2.1

Determination of the major indexes of coaches and their weights

In general, the team’s performance and work experience of coaches are the objective reflections of the comprehensive ability of the coaches. Therefore, according to the available data, the W-L% (Win-Loss Percentage), NC (Number of NCAA tournament championships won), FF (Number of NCAA Final Four appearance), NCAA (Number of NCAA tournament appearance), CTRN (Number of conference tournament championships won), CRGE (Number of regular season conference championships won), and Yrs (Teaching years) are selected as the major indexes of coaches in the sport of basketball; W-L% (Win-Loss Percentage), W-L% of Bowl (Win-Loss Percentage of Bowl), Bowl, G (Total coaching session) and Yrs (Teaching years) are selected as the major indexes of coaches in the sport of football; the W-L% (Win-Loss Percentage), G (Total coaching session)and Yrs (Teaching years) are selected as the major indexes of coaches in the sport of softball.

After determination of the major indexes of coaches in each of 3 different sports (basketball, football and softball), their weights w_p can be determined. In each sport, the major indexes have different levels of importance. For example, in the sport of basketball, it has the following orders

So the weights of the major indexes of coaches in each of 3 different sports are determined by AHP. The rule is defined as follows:

If Level (A) > Level (B), then the result counts as 1; If Level (A) < Level (B), then the result counts as 0; And if Level (A) = Level (B), then the result counts as 0.5.

Therefore, the weights of the major indexes of coaches in each of 3 different sports can be determined and showed in

Table 1, 2, and 3, respectively. In which,

It can be seen that the weight (W-L%) is maximum, and weight (Yrs) is minimum, which indicates that W-L% (Win-Loss Percentage) is the most important index of coaches in each of 3 different sports.

Table 1.

Weights of the each major index of coaches in the sport of basketball.

Table 2.

Weights of the each major index of coaches in the sport of football.

Table 3.

Weights of the each major index of coaches in the sport of softball.

2.2

Normalization of data of the major indexes

In order to be convenient for data processing in programming, it should be normalized the data of the major indexes. In some type of sport, let S be the number of coaches, i = 1,2,…,S ; N be the number of major indexes of coaches, p = 1,2,…,N . S dimensional vector G_p is defined as follows

Each element in G_p is normalized by the Equation

Where G_pmax is the maximum element in vector G_p , and G_pmin is the minimum element in vector G_p S dimensional vector R_p is defined as follows

Now the normalized vector R_p corresponding to vector G_p is obtained.

2.3

Establishment of the model to evaluate the comprehensive ability of the coaches

Based on 2.1 and 2.2, the scores Q_i corresponding to the comprehensive ability of the coaches in each of 3 different sports are obtained by making the weighted summation as follows

Where w_p is the weight of the p-th major index of coaches in each of 3 different sports.

From Equation (4), S dimensional vector Q is defined as follows

From Equation (5), the 5 maximum Q_i can be found out. So the top 5 coaches in each of 3 different sports based on the model can be determined.

2.4

Statistical results and analysis

According to the MATLAB programming, the scatter diagrams of the scores Q_i corresponding to the comprehensive ability of the coaches in each of 3 different sports are obtained, as shown in Figures 1-3. And the top 5 coaches in each of 3 different sports based on the model are shown in Tables 4-6.

Figure 1.

Scatter diagram of the scores Q_i corresponding to the comprehensive ability of the coaches in the sport of basketball.

Figure 2.

Scatter diagram of the scores Q_i corresponding to the comprehensive ability of the coaches in the sport of football.

Figure 3.

Scatter diagram of the scores Q_i corresponding to the comprehensive ability of the coaches in the sport of softball.

Table 4.

The top 5 coaches in the sport of basketball based on the model.

Table 5.

The top 5 coaches in the sport of football based on the model.

Table 6.

The top 5 coaches in the sport of softball based on the model.

From Figure 1 and Table 4, the share of excellent basketball coaches is much smaller, and the scores Q_i of the best basketball coaches are much greater than the average 0.1917. The results of football and softball coaches are similar to those of basketball coaches. From Tables 4-6, it can be seen that the most of the top 5 college coaches in each of 3 different sports are well known to all, which verified the validity of the model to some extent.