1、杰出教练员评定研究Abstract：In this paper， I propose three mathematical models to study coaches clustering， ranking of coaches in the same cluster， and the quantification of time line. Then I tackle two sub-problems， coach evaluation without the factor of time line， coach evaluation considering the influence
2、of time line， the extension of our model for all genders and sports. Problem one deals with coach evaluation without the factor of time line. I select four time-independent metrics， namely， coaching time， winning percentage， total coaching sessions， and championships. I can divide the coaches into t
3、hree groups using k-means methods. Through comparison of the centroid in each group， I determine the coaching level. I score the first-class coaches by using analytical hierarchy process （AHP）. Since coaches of the same group have common characteristics， I strengthen three parameters to determine th
4、e criteria layer， and construct a comparison matrix. Then I obtain the weight of the evaluation metrics， and rank the coaches. Finally I get a list of “the outstanding coach in the 20th century”. Problem two takes time line into consideration. I build a regression model to quantify the growth of the
5、 teams participated， and get a simplified indicator of competitive level. Through analyzing the four strengthened parameters， I get a more scientific ranking of coaches. 一、Problem （一）Clustering Model I extract the date of the coaching time， winning percentage， total number of coaching sessions and c
6、hampionships by the obtained coaches data， which is used to form a primary database. This database will be classified according to the similarity of the data， that is to say， the closer two objects are， the higher similarity two objects have. Hence， they two should belong to the same class. （二）Analy
7、tic Hierarchy Process （AHP） Through clustering model， I select 4 classification parameters， which are coaching time， winning rate， total coaching sessions， and championships and I divide the coaches into 3 levels. According to the assumptions， “the outstanding coaches” are classified in the first-cl
8、ass group. （三）Construct pairwise comparison matrixes Hierarchy reflects the relationship between the factors， but weight for different criteria in the process is not necessarily the same， as different decision makers have their own metrics. Firstly， I need to compare three factors for the impact of
9、an outstanding coach. I compare two factors and each time， and select to represent the intensity of the impact. The interpretations are given in Figure.1. Figure.1 二、 Problem （一）Effect of the time line The impact of the time line is a very broad vague concept， because the time factor is affecting ma
10、ny aspects of modeling， such as competition rules， the intensity of the game， the technology content， different competitive level at different periods and etc. I try to adopt the principle of a simplified model， that is， only one of the factors mentioned above will be taken into account in model con
11、struction. （二）Improved Analytic Hierarchy Process Since I took time line factor into account， I need to modify the AHP judgment matrix. According to the new judgment matrix， I can get a new weight vector. The new weight vector is shown in Figure.2 Figure.2 Weight1 Weight2 Weight3 Weight4 0.0921 0.44
12、52 0.2606 0.2021 Similarly， I get a matrix according to the score of each coach. Then I find the top 5 outstanding coaches. （三）Conclusion According to the reference， my model picks up 4 of the top 5 basketball coaches in the United Stated. They are Mike Krzyzewski， Dean Smith， Jim Calboun and Jim Bo
13、eheim.3 of the top 5 football coaches are in my list. They are Joe Paterno， Bobby Bryant and Mack Brown. All of above shows that the model has good accuracy. 三、Question The impact of genders The description of difference in genders in the requirement isnt clear. So I decide to discuss this question
14、in two aspects， one considering the gender of coaches， the other considering the gender of team players. In the first case， I consider the gender of coaches only， that is， the gender of team player should be the same， so I can select the gender of coaches as a criterion in the AHP. Secondly， differe
15、nt types of competitions differ in the competition rules， competitive level. In the second case， the only factor I consider is the gender of the team players. The evaluation is together with the male teams coaches and the female teams coaches， Ithink that the distribution of the weight should be conclude according the nature of the game. If this game is beneficial for women， I should increase the weight of the female teams coach.
