美国大学生数学建模一等奖31552 - 图文

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Best all time college coach

Abstract

In 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 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 selecting indicators Secondly，Standardized matrix and parameter matrix are combined to construct the weighted standardized decision matrix. Finally, we can get the college men's basketball composite score, namely the order of male basketball coaches, which is shown in Table 7.Adolph Rupp and Mark Few are the last century and this century's \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 century’s coaches and this century’s coaches have significant difference, which demonstrates 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 under 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.

Furthermore, 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 Internet[7], so as to examine 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 article 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; ANOVA

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Contents

Abstract ........................................................................................................... 1 Contents .......................................................................................................... 2 I. Introduction ................................................................................................ 3 П. The Basic Assumption .............................................................................. 4 Ⅲ. Nomenclature ........................................................................................... 5 Ⅳ. Model ........................................................................................................ 5

4.1 Data Processing ................................................................................... 5 4.2 Model analysis .................................................................................... 6 4.3 Model building .................................................................................... 6

4.3.1 Dominant index weights calculation ........................................ 7 4.3.2 Hidden index weights calculation ............................................. 9 4.3.3 Positive and negative ideal solution building ......................... 12 4.3.4 Distance calculation ................................................................ 12 4.3.5 Comprehensive evaluation value ............................................ 13 4.4 Model solution .................................................................................. 13

4.4.1 Dominant index weights calculation ....................................... 13 4.4.2 Hidden factors weights calculation ......................................... 14 4.4.3 Consolidated score .................................................................. 16 4.5 Judgment of significant differences between the last century’s and this century’s coaching score. ................................................................. 16

4.5.1 Preliminary investigation of the last century and the coach of the century standards........................................................................ 16 4.5.2 Further exploration on the influence of different time line horizons on the assessment results ................................................... 18 4.6 Test of model’s applicability to both gender ..................................... 19 4.7 The selection for the top five college coaches of three sports .......... 20 V. Analysis of our Model .............................................................................. 22

5.1 Applications of our models ............................................................... 22 5.2 Strengths ........................................................................................... 22 5.3 Weaknesses ....................................................................................... 22 5.4 Future Improvements ..................................................................... 22 Ⅵ. Conclusions ............................................................................................. 23 Ⅶ.A letter to the sports enthusiasts ............................................................ 23 Ⅷ. References ............................................................................................... 24

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I. Introduction

The paper is to help \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, football, 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 model’s top 5 coaches in each of 3 different sports.

? 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 will understand.

To tackle the first problem, we searched the indicators of Top 600 men’s 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 indicator’s weight by using Entropy method; for those implicit factors, we calculate the weight through experts’ evaluation. The determination of each indicator’s score should be given by experts evaluation of each indicator. These indicators are then numericalized, and the importance of each indicator is determined through weight 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 difference 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 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 found 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, 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.

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Figure1. The source of the best college coaches

П. The Basic Assumption

? Experts recessive factors evaluation criteria 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 this 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).

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Ⅲ. Nomenclature

Variable X

Meaning Index data normalization matrix

j Index weights

wj

?ij

??

Transformed normalized matrix \\

i comprehensive evaluation index values of being evaluated

j Index entropy

j Index Information utility

??

?i

ejj

?

F

F statistic

Ⅳ. Model

4.1 Data Processing

In order to better assess the extent of outstanding coaches, we selected a number of indicators to determine the coach for the \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 poor conversion get a normalized matrix X???xij??m?n ,

x11 X?x1n, i?1,2,m;j?1,2,xm1xmnn ?4?1?

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