U 0.234,0.879,0.738,0.106,0.359,0.296,0.383,0.193,0.291,0.453,0.494,0.248,0.180,0.615,
1.000,0.316,0.151,0.047,0.392,0.052
T
By sorting the value of Ui (i=1,2, ,n), we can obtain the ranking result of Si. And the ranking vector is:
mo.crotha.mww w数
No.1
No.2 S14
No.4 S12
No.5 S9
Dean Smith
Mike Krzyzewski
Adolph Rupp
Bob Knight
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Rank 2 15,2,3,14,11,10,19,7,5,16,6,9,12,1,8,13,17,4,20,18
T
Therefore, we list top five coaches of basketball in the previous century inTable 4:
Table 4: Top 5 Coaches of Football
No.1 S15 Joe Paterno
No.2 S2 Bobby Bowden
No.3 S3 Bear Bryant
No.4 S14 Tom Osborne
No.5 S11 Don James
校
This result is largely agreement with the widely accepted result[12].
3.4.3. Baseball
Searching and selecting data
Like what we do in basketball, we search and select data through the Internet[13][14]. But in this sport, we assume that the number of final fours is the number of champions of NCAA competitions that teams can achieve. And we assume that the number of champions is the number of champions of National competitions that teams can get. Determining the final evaluation index matrix
At first, we determine x’. For x1, due to scarcity of the data, we can only search a little information of several years[9]. We use W(ti)=Num2, where Num represents the total number of competitions of champion in ti.
苑
We can obtain W(3)(t) by simulating and curve fitting of data. So we can get pi for each Si, and then we obtain the vector x1’.
For x2, due to lacking the standard difference of winning-percentage in every ten year, we choose another approach to get x2’. Considering the influence of time, first, we employ extreme difference method to nondimensionalize tm into tm’, where tmi is the middle year of tenure of Si. Then, we define
''tm
'''''
and then we define x2i x2i tmi. So from (3), we obtain x2.
Finally, from (4), we can obtain x*. We list the quantitative value of x*. Obtaining the result via ultimate evaluation vector
Like what we do in Basketball, we can obtain the ultimate evaluation vector:
0.022,0.044,0.232,0.225,0.138,0.118
T
U 0.353,0.278,0.587,0.223,0.205,0.302,0.208,0.189,0.314,0.494,0.203,1.000,0.214,0,
By sorting the value of Ui (i=1,2, ,n), we can obtain the ranking result of Si. And the ranking vector is:
Rank 3 12,3,10,1,9,6,2,17,18,4,13,7,5,11,8,19,20,16,15,14
T
Therefore, we list top five coaches of basketball in the previous century in Table 5:
Table 5: Top 5 Coaches of Baseball
mo.crotha.mww w模数
1'tm 5
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No.1 S15 John Barry
No.2 S2 Mike Martin
No.3 S3 Rod Dedeaux
No.4 S14 Augie Garrido
No.5 S11 Jim Morris
This result is largely agreement with the widely accepted result[15].
3.4.4. Sensitivity analysis
By changing the weight of AHP and GRAP in equation (8), we analyze the changing result of basketball. For example, we define 0.5, 0.5, and the result is listed in Table 6. The coaches who rank top 5 do not change:
Table 6: Top 5 Coaches of Basketball
No.2 S12 Adolph Rupp
No.3 S14 Dean Smith
No.4 S8
Mike Krzyzewski
No.5 S9 Bob Knight
校
S19 S19 S19
No.1
John Wooden
When defined 0.4, 0.6, the result changes, which is listed in Table 7. The coaches who rank top five change:
John Wooden
When defined 0.7, 0.3, the result is listed in Table 8. The coaches who rank top five do not change:
John Wooden
As can be seen from above, when there is a slight change of weights, the result do not change. But with a relatively greater change, weights have an effect on the result.
4. Model
How could one s reputation affect another s? One way is to follow the implication in the saying: You wouldn t mention A and B in the same breath. It means if the difference between two people is too wide, it would be unlikely for most of individuals to mention them in a same talk. The same holds true for the sports coaches. That means, if two coaches are absolutely not on the same level, more likely than not, there will be few reports on these two coaches. On the other hand, if two of them are top coaches, there will be a plethora of reports: such as The Greatest Coaches Ever Basketball Hall of Fame , on the two coaches. Informed by this natural law, we may find an innovative approach to estimate a coach s level of excellence and popularity. The working flow is shown as follows:
mo.crotha.m w数
Table 7: Top 5 Coaches of Basketball
No.3 S14
No.1
No.2 S12
No.4 S7
No.5 S8
Adolph Rupp