基于滑动窗口模型的合作结构分析及队伍战略优化-以足球比赛为例资源-CSDN下载

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MATHmodels

Problem Chosen

2020

MCM/ICM

Summary Sheet

Team Control Number

2013245

Analysis Cooperation Structure of Network and Making Teaming Strategies

——based on Sliding Window Model

Teamwork can solve complex problems that may be difficult for individuals to handle,

so improving team effectiveness is meaningful. We analyzes the typical

cooperation

structure

from the ball passing network, and establishes the Sliding Window Model to

identify the cooperation mode suitable for the Huskies, and then puts forward the

suggestions of strategic adjustment.

Firstly, we set up a directed ball flow network with the soccer players as the node and

the passing as the arc. The we select the structure of all passes larger than 5 from

network as

cooperation structure

and set the feature vector for it. According to the

feature vector value, we use the average-linkage method of hierarchical clustering to

cluster the path, and use the main component analysis method to reduce the dimension.

Eventually, we extract six kinds of typical strategy patterns from the network and

analyze their structural characteristics.

Secondly, we choose the

average node connectivity

transitivity

and other indicators to

measure teamwork. We establishes a Sliding Window Model to describe the changes

of the performance indicators during the match, which sets a 900-second (1/3-half-time)

window to slide. The window is a time-sharing subplot of the match, which can

precisely capture the configuration and dynamic strategy of the team at that time

sliding the position of the highlight time period .

Thirdly, after analyzing the structure that the Huskies often used in highlight

performance., we find that the Huskies is more inclined to use defensive counterattack

strategy. The Huskies usually performs better in the middle-front and back courts, but

is very weak in the middle-back courts. Therefore, we recommend that the Huskies

carries forward the long-pass punching mode and use the 4-4-2 formation.

Finally, we find that enhancing the flexibility of the team structure and establishing a

local coordination structure are beneficial to improve the team's efficiency. It is

necessary to refine and analyze the main mode of team contact. When the overall

indicators are too difficult to explain in detail, the idea of sliding window may be useful.

If we can capture more information about the characteristics of successful teams, we

may be able to build a more generalized model for measuring team performance.

Keywords: Network, Cooperation Structure, Sliding Window Model, Teaming Strategies

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2
MATHmodels
  Team 2013245  Page  1  of  28 
Contents 
Contents ..................................................................................................................................................................... 1 
Introduction ...................................................................................................................................................... 2 
1 Background ............................................................................................................................................... 2 
2 Restatement of the Problem ................................................................................................................. 2 
3 Core Tasks at hand ................................................................................................................................. 2 
Assumptions ..................................................................................................................................................... 3 
Model Developments .................................................................................................................................... 3 
1 From global to local: Identify Cooperation Structure .................................................................. 4 
2 The Features of Different Cooperation Structures ........................................................................ 7 
Performance Evaluation & Structure Characterization ................................................................... 10 
1 Selection of performance indicators ............................................................................................... 10 
2 Sliding Window Model ...................................................................................................................... 11 
Characteristic Analysis and Structural Advice ................................................................................... 14 
1 Universality Analysis Based on Performance ............................................................................. 14 
2 Our Advice ............................................................................................................................................. 14 
how to design more effective teams ...................................................................................................... 16 
1 Key elements of designing effective teams .................................................................................. 16 
2 Other aspects of teamwork we want to know .............................................................................. 16 
Strengths and Weaknesses ........................................................................................................................ 16 
1 Strength ................................................................................................................................................. 16 
2 Weakness .............................................................................................................................................. 17 
References ..................................................................................................................................................... 17 
Appendices .................................................................................................................................................... 18 
1  Codes .................................................................................................................................................. 18 
 
   

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Team 2013245 Page 2 of 28

1 Introduction

1.1 Background

Soccer is a complex system based on people’s general understanding. The overall performance

of a team does not equal to the sum of all players’ skills. The victory of a game calls for suitable

strategies and flawless cooperation. Both attack and defense subsystems are relatively

independent in structure, functions, and behaviors. They are interrelated and restrict each other.

Meanwhile, soccer match is also an open system interacting with outside. A variety of factors

influence the outcome of a match.

1.2 Restatement of the Problem

According to the competition data of this season, our home soccer team Huskie did not behave

so well. We are invited by their coach to explore how their interactions lead to final results.

Various types of team style and strategy may affect team’s performance greatly, sometimes even

be a constraint. Thus, we will also offer suggestions based on past defect to improve Huskie’s

outcome next season.

Problem 1 requires us to create a network in accordance with passing data. We use nodes and

edges to represent players and the ball passing routes respectively. The number of passing routes

reflects the player’s importance in a match. Moreover, the direction of arrows shows a player’s

function such as forward and center. We identify the network’s pattern both in space and time

dimension.

Problem 2 requires us to explore indicators of successful teams in addition to scores and wins.

We briefly summarize several indexes to describe Huskie’s performance despite the final result.

All indexes are come from full events data. There are thirty-eight matches in total. We only use

half of them to set up a model. And the next half is used to evaluate the model’s universality.

Problem 3 requires us to give Huskies’ coach some suggestions. We analyze the network of

problem 1 and consider all the success indicators. There are mainly three kinds of team style,

which is defensive, offensive and balanced one. We will offer structural tactics depending on

opponents’ level. When the team is competing against low-level opponents, athletes often have

more space and time to apply techniques because of less confrontation or even none. Since

players can fulfill observation and judgement timely, the success rate of a technique is relatively

high. On the contrary, high-level opponents oppress our players in space and time. Their strong

defense ability causes the declination of our technique success rate.

Problem 4 requires us to widen the use of our model. With the specialization process becomes

popular, team work gains great popularity in the society. Since we have functions to evaluate the

effect of a collaborative working system, it is easy to pick out the best combination. We

generalize the characteristic of a large number of excellent teams; then give a model of team

work which can apply universally. We need extra information if put into common use.

1.3 Core Tasks at hand

 Design a network for passing activities.

 Identify elements that can lead to success in addition to points.

 Offer some advice to coach on the strategy improvement of next season.

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Team 2013245 Page 4 of 28

3.1 From global to local: Identify Cooperation Structure

To depict the passing network between players, we need to extract possibly valuable accesses

for statistics to analyze the feature of passing event.

Now we must define a professional concept cooperation structure. It represents a short-time

cooperation tactics between several players, which can be reflected by continuous soccer ball

passing access. Unlike overall strategies in a match, cooperation structure more emphasizes the

effect on the micro level.

Every cooperation structure is regarded as a unit. Continuous passes per unit is a significant

standard describing structure characteristic. More passes will result in the lack of cooperation

structure. If we choose fewer passes as initial screening conditions for cooperation structure,

although we can get enough data, it cannot reflect obvious features. Considering the actual

situation, we select all cooperation structure that passes is larger than 5 for quantitative process.

3.1.1 Selecting Accesses and Feature Vector Calculation

We find the feature vector that can describe the property of a cooperation structure.

󰇩







󰇛















󰇜



󰇪

The definition of variables is as follows

Variable Name

Explanation





the arithmetic center’s horizontal coordinate, reflects the position of

cooperation structure





the arithmetic center’s vertical coordinate, reflects the position of

cooperation structure

󰇛















󰇜

average passing distance, directly describes the size of cooperation

structure



passes, reflects the scale and complexity of cooperation structure



number of passer, reflects the scale and complexity of cooperation

structure





average passing time

, reflect the tempo of cooperation structure

We select 1352 accesses to represent typical cooperation structure. Since the change of field, it is

easy to misjudge the average passing time. We get rid of seven abnormal accesses data and get

1345 accesses.

When choosing the soccer ball movement track, we believe that continuous passing can reflect how players cooperate

with each other. At first, we only plan to use passing events of the season. However, players’ actions are changeable and

coordinates of the ball are dispersed. Hence we are not able to get a complete ball track. Therefore, we finally decided to

use full events for cooperation structure screening.

There is no need to normalize coordinates as absolute location. We use the relative coordinates given by problem. It is

more persuasive to design cooperation structure.

Average passing time equals to the difference between the start time and the end time divided by the passing times.

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