1、Team#28414 Page 1 of 33 Evaluation System for College Coaching Legends Summary In order to evaluate the performance of a coach,we describe metrics in five aspects:#historical record,game gold content,playoff performance,honors and contribution to the sports.Moreover,each aspect is subdivided into se
2、veral secondary metrics.Take playoff performance as example,we collect postseason result（Sweet Sixteen,Final Four,etc.）per year from NCAA official website,Wikimedia and so on.First,Analytic Hierarchy Process（AHP）Model is established to determine the weight of each metric to coaches evaluation grade.
3、All metrics are adequately filled into the three-hierarchy structure,and then we obtain the metric weight based on which evaluation grade is calculated.Second,Fuzzy Synthetic Evaluation（FSE）is built to overcome weakness of excess subjective factors in AHP.This model takes data processing by membersh
4、ip function to generate fuzzy matrix.After that,entropy method and linear weighted method are applied to obtain evaluation grade.To evaluate the accuracy of the two models,hit score is defined.It is supposed to reflect the difference between our results and standard rankings from several authorities
5、 such as ESPN and Sporting News.Take NCAA basketball as a case study,AHP receives 78.77 hit score while FSE gets 81.81,which indicates that FSE performs better than AHP.Afterwards,Aggregation Model（AM）can be developed by combining the two models based on hit score.The top 5 college basketball coache
6、s,in turn,are John Wooden,Mike Krzyzewski,Adolph Rupp,Dean Smith and Bob Knight.Time line horizon does make a difference.According to turning points in NCAA history,we divide the previous century into six periods with different time weights which lead to the change of ranking.We apply our model into
7、 college womens basketball only to find that genders do not matter.Model proves to be efficient in other sports.The ranking of college football is:#Bear Bryant,Knute Rockne,Tom Osborne,Joe Paterno,Bobby Bowden,and the top 5 coaches in college hockey are Bob Johnson,Red Berenson,Jack Parker,Jerry Yor
8、k,Ron Mason.We conduct sensitivity analysis on FSE to find best membership function and calculation rule.Sensitivity analysis on aggregation weight is also performed.It proves AM performs better than single model.As a creative use,top 3 presidents（U.S.）are picked out:#Abraham Lincoln,George Washingt
9、on,Franklin D.Roosevelt.At last,the strength and weakness of our mode are discussed,non-technical explanation is presented and the future work is pointed as well.Team#28414 Page 2 of 33 I.Introduction.3 1.1 Problem Background.3 1.2 Previous Research.3 1.3 Our Work.3 II.Symbols,Definitions and Assump
10、tions.4 2.1 Symbols and Definitions.4 2.2 General Assumptions.5 III.Articulate our metrics.5 3.1 Specify evaluation norms.5 3.2 Collect data.8 3.3 Preprocess data.9 IV.Two models for coach ranking.10 4.1 Model I:#Analytic Hierarchy Process（AHP）.10 4.1.1 The three-hierarchy structure.10 4.1.2 Obtain
11、the index weight.10 4.1.3 Results&#analysis.11 4.2 Model II:#Fuzzy Synthetic Evaluation（FSE）.12 4.2.1 Quantify grades in the five aspects.12 4.2.2 Determine membership functions.13 4.2.3 Determine the weights using entropy method.14 4.2.4 Results&#analysis.15 V.Models Combination.15 5.1 Evaluation o
12、f individual model.15 5.2 Aggregation Model.17 5.3 Results&#analysis.17 VI.Extend Our Models.18 6.1 Genders do not matter.18 6.2 Time factor does make a difference.19 6.2.1 Why time factor matters?#.19 6.2.2 How time factor matters?#.19 6.2.3 What is the variation tendency?#.23 6.3 Model also works
13、in other sports.23 VII.Further discussion.25 7.1 Sensitive Analysis on FSE.25 7.1.1 Vary Membership function.25 7.1.2 Vary calculation rule.27 7.2 Sensitive Analysis on Aggregation weight.28 7.3 Explore:#Evaluating Best President.29 VIII.Strength and Weakness.30 IX.Non-technical Explanation.30 X.Fut
14、ure work.32 XI.References.32 Team#28414 Page 3 of 33 I.Introduction 1.1 Problem Background Sports Illustrated is an American sports media franchise owned by media conglomerate Time Warner 1.This magazine is looking for the“best all time college coach”male or female for the previous century.The best
15、college coach or coaches can be from among either male or female coaches in different fields,such as college hockey or field hockey,football,baseball or softball,basketball,or soccer.We face mainly four problems:#Articulate our own metrics and build a mathematical model;#Set up the evaluation system
16、 for the performance of the model.Discuss how our model can be applied with time factor or across both genders and all possible sports;#Analyze the influences of the parameters,then discuss whether your model could be applied into wide fields.1.2 Previous Research Some magazines or websites that focus mainly on college sports have ranked the top college coaches of different sports.For example, has made a basket-ball power rankings 2 which shows the top 25 coaches of college basketball.Considering the best coll
