美赛论文

The Best College Coach or the Frivolous Century

Abstract:

In order to evaluate the best college coach or coaches, we describe metrics in five categories: years (experience), wins, winning percentage, champions, awards. In the incomplete induction model, we use the Analytic hierarchy process method to evaluate the significance of each metric. We construct three mathematic models.

Firstly, in model 1, we construct the positive reciprocal matrix by using AHP. Feature vectors are calculated by using mathematical software as the weight index.

Secondly, in model 2, we recognize that some greatest college coaches not ranked in the top 5, so we revise the model 1. The time line horizon was considered, we were grouped according to the time for the college coach, 20-30, 30-40, 40-50, more than 50. The formula: Wi/Ye is an indicator, each team to get a best college coach.

Finally, in model 3, we construct a Fraction System method. We only think about winning or losing the game. To answer this question we created a formula: three points for each win, negative two points for each loss, and one point for each tie. The highest score of the top 5 were being founded.

From the above three models, for example, the best college coach of the college football is below: John Gagliardi，Larry Kehres Bear Bryant，Bobby Bowden，Tom Osborne.

We also analyze the strengths and weaknesses of each model.

Key words: Analytic hierarchy process Fraction System

Mathematic software Positive reciprocal matrix Time line horizon

Team # 31905 Page 2 of 25

I. Introduction

In order to evaluate the best college coach, the following background is worth mentioning.

Sports Illustrated, a magazine for sports enthusiasts, is looking for the “best all time college coach” male or female for the previous century. 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. Does it make a difference which time line horizon that you use in your analysis, i.e., does coaching in 1913 differs from coaching in 2013? Clearly articulate your metrics for assessment. Discuss how your model can be applied in general across both genders and all possible sports. Present your models top 5 coaches.

The National Collegiate Athletic Association (NCAA) is a nonprofit association of 1,281 institutions, conferences, organizations, and individuals that organizes the athletic programs of many colleges and universities in the United States and Canada. It is headquartered in Indianapolis, Indiana. [1]

We choose the college football, college basketball, college hockey as the object of study. Firstly, we discuss the college football in model 1 by using the Analytic hierarchy process method. Secondly, we revise the model 1 the positive reciprocal matrix was be reset. The time line horizon was be thinking about. We were grouped according to the time for the college coach, 20-30, 30-40, 40-50, more than 50. The formula: Wi/Ye is an indicator, each team to get a best college coach. Finally, in model 3, we construct a Fraction System method. We only think about winning or losing the game. To answer this question we created a formula: 3 points for each win, -2 for each loss, 1 point for each tie. The highest score of the top 5 were founded.

Team # 31905 Page 3 of 25

II. Description and Analysis 2.1 Assumptions

1. Basic assumptions seek data sets and all awards and personal information

exactly.

2. Assuming that the selected three kinds of ball games can represent in any

kind of ball games.

3. The game is fair, all the teams there is no cheating.

4. Assuming the main influence factors of the best coach selection is the

consideration of the model, the other is neglected.

5. Assuming that the analytic hierarchy process indicators of quantitative

value is on the basis of extensive expert consultation and public investigation.

6. Assuming that the evaluation of model index listed, each coach has no objection, indicators can reflect their level.

2.2 Evaluation criteria

Because the selection of the best college coach activities have social evaluation of concrete examples, therefore we should always adhere to the evaluation activities in the process of evaluation of sociality, stick to the main sociality, adhere to the object of social evaluation.

2.3 The principle of evaluation index selection

Outstanding university coaches’ evaluation activity is a particular case of social evaluation; therefore, in the process of the construction of the evaluation index system, we should insist the principle of social evaluation. Considered

Team # 31905 Page 4 of 25

with the main several factors, the basic principles of social evaluation activity index selection are: comprehensive principle, index mutual independence principle, and the combination of quality and quantity.

2.3.1 Principle

The comprehensive evaluation index system principles refer to: evaluation index must fully reflect the objective relationship between the evaluation object and evaluation of subject from the multi-level and multi angle. We observe the college coach’s date of coaching years, winning numbers, winning rate, winning awards and the title of outstanding coaches by searching information.

2.3.2 Mutual independence and the principle of consistency

The evaluation index system should possess consistency principle about low and up levels indicators. The same index should not repeat between indicators, no causal relationship, no contradiction in logic confusion, in order to ensure the scientific and fair evaluation index system.

2.3.3 The combination of qualitative and quantitative

The evaluation index should be quantitative as far as possible. When comes to the difficult evaluation index we should take the method of numerical transformation which is on the basis of the qualitative description, so that the evaluation can obtain definite conclusion through the actual observation and measurement.

2.4 Flow chart of problem solving