美国大学生数学建模一等奖31552.docx

1、美国大学生数学建模一等奖31552Best all time college coachAbstractIn order to select the “best all time college coach” in the last century fairly, We take selecting the best male basketball coach as an example, and establish the TOPSIS sort - Comprehensive Evaluation improved model based on entropy and Analytical

2、 Hierarchy Process. The model mainly analyzed such indicators as winning rate, coaching time, the time of winning the championship, the number of races and the ability to perceive .Firstly ，Analytical Hierarchy Process and Entropy are integratively utilized to determine the index weights of the sele

3、cting indicators Secondly，Standardized matrix and parameter matrix are combined to construct the weighted standardized decision matrix. Finally, we can get the college mens basketball composite score, namely the order of male basketball coaches, which is shown in Table 7.Adolph Rupp and Mark Few are

4、 the last century and this centurys best all time college coach respectively. It is realistic. The rank of college coaches can be clearly determined through this methods.Next, ANOVA shows that the scores of last centurys coaches and this centurys coaches have significant difference, which demonstrat

5、es that time line horizon exerts influence upon the evaluation and gender factor has no significant influence on coaches score. The assessment model, therefore, can be applied to both male and female coaches. Nevertheless, based on this, we have drawn coaches coaching ability distributing diagram un

6、der ideal situation and non-ideal situation according to the data we have found, through which we get that if time line horizon is chosen reasonably, it will not affect the selecting results. In this problem, the time line horizon of the year 2000 will not influence the selecting results. Furthermor

7、e, we put the data of the three types of sports, which have been found by us, into the above Model, and get the top 5 coaches of the three sports, which are illustrated in Table10, Table 11, Table12 and Table13 respectively. These results are compared with the results on the Internet7, so as to exam

8、ine the reasonableness of our results. We choose the sports randomly which undoubtedly shows that our model can be applied in general across both genders and all possible sports. At the same time, it also shows the practicality and effectiveness of our model. Finally, we have prepared a 1-2 page art

9、icle for Sports Illustrated that explains our results and includes a non-technical explanation of our mathematical model that sports fans will understand.Key words: TOPSIS Improved Model; Entropy; Analytical Hierarchy Process; Comprehensive Evaluation Model; ANOVAContentsI. IntroductionThe paper is

10、to help Sports Illustrated to find the “best all time college coach” male or female.We tackle five main problems:Build a mathematical model to choose the best college coach or coaches (past or present) from among either male or female coaches in such sports as college hockey or field hockey, footbal

11、l, baseball or softball, basketball, or soccer, and clearly articulate our metrics for assessment. Does it make a difference which time line horizon that you use in your analysis, i.e., does coaching in 1913 differ from coaching in 2013? Present our models top 5 coaches in each of 3 different sports

12、.Discuss how our model can be applied in general across both genders and all possible sports.In addition to the MCM format and requirements, prepare a 1-2 page article for Sports Illustrated that explains our results and includes a non-technical explanation of our mathematical model that sports fans

13、 will understand.To tackle the first problem, we searched the indicators of Top 600 mens basketball coaches of the American colleges. Take selecting the best male basketball coach as an example: for the explicit factors that affect assessment standards, we calculate each indicators weight by using E

14、ntropy method; for those implicit factors, we calculate the weight through experts evaluation. The determination of each indicators score should be given by experts evaluation of each indicator. These indicators are then numericalized, and the importance of each indicator is determined through weigh

15、t coefficients. Then through the multiplication of the scores of coaches different ability indicator with corresponding weight coefficients, we get the corresponding scores, and the highest score indicates the best choice.For the second question, we first use ANOVA to determine whether significant d

16、ifference exists between the scores of coaches in the last century and this century and the gender factor Significance difference shows that the time line horizon, the gender factor has influence on the assessment, whereas insignificant difference shows no influence. And based on this, we have drawn

17、 coaches coaching ability distributing diagram under ideal situation and non-ideal situation according to the data we have found, which help us further research the influence of time line horizon on the assessment.For question 3 and 4, we put the data of the three types of sports, which have been fo

18、und by us, into the Model , and get the top 5 coaches of the three sports, which are illustrated in Table10, Table 11, Table 12 and Table 13 respectively. These results are compared with the results on the Internet, so as to examine the reasonableness of our results. We choose the sports randomly, w

19、hich undoubtedly shows that our model can be applied in general across both genders and all possible sports. At the same time, it also shows the practicality and effectiveness of our model.Figure1. The source of the best college coaches . The Basic AssumptionExperts recessive factors evaluation crit

20、eria evaluation is fair and equitable.Coaches coaching level will increase with increasing age, but it will decline due to mental declination and the lack of the physical strength.Assessment experts are fully known on college coaches. The evaluation criteria only consider the factors enumerated in t

21、his paper, without considering other factors.The evaluation criteria apply equally to men and women coaches.We used the general data from a reliable website, Website (see Appendix). NomenclatureVariableMeaningIndex data normalization matrix Index weightsTransformed normalized matrixPositive ideal so

22、lutionNegative ideal solutioni comprehensive evaluation index values of being evaluated Index entropy Index Information utilityF statistic. Model4.1 Data Processing In order to better assess the extent of outstanding coaches, we selected a number of indicators to determine the coach for the best all

23、 time college sports coach. We found information on the various indicators of data on the site and get some reliable indicators data of these college coaches. Due to the dimensions of each index inconsistencies exist, so we transformed the data to eliminate the effects of dimensionless. And through

24、poor conversion get a normalized matrix , , , is a dimensionless quantity and, .4.2 Model analysisIn order to address the problems mentioned above and provide a valid, feasible assessment strategy for Sports Illustrated, we decide to select softball, basketball and football by reviewing the relevant

25、 literature. Coaching time, Competition winning rate, Cultural qualities, Athletic ability, Social skills, Ability to withstand, Innovation capacity, Ability to perceive, and so on, which are evaluation indexes. These evaluation indexes are divided into dominant factors and recessive factors. Specif

26、ic factors of affecting the evaluation criteria are shown in Figure X. These indicators will be quantified and determine the degree of importance of each index by weight coefficient. When selecting coaches, the scores of the indicators multiply corresponding weight coefficient, getting corresponding

27、 scores, and the person with the highest score is the best candidate.Multi-level analysis method to determine the weight is more subjective. It is suitable to determine the weights for hidden factors, which are not used widely in both sexes and all possible requirements for sport. We need to build a

28、 more reasonable model to determine the weight for the dominant factor and recessive factors. Finally, we determine the “best all time college coach”.4.3 Model buildingWe look for the “best all time college coach” by establishing a mathematical model in Technique for Order Preference by Similarity t

29、o Ideal Solution. Take choosing the best college coach or coaches from among male coaches in such sports as basketball as an example. For the dominant factor, we calculate the weight of each indicator in Entropy Method; For the hidden factors, we calculate the weight of each indicator in expert asse

30、ssment method. According to the situation of the coaches , the scores of all levels should be determined by experts, and these indicators should be quantified. Weighting coefficients represent the importance of each indicator. The scores of the indicators multiply corresponding weight coefficient to

31、 obtain the total score, and the person of highest score is the best candidate. This method is more objective, comprehensive, accurate and wide-applicable than the previous evaluation model. Flow chart of looking for the “best all time college coach” is shown in Figure 2.Figure 2. Flow chart of Mode

32、lTOPSIS Model (Technique for Order Preference by Similarity to an Ideal Solution ) was firstly introduced by C.L.Hwang and K.Yoon in 1981.TOPSIS Model is based on the proximity of a limited number of evaluation objects and idealistic goals and evaluate the relative merits of existing objects. Meanwhile, TOPSIS Model is an approximation of the ideal solution in order model, the model requires only a monotonically increasing (or decreasing) of each Utility function. Furthermore, TOPSI