1、 For office use only T1 _ T2 _ T3 _ T4 _ Team Control Number 26443 Problem Chosen B For office use only F1 _ F2 _ F3 _ F4 _ 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 cal

2、culation 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

3、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 perf

4、ormance assessments objectivity, simulative matches possibility and trainings 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

5、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 transfor

6、m 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 Inventor

7、y (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 ind

8、ex. 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 t

9、he 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, D

10、ean 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 g

11、ender factor competitive factor Team#26443 page 1 of 26 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 o

12、f sport performance assessments objectivity . 6 2.2.3 Characteristics of simulative matches possibility . 6 2.2.4 Characteristics of trainings 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

13、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 considerin

14、g 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

15、and evaluation . 22 4.1 Conclusions . 22 4.2 Evaluation . 23 5 Reference . 23 6 Special report . 25 Team#26443 page 2 of 26 1 Introduction Jack Welch, former chairman and CEO of General Electric, has ever said, “The best leader is coach”. An appropriate coach assessment system plays an essential rol

16、e 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 ones eye is quite different, we should deter

17、mine rational and justice assessment metrics while discussing all possible sports, both genders and times 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-c

18、ompetency 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 couldnt be the exclusive standard to access a coach and we should pay more attention to his con

19、tributions to players and sport development 2. In 2004, Li Yong adopted research method of literature, Delphi method and analytic hierarchy process (AHP) 3to assess coaches objectively, reasonably and comprehensively which we can learn from. In 2006, Zhang Xinzhong introduced the Coaching Behavior A

20、ssessment 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 c

21、omprehensive 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. Synth

22、esizing previous assessment metrics, on the one hand, we know that we cannot evaluate coach only by his external conditions such as teams sport performance, numbers of championships or educational background, we should also take his potential and deep traits and characteristics into account. On the

23、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 ob

24、jective 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: Team#26443 page 3 of 26 (1) Research method of literature: (a) Study theories of coaches competency in the lite

25、rature 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

26、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 quantitative

27、ly. To deepen our model, we need take sport event groups, gender and times 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 tha

28、t 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 NCAAs database. Eventually, we will present our models

29、 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

30、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 e

31、vents Team#26443 page 4 of 26 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

32、 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 tr

33、aits 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 n

34、ew 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 NCAAs sport events into two groups:

35、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 charact

36、eristics 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. Acc

37、ording 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 com

38、petitive 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

39、 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 even

40、ts in NCAA are presented as follows: Team#26443 page 5 of 26 Table 1 Classification of sport events in NCAA Competitive nature Competitive characteristic Sport events Direct Grapple boxing, wrestling, fencing Body-contact football, soccer, basketball, field hockey, ice hockey, lacrosse water polo No

41、n-body-contact baseball, softball, bowling, golf Net-separated Tennis, volleyball Indirect Simultaneous outdoor track, indoor track, cross country, rowing Consecutive outdoor field, indoor field, gymnastics, rifle, skiing 2.2 Characteristics of different sport events After an appropriate classificat

42、ion, we will research and analyze the characteristics of different competitive event groups so that we can determine reasonable evaluation indexes for coach assessment. We study different competitive event groups from four characteristics: operational requirement, objectivity of sport performance as

43、sessment, possibility of simulative matches and difficulty of training 8. 2.2.1 Characteristics of operational requirement According to the classification of sport events in NCAA, the degrees of competitive confrontation of different event groups make great difference and the ranking from highest to

44、 lowest is: grapple, body-contact, non-body-contact, net-separated, simultaneous, and consecutive competitive event group. Differences in degree of competitive confrontation will contribute to differences in anti- interference requirements of skilled movement and it has a positive correlation betwee

45、n each other, i.e., a higher degree of competitive confrontation is accompanied with a higher anti-interference requirements of skilled movement. And operational requirement of sport event bear a relationship to degree of competitive confrontation, anti-interference requirements of skilled movement

46、and number of a teams members. The eventual evaluation standards of operational requirement in different competition event groups are expressed as follows: Team#26443 page 6 of 26 Table 2 Operational requirement characteristics of different event groups Event groups Degree of competitive confrontati

47、on Anti-interference requirements of skilled movement Operational requirement Grapple Body-contact Non-body- contact Net-separated Simultaneous Consecutive Note: morerepresents higher operational requirement. 2.2.2 Characteristics of sport performance assessments objectivity The appraising methods o

48、f sport performance about different competitive event groups are quite different from each other, which cause significant differences of sport performance assessments objectivity. And controllability of matches is related to objectivity of sport performance assessment. The less the objectivity of sp

49、ort performance assessment is, the less the controllability of matches is. Table 3 Sport performance assessments objectivity of different event groups Competitive nature Competitive characteristic Objectivity of sport performance assessment Direct Grapple Body-contact Non-body-contact Net-separated

50、Indirect Simultaneous Consecutive Score Measure Note: morerepresents greater objectivity of sport performance assessment. 2.2.3 Characteristics of simulative matches possibility One of effective and efficient methods to improve sport performance is to conduct abundant training and practice including

51、 simulative matches. Different event groups have different possibility of simulative matches. The direct competitive event groups are relevant to attack-and-defense relationship. The skill and tactics can improved accessibly, and players as well as coaches can achieve practical experience under the

52、background of simulative matches with attack-and-defense relationship. Thus, such Team#26443 page 7 of 26 competitive event groups have more requirements and less possibility in simulative- match training. Furthermore, possibility of simulative matches is related to gender and the concrete results are as follows: Table 4 Simulative matches possibility of different event groups Competitive nature Competitive characteristic Possibility of simulative matches Whole Men Women Direct Grapple Body-contact Non-b