For office use only T1 ________________ T2 ________________ T3 ________________ T4 ________________
Team Control Number
29696
For office use only
Problem Chosen
F1 ________________
F2 ________________
F3 ________________
B
F4 ________________
2014 Mathematical Contest in Modeling (MCM) Summary Sheet
College Coaches? Mount Rushmore
Summary
College coaches? exposure is growing these days, as a result of the increase on attention to college sports. In this paper, we build a mathematical model to rank college coaches among either gender across generations in varied sports.
Firstly, we build a factors pool to collect evaluation factors of all sports. By principle component analysis (PCA), we obtain three components used to evaluate the coach?s performance. Then we take American college basketball as an example to build the Coaches Ranking Model (CRM). The first step of CRM is to classify the ranking coaches by Cluster Analysis. Next we compare all coaches with the “idealistic coach” whose factors are the best of factors pool by means of adjusted Cosine Similarity. We hereby obtain the top 5 college basketball coaches in the previous century.
Secondly, we optimize CRM across generations by modified coefficient of coaching difficulty and social influence. The coefficients are calculated by Regression Analysis. Based on the optimized model, we take the impacts of genders into consideration. Modified coefficient in genders is calculated by Analysis of covariance (AVOVA) and Data Whitening. We hereby obtain the optimized CRM.
Thirdly, the optimized model is applied to other sports in the worldwide. As for sports, we figure out an advanced ranking model related to different sports with the update of factors pool. Hence, we obtain the coaches ranking list of football, baseball and softball. As for countries, we obtain a list of top 5 college basketball coaches in China.
Finally, we test the sensitivity and robustness of the coaches ranking model. The test result illustrates the stability and adaptability of the model. Besides, based on the ranking results, we discuss the significance of the relation between ranking state distribution and economy, society, culture development in America. Generally, the prosperity of sports stimulates the development of the region.
Above all, our model is accessible to both genders across generations in varied sports. It can be applied further to other countries and organizations. Therefore, our model has a high degree of adaptability and stability.
Key Words: Adjusted Cosine Similarity, Principle Component Analysis, Data Whitening, Cluster Analysis, CRM
Team # 29696
Page 1 of 42
Model Execution Flow College Coaches Ranking Model
STEP1: Collect evaluation factors of college coaches
STEP2: Results and Conclusion Principle Component Classify 12 factors into 3 Principle components Analysis (PCA) of principle components ranking by importance
Zdata for basketball 1 : coach-ability,
Sensitivity and Robustness
coaches
Z2 : coach-influence-school, Z3 :coach-influence-society.
Z1
? Z 2 ? Z3
STEP3:
Cluster analysis of data STEP4：
Results and Conclusion
Pick out the better groups in 9 for ranking with simplification the latter calculation.
Results and Conclusion
Best coaches ranking Ranking result： by Cosine Similarity
1st:John Wooden 2nd:Geno Auriemma 3rd:Pat Summitt 4th:Dean Smith 5th:Mike Krzyzewski STEP1：
Model Optimization
Process and Approach
Conclusions and Results
Find the relation
1st:John Wooden 2nd:Geno Calculate modification
between generations
Auriemma 3rd:Pat Summitt coefficient of time line
andcoaching
4th:Dean Smith 5th:Mike horizon by linear
difficulty across time
Krzyzewski regression analysis
line horizons.
Conclusions and Results STEP2： Process and Approach Analysis of variance Analyze the significant 1st:John Wooden 2nd:Geno
difference in factors across Auriemma 3rd:Pat Summitt
(ANOVA) of data the gender and modify 4th:Dean Smith 5th:Mike
Krzyzewski data by Data Whitening.
and discussion of
gender differences
Analysis
??
?
?
Factors pool extension
?
Model Extension
??
?
Sports extension: baseball, football, softball.
Countries and organizations extension: China
Further Discussion Upon Model
Discussion upon sports impact on economy, culture, social developments.
美赛：29696---数模英文论文
