F奖论文 2020年美国大学生数学建模竞赛ICM-D题 特等奖提名
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2020-04-29
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Problem Chosen
D
2020
MCM/ICM
Summary Sheet
Team Control Number
2008495
Summary
Soccer Teamwork Evaluation Models
This paper proposes a method, with graph theory, probability theory and calculus, to build
machine learning models based on data analysis, which aims at providing strategies for soccer
coach's lineup arrangement and players' training.
Firstly, the Pass Network Model can be established according to the graph theory, whose
edge-weights are evaluation of coordination degree of each dyadic configurations. Pass Evaluate
Index is designed for evaluate a single pass, and the summation of each pass can be defined as
the edge-weights of PNM. For analysis, the adjacency matrix of N participating players within a
period. Several outstanding M configurations can be found by the sort of M-element combination
with the key of the sum of the sub-complete graph edge weights. What’s more, investigation of
the influence of time on pass density depends on the constructed and approximate function of
time and pass.
Secondly, performance indicators that reflect successful teamwork can be divided into
dynamic indicators and static indicators. Static indicators include player position arrangement
and line-up with which player season heatmap models and player position models can be
established while the dynamic indicators include opponents’ strength, side, coach, passes,
defense, attack and fail. etc. After visualized analysis of the correlation between the dynamic
indicators extracted after data cleaning, and with the setting label by the goal difference, the
random forest classifier, a machine learning model, is used as a evaluation model of dynamic
indicators. After the Grid Search used for tuning parameters, and cross-validation, the accuracy
of the model achieving 80% approximately.
Thirdly, the study focuses on the role of static indicators in the performance of the team and
establishes different players' value evaluation models in different positions which
comprehensively consider the player’s positions and technical statistical data evaluation. To
optimize the value of 11-person permutation, we choose simulated annealing (SA) algorithm
which searches the global optimal solution in cousin points in the same minimized search tree
after the local optimal solution has attained. The model finally gave the best starting lineup
formation. In addition, we also consider the following three secondary factors: tacit
understanding between players, home and away influence, and coaching arrangements. All
analysis above can be concluded as comprehensive suggestion to the coach.
Finally, we use the case of the Huskies to explain group dynamics. And use the conclusions
obtained by the Huskies to build a model to explain how to design a more effective team and
supplement the team performance indicators.
Key words: Network; Graph theory; Calculus; Machine learning; Random forest classifier;
Simulated annealing; Heat map; Group dynamics
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