2014年美国大学生数学建模比赛获奖论文-F奖(2)

4. Model ......................................................................................................................... 13 

4.1. Additional assumptions ......................................................................................... 14 4.2. Notations ............................................................................................................... 14 4.3. The Individual Influence Vector............................................................................ 14 4.3.1. Original data ................................................................................................................. 15 4.3.2. The influence coefficient of time ................................................................................. 15 4.3.3. The influence coefficient of reputation ........................................................................ 16 4.3.3. The individual influence vector ................................................................................... 16 4.4. The Cross-Reference Matrix ................................................................................. 16 4.4.1. The weight function ..................................................................................................... 17 4.4.2. The final cross-reference matrix .................................................................................. 17 4.5. The Evaluation Vector ........................................................................................... 18 4.6. Solutions to Model II ............................................................................................. 18 4.6.1. Basketball ..................................................................................................................... 18 4.6.2. Football ........................................................................................................................ 19 4.6.3. Baseball ........................................................................................................................ 19 4.6.4. Sensitivity analysis ....................................................................................................... 19 

5. Applicability .................................................................................................................... 20 6. Strengths and Limitations ............................................................................................. 21 

6.1. ModelⅠ ................................................................................................................. 21 6.2. Model II ................................................................................................................. 21 7. Conclusions ..................................................................................................................... 21 8. The Article for Sports Illustrated ................................................................................... 22 References .............................................................................................................................. 23 Appendix ................................................................................................................................ 24

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Team # 24270 Page 3 of 26

1. Introduction

1.1. Restatement of the Problem

Sports, by definition, is all forms of usually competitive physical activity which aim to use

physical ability while providing entertainment to participants and spectators[1]. No wonder the word sports gives us a first impression of fierce competition, agitated spectators, sweating on the running track, combined with a joy of victory. It is the uncertainty that makes the sports game so intriguing. However, where there is competition, there will always be victory, defeat, and ranking. Loyal sport fans could debate day and night over the question who is the best player or coach. These debates have called forth a need for certain criterion of sports coaches and players. The criterion has to be: (1) all-encompassing to take into consideration a variety of factors; (2) applicable to various sports; (3) robust enough to remain unaffected by fluctuation.

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1.2. Model Overview

Model

The evaluation method in ModelⅠis based on a comprehensive method sophistically combining Analytic Hierarchy Process(AHP) and Gray Relational Analysis Grade Method(GRAP). In the evaluation process, we take into consideration the influence of time horizon, and incorporate Fuzzy Analysis Method, which make it feasible to compare diverse factors on the same level. The ranking results in three different sports accord with previous media report, which attest the validity of this method. Model

In model II, we assume that the excellence of a certain coach can be reflected from the media impact over the span of history and thus can be gauged by the impact on another coach within or without the same period of time. We use Google search results to quantify the impact of one coach on another. The relationship between coaches can be established as a cross-reference matrix. By further taking into account the influence of time, influence of reputation, and a modification to rule out the redundant information, we obtain a final evaluation vector. The final ranking result is roughly approximate to the result in model I. To sum up, we only need the search results returned by Google search engine to estimate the excellence of certain coach with high accuracy.

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