Dean Smith
Hank Iba
Mike Krzyzewski
Table 8: Top 5 Coaches of Basketball
No.3 S12
No.1 No.2 S14
No.4 S8
No.5 S9
Dean Smith Adolph Rupp Mike KrzyzewskiBob Knight
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校苑
Figure 5: Flow chart of model II
4.1. Additional assumptions
The excellence of a coach and association between two coaches can be accurately
reflected by the mass media.
The attention that the mass media have on certain coach is related to the search results on
Google, in terms of number of pages, report orientation and report time.
The media attention is related to time and the excellence of certain coach. The influence
of time and excellence on the media attention remains unchanged to different kinds of people.
4.2. Notations
Notations
k, b u ICT ICR l Z WF W α, β
4.3. The Individual Influence Vector
By our hypotheses, the excellence of a coach can be accurately reflected by the mass media. There are several ways to evaluate the media attention on a celebrity. One of the most simple and direct way is to record the number of search results on Google. However, the search results can be influenced by a variety of factors, such as time periods, tenure, etc. By simulating and curve fitting of sorted data, we evaluate the impact of such factors separately. Finally, we obtain a normalized individual influence vector.
mo.crotha.m w模数
Table 9: Notations and Descriptions
Descriptions
The number of search results of coach i
Coefficient of the function through linear regression Characteristic year of coach i
The number of search results about sports career Influence coefficient of time
Influence coefficient of reputation Individual influence vector Original cross-reference matrix Weight function
Weighted cross-reference matrix Partial coefficient
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4.3.1. Original data
Here we define ti as the characteristic year, the average of the year that the coach i start coaching and the year of his or her retirement. (If the coach i is still active, then t is the average of the year that the coach i start coaching and this year, that is, 2014)
The search results vector a is the original data we use to estimate the individual influence, where ai is the number of search results of coach i. Particularly, the coaches here are sorted by characteristic year in a descend order. This can be a great convenience to our later discussion about time factor.
4.3.2. The influence coefficient of time
According to the growth law of web information[16], the information aiming at a certain field is similar to an exponent increase. To test this hypothesis and better apply it to sports, we entered the Google website. Using 1910 basketball , 1920 basketball ，and 1930 basketball as the exact keywords [17] respectively. The numbers of search results are shown in Table 10:
Table 10: The Numbers of Search Results
1940
1950
1960
1970
1980
16200
26400
40200
25800
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苑
Year
Results 2750 5160
Assuming that this is an exponential function: y1 c edt. We use the least squared method to obtain the unknown numbers in the function. See Figure 6.
The result gives a satisfying simulation to the numbers of search results. However, the distinction between 2000s and 1900s is too large. In our observation, the search results of coaches at different period of time is almost of the same magnitude of as each other. So, here we use the natural logarithm of the search results. Again we obtain a linear function y2 as showed in Figure 7.
The difference between maximum and minimum is about half of the minimum value. This is a modest value that we can safely put into use to estimate ICT. Common sense told us that the greater number of total reports is, the more valuable the search result is, the greater weight the search result will get. So, we define ICT as
mo.crotha
.mww w数
1910 1920
1930
1990
2000
2010
7440 11700
27000 67700 326000
Figure 6: Trend of exponential function y1 Figure 7: Trend of linear function y2
ICTi(influence coefficient of time)=
1
i 1,2, ,n kti b
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Team # 24270 Page 16 of 26 where k and b are the unknown variables related to searching data.
4.3.3. The influence coefficient of reputation
As mentioned in the overview, by searching data with different methods and using diverse keywords, we observe that on the track of fame, the media will turn at first to the achievements of sports one has then to the other aspects in his or her life. Therefore, the media attention can be interpreted and quantified by using the overall search results of one coach and his or her triumph and achievement.