2014年美赛数模B题-Finalist

Team Control Number

For office use only For office use only T1 ________________ F1 ________________ T2 ________________ F2 ________________ T3 ________________ F3 ________________

Problem Chosen T4 ________________ F4 ________________ 24270 B

2014 Mathematical Contest in Modeling (MCM) Summary Sheet

Summary

In order to estimate the excellence of different sports coaches and to give a ranking result, two distinct models are developed. The first model is a comprehensive evaluation method. And the second model is a ranking algorithm analogous to the Journal Influence Algorithm. In the first model, we take into account a variety of metrics, and divide them into two

categories: Objective Metrics and Subjective Metrics. In the Objective Metrics, we consider four factors, the number of wins, winning percentage, champions and final fours. All these factors have contributions to the excellence of a coach. We deem that the total number of

games in a year could affect the number of wins, and the unevenness of team quality could

affect the winning percentage. By employing statistical regression method to process collected data, we establish two functions of influence coefficient to eliminate the

discrepancy caused by the two kinds of effect. In the Subjective Metrics: we consider two factors, media popularity and tenure. We employ Fuzzy Analysis Method to quantify these two subjective factors. We further incorporate Analytic Hierarchy Process (AHP) and Gray Relational Analysis Grade Method (GRAP) to determine the weight allocation to different metrics. The final ranking gives a comprehensive result by weighing results returned by these two methods. Using data from Sports Reference and other websites, the rankings in basketball, football and baseball accord with previous media commentaries.

In the second model, we deem that the excellence of a certain coach can be reflected from the media impact over the span of history and that the interactions between two coaches can reflect the disparity of skill level between them. We use search results returned by Google to quantify the impact of one coach on another. Based on the search results, we build a

cross-reference matrix to represent relationships between coaches. In view that the different time periods that two coaches were in may largely affect the interaction between them, and the personal reputation may influence the number of search results, we develop a weight function of two variables to compensate the influence of time and to rule out the redundant information.

In consideration of the similarity between personal influence and journal influence, we refer to the Journal Influence Algorithm introduced by Eigenfactor and establish a new ranking algorithm. The basic idea of the algorithm is subtle: using weight function to modify the cross-reference matrix, and taking into consideration of individual influence, the algorithm gives an evaluation vector to rank different coaches. To test the validity of this algorithm, we apply the algorithm into basketball, football and baseball. The algorithm gives a result that is similar to the result obtained in the first model. The ranking also agrees with

previous media commentaries. Furthermore, by slightly adjusting the coefficients, we can apply the algorithm into various sports.

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“Dream Team” of College Coaches

# Team 24270

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Team # 24270 Page 2 of 26

Contents

1. Introduction ...................................................................................................................... 3

1.1. Restatement of the Problem..................................................................................... 3 1.2. Model Overview ...................................................................................................... 3 2. Assumptions ...................................................................................................................... 3 3. Model Ⅰ ........................................................................................................................... 4

3.1. Additional assumptions ........................................................................................... 4 3.2. Notations ................................................................................................................. 4 3.3. Evaluation System ................................................................................................... 5 3.3.1. The influence of time on the total number of wins ........................................................ 6 3.3.2. The influence of time on the winning-percentage .......................................................... 6 3.3.3. Fuzzy Analysis............................................................................................................... 7 3.3.4. Nondimensionalization process ..................................................................................... 8

3.3.5. Final result ..................................................................................................................... 8

3.4. Solutions to ModelⅠ ............................................................................................ 10 3.4.1. Basketball..................................................................................................................... 10 3.4.2. Football ............................ …… 此处隐藏：11539字，全部文档内容请下载后查看。喜欢就下载吧 ……