2014年美赛B题优秀论文.pdf

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For office use only 26443

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B

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2014

Mathematical Contest in Modeling (MCM/ICM) Summary Sheet

Summary

Coach assessment is a kind of multi-index problem, which means the result cannot be gotten by accurate calculation directly. In this paper, the coach assessment model is built to make a comprehensive evaluation of coach competency in order to solve this problem. Meanwhile, gender factor and competitive factor are put forward to deal with the influence of time and gender.

Considering differences between different sports events, which can affect the determination of index and weights, sports can be divided into 6 parts according to competitive nature and competitive characteristics. Furthermore, analyzing the different groups from the aspect of the operational requirement characteristics, sport performance assessment’s objectivity, simulative matches’ possibility and training’s difficulty, the difference degree can be gotten, which is helpful in weight determination.

Then we build the coach assessment model based on Analytic hierarchy process (AHP) and fuzzy mathematics. AHP is a decision-making method for multi-index problems. It is particularly suitable in situation where results cannot be got by accurate calculation directly. So we can make the assessment based on AHP. However, AHP is not accurate in date processing, especially when there are too many dates. Thus shift and range transform method in fuzzy mathematics is applied to accomplish data processing in order to improve the accuracy of the result.

Meanwhile, the influence of gender and time should be considered in the model to improve the model accuracy. Career barriers for female first is analyzed by Career Barriers Inventory (CBI) and the difference between male and female coaches is proved to be not ignored when assessing their career performance. Then the gender factor which is decided by the gender inequality index of the United Nations is introduced to our mode because of its impact on score of influence force index. Competition fierce degree, which is represented by competitive factor and gotten by quantitative calculation, is proved to be related to the time because competition and team number increases when time goes by according to the data. This factor is introduced in the data processing of model and the influence of time can be given in this way. Actually, winning in 2013 is more meaningful than in 1913 after calculation.

The model is solved by AHP method as well as shift and range transform method .The top 5 coaches (from No.1 to 5) in basketball are Pat Summitt, Mike Krzyzewski, Adolph Rupp, Dean Smith and Bob Knight respectively. Top 5 coaches in football are Bear Bryant,Tom Osborne, Nick Saban and Eddie Robinson,Bobby Bowden. And top 5 coaches in baseball are Mike Martin, Gordie Gillespie, Paul Mainier, Augie Garrido and Mark Marquess.

Key words: sports division AHP fuzzy mathematics gender factor competitive factor

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Contents

1 Introduction (2)

2 Classification and characters of sport events (3)

2.1 Classification of sport events (3)

2.2 Characteristics of different sport events (5)

2.2.1 Characteristics of operational requirement (5)

2.2.2 Characteristics of sport performance assessment’s objectivity (6)

2.2.3 Characteristics of simulative matches’ possibility (6)

2.2.4 Characteristics of training’s difficulty (7)

3 Coach assessment model (7)

3.1 Model building (8)

3.1.1 Evaluating index system determination (8)

3.1.2 Weight determination (10)

3.1.3 Data processing based on shift and range transform (11)

3.1.3 Comprehensive assessment indicator determination (12)

3.2 Coach assessment model considering genders (12)

3.2.1 Differences of male and female coaches (12)

3.2.2 Gender factor to coach assessment model (13)

3.3 Coach assessment model considering time (14)

3.3.1 Relationship between time and coach assessment (14)

3.3.2 Competitive factor to coach assessment model (14)

3.4 Model solving (16)

3.4.1The assessment of basketball coaches (16)

3.4.2The assessment of football coaches (20)

3.4.3 The assessment of baseball coaches (21)

4 Conclusions and evaluation (22)

4.1 Conclusions (22)

4.2 Evaluation (23)

5 Reference (23)

6 Special report (25)

Team#26443page 2 of 26 1 Introduction

Jack Welch, former chairman and CEO of General Electric, has ever said, “The best leader is coach”. An appropriate coac h assessment system plays an essential role for the reform and development of sports and cultivation of management talents. We accept a task to help Sports Illustrated look for the “best all time college coach” male or female for the previous century. Considering the fact that coach through every one’s eye is quite different, we should determine rational and justice assessment metrics while discussing all possible sports, both genders and time’s influence with a mathematical model.

The metrics and methods of coach assessment have been extensively study in the world since the late 20th century. In 1973, McClelland proposed a new notion--competency to replace traditional intelligence measure for coach assessment and built a coach competency model [1]. In 2001, Wean Goldsmiths pointed out that players’ sport performance and number of champions couldn’t be the exclusive standard to access a coach and we should pay more attention to his contributions to players and sport development [2]. In 2004, Li Yong adopted research method of literature, Delphi method and analytic hierarchy process (AHP) [3]to assess coaches objectively, reasonably and comprehensively which we can learn from. In 2006, Zhang Xinzhong introduced the Coaching Behavior Assessment System (CBAS) which was proposed by Smiths and Small of Washington University to access coaches’ performance [4]. Actually, CBAS only concludes on-the-spot behaviors of coaches, and we should add extra assessment metrics to complement the assessment method of CBAS. In addition to AHP, fuzzy comprehensive evaluation method, structural equation model and so forth have been applied in the coach assessment system.

In our work, to build an appropriate model to assess coaches, we need to choose the fair and reasonable assessment metrics, i.e., evaluating index system named in our model. Synthesizing previous assessment metrics, on the one hand, we know that we cannot evaluate coach only by his external conditions such as team’s sport performance, numbers of championships or educational background, we should also take his potential and deep traits and characteristics into account. On the other hand, we hope the metrics in our assessment systems are as objective as possible to make evaluating work towards scientifically quantitative analysis. So when determining evaluating index system, we should combine subjective metrics with objective metrics, and quantify subjective metrics by objective indexes as far as possible to build a coach assessment model with rationality, objectivity and justifiability.

After preliminary analysis, we intend to apply such study approaches:

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(1) Research method of literature:

(a) Study theories of coaches’ competency in the literature about sport training theory, psychology and management science.

(b) Papers about systemic evaluation methods in the world.

(2) Questionnaire survey:

Design and give out questionnaires to specialists in relevant field and acquire helpful evaluating information.

(3) Transplantation method:

Use the evaluating achievements in other field as a reference and optimize the assessment programs.

(4) Mathematical statistics method:

Adopt analytic hierarchy process (AHP) and shift and range transform method in fuzzy mathematics to dispose of coaches’ assessment metrics qualitatively and quantitatively. To deepen our model, we need take sport event groups, gender and time’s influence into consideration to make our model more universal. We know that the National Collegiate Athletic Association (NCAA) is a nonprofit association of 1,281 institutions, conferences, organizations, and individuals that organizes the athletic programs of many colleges and universities in the United States and Canada [5]. In our paper, because of the large scale and authority of NCAA, we only rank the college coaches based on the data and information we get from NCAA’s database. Eventually, we will present our model’s top 5 coaches in each of 3 different sports and explain our results for sports fans.

2 Classification and characters of sport events

Before determining an appropriate model to look for best American college coach for all possible sports, it is essential for us to classify sport events into several groups. Considering NCAA (National Collegiate Athletic Association) which is authoritative and representative for competitive sports of college level in U.S., we will merely classify sport items of NCAA and research their characters for further college coach assessment.

2.1 Classification of sport events

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Since a valid classification of sports events makes great contributions to researching and understanding the traits and principles of different sport events, the method of classification has been rationalized and improved gradually. Up till now, specialists in the field of sport theory have proposed three major methods [6] to classify based on main factors of competitive ability, movement structure, and appraising method of sport performance which can classify all possible sports from different angles.

As we know, the essence of competitive sports, and the common traits in NCAA competitive sport events are competitiveness which can reflect the difference of sport events and groups apparently. It is more beneficial for revealing the traits and item groups’characters through the view of competition. Therefore, to take above three classification methods and our new discover into account, we adopt a classification method based on the standard of competitive nature and characteristics to systematically analyze sport events and groups in NCAA.

Competitive nature is chosen as the first-order standard to classify, we can sort NCAA’s sport events into two groups: direct competitive event group and indirect competitive event group. Direct competitive event group are composed of sport events with attack-and-defense relationship while indirect competitive event group are composed of sport events without attack-and-defense relationship.

Then competitive characteristics are determined as the second-order classification standard. We can further classify direct competitive event group into four parts: grapple competitive event group, body-contact competitive event group, non-body-contact competitive event group, and net-separated competitive event group. According to the existing sport events in NCAA [7], grapple competitive event group includes 3 sport events: boxing, wrestling, and fencing; body-contact competitive event group includes 7 sport events: football, soccer, basketball, field hockey, ice hockey, lacrosse, and water polo; non-body-contact competitive event group includes 4 sport events: baseball, softball, bowling, and golf; net-separated competitive event group includes 2 sport events: tennis, and volleyball.

Similarly, we can classify indirect competitive event group into two parts: simultaneous competitive event group and consecutive competitive event group. And simultaneous competitive event group includes 4 sport events: outdoor track, indoor track, cross country, and rowing; consecutive competitive event group 5 sport events: outdoor field, indoor field, gymnastics, rifle, and skiing. The classification results of sport events in NCAA are presented as follows: