players from opposing teams), and 59,271 game events.

As requested by the coach of Huskies, we finished the following tasks:

1. Create a Passing Network: Construct a network where nodes represent players and links represent passes. Analyze network patterns, such as dyadic and triadic configurations, team formations, and other structural indicators across games.

2. Identify Performance Indicators: Beyond points or wins, identify indicators of successful teamwork, such as play diversity, player coordination, and contribution distribution. Consider factors like adaptability, flexibility, tempo, and flow.

3. Develop a Teamwork Model: Create a model that captures the structural, configurational, and dynamical aspects of teamwork using the identified performance indicators and team processes.

4. Provide Insights and Recommendations: Advise the coach on effective structural strategies and recommend changes for the next season to improve team success based on network analysis insights.

5. Generalize Findings: Extend the insights gained to generalize about designing more effective teams in broader contexts, considering additional aspects of teamwork needed for generalized models of team performance.

Our Work

We put forward an array of key performance indicators to evaluate the team’s overall performance, followed by correlation analysis, principal component analysis (PCA), and factor analysis to identify key factors underlying the team’s collaboration effectiveness. Two distinctive models were proposed: 1) a ball-passing network model to analyze the interactions among team players, and 2) a Back Propagation Neural Network (BPNN) model with five input layers to evaluate the effectiveness of teamwork. We then implemented the two models to analyze the team’s performance based on team statistics and proposed an array of recommendations for performance improvement based on prescriptive data analyses.In the ball-passing network model, we developed the Average Passing Network and the N-Pass Network to analyze the interaction among players according to the ball-passing number and weighted passing number. The specific process is as follows.

1. Firstly, we chose the social relation model and made an analogy between the set of relationships among social actors and the set of players passing the ball in a football match. This model simplifies the multivariate relationship and lays a foundation for the establishment and solution of the ball-passing network model. Moreover, we assigned different weights to different types of passes and valued each pass to make the connection between players more meaningful. Meanwhile, Gephi was used to visualize the network and observe the interaction of players throughout the whole game. We also used Ucinet6 to analyze the network not only as a whole but also locally and individually.

2. Next, we developed the N-pass network, which focuses more on interactions between players than just the number of passes. Based on three aspects (X coordinate of the network centroid, ratio of advance, and centrality dispersion), we developed a dynamic network, facilitating time-dependent analysis of the whole game.

In the BPNN-teamwork evaluation model, we used BPNN to establish our model and develop a solution. Firstly, we analyzed what makes a perfect football team and found that pass completion rate, weighted passes, game tempo, coach, and home or away status are all indispensable influencing factors. After processing the data of these five influencing factors, the BPNN was built. Then, using the two models we had built, we analyzed how the Huskies could perfect themselves and become better next season. We made some graphic analyses from the network graph and the coefficients we obtained in the network. The factors influencing team interaction were explored from the BPNN by utilizing the control variable method. Finally, we demonstrated the model’s stability and general applicability to other human behaviors via sensitivity analyses and extracted constructive insights on how to design effective teams.