The evaluation of coaches in college ball game is very essential, since a better choice of coaches will help get more scores for a team. In this paper, a simple, however, comprehensive model is proposed to evaluate college coaches of a century. By comparing the compressive index of different coaches in the evaluation, the top five coaches are found with their influence over time discussed either. Based on data of certain sport, a basic model is introduced. The superimposed application of the model makes it possible for the data of different levels to deliver proper evaluation. And by optimizing the data, we can provide precise evaluation items and authentic synthetic scores for each coach. Among their applications, the models of various sports are obtained in which relatively accurate results are still available. Although a number of deficiencies were disclosed by multiple expansions, this model is still simple, accurate, and valuable to select the best coaches.
Volumes have explored the success of the sport teams or the related competitive pattern based on simple data analysis and statistics [
As an important member of the sports team, coaches played a role of selecting outstanding athletes and drawing up the whole plans for their training [
Firstly, we determine the basic model as the basis of our work. After the analysis upon the subject, we find that this can be evaluated by different indexes—qualitative and quantitative [
After that, we define, screen out, and classify the specific conditions for the evaluation. In practice, we build a submodel firstly to test the influence of gender and time axis which are both not clear yet. During our test on time axis, we screen out secondary index to build statistics model which shows the relationship between times and team intuitively. This model also gives us a clear vision of the changing of American basketball competence. It is easy to find that coaches who work in an environment of higher competence tend to have higher professional level. At the meantime, we select index sharing the same level with time to finish the whole analysis hierarchy process.
Finally, we use our model to do the appraisal of the ten greatest CBC and more persuasive top five in them after more indexes being added in the model. With the existing data, this model can be applied to different sports to select the greatest coaches in different fields. However, the comparison between results of the model and common sense can help us find that the results do not seem to be so accurate which means more analysis is needed to contribute to the optimization.
The goal of our team is quite clear which is to look for “the best of all time college coach” of both male and female for the previous century. This paper introduces a quantifying model with factors that have already been precisely classified. The model can be used to evaluate coaches on their excellence directly. It contains impersonal data such as time, winning rate, and game award and, at the meantime, personal factors such as experiment experience which works in importance classification process.
Figure
General graph model.
Other factors such as individual personalities do not influence our results [
The assuming ranking of the factors is accurate while creating and using the model [
In this part, we consider as many as possible direct factors that influence coaches’ professional level and career awards, among which choose four as key indexes, which are coaching career length, winning rate, individual award, and team award [
Winning rate refers to the ratio between NACC team quantity in middle year of objective’s career [
Moreover, we can achieve the comparability between each decisive factor by quantizing and sequencing the importance of indexes of the same class. The model we introduced adds more persuasion to index of high level with integrative use of indexes of lower level and reference to objective law. In this way, we fully utilize the existing data and optimize high level index to make our model closer to reality.
First we assign different letters to the variables in favor of the later modeling (Table
Variable definitions mentioned in model 1.
Items | Characters |
---|---|
Year |
|
Team quantity |
|
Average team quantity in near a century |
|
Participation times in middle year of coach’s career |
|
Winning rate |
|
By searching quantity of NCAA participating teams of different years and conducting simple regression analysis, we get the curve graph in Figure
Coefficients in Figure
Unstandardized Coefficients | Standardized Coefficients | ||||
---|---|---|---|---|---|
|
Std. Error | Beta |
|
Sig. | |
(Constant) | −3729.584 | 116.622 | 0.954 | −31.980 | 0.000 |
Curve of year and teams (basketball).
We can find from this graph that quantity of participating teams first experiences a fast rising section and then gradually decreases:
Then we compute and find the fitting formula of participating teams, in which 2.015 is regression coefficient and other factors that influence
After this, we optimize the winning rate, one of the indexes, by using relation between teams. It is easy to understand that competence of each team ascends with the participating team and so is level to win. With the data of winning rate of related team as reference and the optimization, now we can give better evaluation to coach.
We assume the winning rate after optimization is (model 1)
Relevant data in optimization.
Attached list one | ||||
---|---|---|---|---|
Coach | Year |
|
|
|
John Wooden | 1961 | 0.804 | 221.831 | 0.783 |
Adolph Rupp | 1951.5 | 0.822 | 202.689 | 0.731 |
Jim Calhoun | 1992.5 | 0.697 | 285.304 | 0.873 |
Mike Krzyzewski | 1995 | 0.764 | 290.341 | 0.973 |
Bob Knight | 1987 | 0.776 | 274.221 | 0.934 |
Dean Smith | 1979.5 | 0.793 | 259.109 | 0.902 |
Rick Pitino | 1996.5 | 0.706 | 293.364 | 0.909 |
Billy Donovan | 2004.5 | 0.710 | 309.484 | 0.964 |
Branch McCracken | 1952 | 0.750 | 203.696 | 0.670 |
Denny Crum | 1986.5 | 0.666 | 273.214 | 0.799 |
Hank Iba | 1950 | 0.731 | 199.666 | 0.641 |
Roy Williams | 2001.5 | 0.696 | 303.439 | 0.927 |
Jim Boeheim | 1995.5 | 0.756 | 291.349 | 0.967 |
Tubby Smith | 2003 | 0.790 | 306.461 | 1.062 |
Tom Izzo | 2005 | 0.774 | 310.491 | 1.055 |
Gary Williams | 1995 | 0.688 | 290.341 | 0.877 |
Jud Heathcote | 1983.5 | 0.740 | 267.169 | 0.868 |
Jerry Tarkanian | 1986 | 0.711 | 272.206 | 0.849 |
John Calipari | 2001.5 | 0.649 | 303.439 | 0.864 |
Jim Harrick | 1991.5 | 0.656 | 283.289 | 0.816 |
Al McGuire | 1971 | 0.693 | 241.981 | 0.736 |
Phog Allen | 1931 | 0.804 | 161.381 | 0.569 |
Data of winning rate after optimization are as in Table
First we search and gather over 3000 sets of data about different college coaches, including their coaching career length, individual award, winning rate under his or her lead, and team award. Then we remove those who can hardly be the top five due to their too short career or very low winning rate. Finally, we have minimized our database to 150 coaches.
Then we optimize data about award of coaches left and carry out a small-scale analysis hierarchy process (AHP). (Model 2) [
The evaluation of importance of award in this approach is accurate. The higher this value is, the bigger the influence on objectives hierarchy it has.
Variable definitions mentioned in Model 2.
Items | Characters |
---|---|
Winning rate |
|
Individual honor |
|
Team honor |
|
Coaching career length |
|
Final score |
|
Priority order evaluating different games.
Award | Importance level |
---|---|
|
|
|
|
|
|
NC |
|
After matrix
In order to judge whether the inconsistency of
Steps are as follows: computing consistency index average random consistency index computing consistency index
Index of RI while “
|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|
|||||||||||
RI | 0 | 0 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.49 | 1.51 |
Computing formula is
Result of weight.
|
|
|
|
Weight | |
---|---|---|---|---|---|
|
1 | 1/2 | 1/3 | 1/5 | 0.0882 |
|
2 | 1 | 1/2 | 1/3 | 0.1570 |
|
3 | 2 | 1 | 1/2 | 0.2720 |
|
5 | 3 | 2 | 1 | 0.4829 |
We can find that
After normalization, we find that
Using formula (
Ranking result.
Coach | CREG | NCAA | FF | NC |
|
---|---|---|---|---|---|
John Wooden | 16 | 16 | 12 | 10 | 12.0162 |
Adolph Rupp | 28 | 20 | 2 | 4 | 10.6766 |
Jim Calhoun | 16 | 23 | 4 | 3 | 8.9613 |
Mike Krzyzewski | 12 | 29 | 6 | 4 | 10.0464 |
Bob Knight | 17 | 27 | 6 | 2 | 9.6892 |
Dean Smith | 15 | 23 | 5 | 2 | 7.6514 |
Rick Pitino | 11 | 28 | 5 | 3 | 7.0053 |
Billy Donovan | 9 | 26 | 7 | 0 | 6.8662 |
Branch McCracken | 11 | 30 | 4 | 1 | 6.7289 |
Denny Crum | 16 | 13 | 11 | 0 | 7.5926 |
Hank Iba | 13 | 28 | 7 | 1 | 7.5255 |
The second is rule hierarchy
The third hierarchy is project: we define
We can normalize
Obviously all
That is, find weight vector of
Put them in order and then we get our resolution.
Take
Varies data after normalization (basketball).
|
|
|
| |
---|---|---|---|---|
John Wooden | 0.009 | 0.009 | 0.033 | 0.028 |
Adolph Rupp | 0.012 | 0.009 | 0.005 | 0.025 |
|
0.012 | 0.006 | 0.005 | 0.023 |
|
0.011 | 0.008 | 0.005 | 0.022 |
|
0.012 | 0.008 | 0.011 | 0.021 |
|
0.009 | 0.004 | 0.005 | 0.018 |
|
0.008 | 0.008 | 0.016 | 0.018 |
|
0.012 | 0.008 | 0.005 | 0.017 |
|
0.010 | 0.007 | 0.005 | 0.017 |
|
0.013 | 0.005 | 0.022 | 0.016 |
Using the weight of the solution layer to the guideline layer, find the weight of combination. (We omit the formula because the data is fussy.)
Rank the scores of each sample, comparing their priority [
Comparison of priority (basketball).
Coach |
|
|
|
|
|
---|---|---|---|---|---|
John Wooden | 29 | 0.672 | 6.000 | 12.016 | 0.024 |
Adolph Rupp | 41 | 0.627 | 1.000 | 10.677 | 0.017 |
Jim Calhoun | 40 | 0.751 | 2.000 | 8.961 | 0.015 |
Mike Krzyzewski | 39 | 0.837 | 1.000 | 10.046 | 0.015 |
Bob Knight | 36 | 0.803 | 1.000 | 9.689 | 0.015 |
Dean Smith | 26 | 0.775 | 3.000 | 7.651 | 0.015 |
Rick Pitino | 42 | 0.782 | 4.000 | 7.005 | 0.015 |
Billy Donovan | 37 | 0.830 | 3.000 | 6.866 | 0.014 |
Branch McCracken | 38 | 0.575 | 2.000 | 6.729 | 0.013 |
Denny Crum | 41 | 0.687 | 1.000 | 7.593 | 0.013 |
Using the above method fitting the number of teams and time, get the line (Figure
Coefficients in Figure
Unstandardized Coefficients | Standardized Coefficients |
|
Sig. | ||
---|---|---|---|---|---|
|
Std. Error | Beta | |||
(Constant) | −331.208 | 79.890 | 0.464 | −4.146 | 0.000 |
Curve of year and teams (football).
Data preprocessing: first, we also collected a lot of data, eliminated the project with obvious flaw, and thus selected 150 samples from 3000 teams from all over USA. Applying molds 2 and 3, we got the data (Tables
Varies data after normalization (football).
|
|
|
|
|
---|---|---|---|---|
Joe Paterno | 0.016577 | 0.007846 | 0.025862 | 0.030626 |
Bobby Bowden | 0.014414 | 0.007767 | 0.008621 | 0.027922 |
Bear Bryant | 0.013694 | 0.007785 | 0.008621 | 0.020647 |
Mack Brown | 0.01045 | 0.007158 | 0.00431 | 0.01662 |
Tom Osborne | 0.009009 | 0.0087 | 0.00431 | 0.016413 |
Comparison of priority (football).
|
|
|
|
|
|
---|---|---|---|---|---|
Joe Paterno | 46 | 0.756 | 6.000 | 16.803 | 0.024 |
Bobby Bowden | 40 | 0.749 | 2.000 | 15.319 | 0.019 |
Bear Bryant | 38 | 0.750 | 2.000 | 11.328 | 0.015 |
Mack Brown | 29 | 0.690 | 1.000 | 9.119 | 0.012 |
Tom Osborne | 25 | 0.839 | 1.000 | 9.005 | 0.012 |
Thus, we selected the top five “greatest coaches” (football).
Owing to limited data, 30 groups of hockey coaches were selected for the test. Because of the limited amount of actual data, the model was not suitable for the application in winning rate or may cause some errors.
Applying models 2 and 3, we got the data as in Tables
Varies data after normalization (hockey).
|
|
|
|
|
---|---|---|---|---|
Jerry York | 0.0455 | 0.0313 | 0.0516 | 0.0922 |
Red Berenson | 0.0341 | 0.0338 | 0.0323 | 0.078 |
Bill Beaney | 0.0375 | 0.0355 | 0.0452 | 0.0745 |
John “Snooks” Kelley | 0.0409 | 0.0339 | 0.0258 | 0.0603 |
Mike McShane | 0.0364 | 0.0333 | 0.0387 | 0.0603 |
Comparison of priority (hockey).
|
|
|
|
|
|
---|---|---|---|---|---|
Jerry York | 40 | 0.614 | 8.000 | 13.000 | 0.0686 |
Bill Beaney | 33 | 0.697 | 7.000 | 10.500 | 0.0584 |
Red Berenson | 30 | 0.663 | 5.000 | 11.000 | 0.057 |
Mike McShane | 32 | 0.654 | 6.000 | 8.500 | 0.0489 |
Jack Parker | 40 | 0.643 | 9.000 | 7.000 | 0.0477 |
Thus, we selected the top five “greatest coaches” (hockey).
The correction of the winning rate improves the influence of timeline, which means that there is a certain time having an influence on the coach’s achievement. By applying the model, we have successfully elected five “best ever coaches” in different sports. Verified with network selection by coaches ranking model, we established our model with certain accuracy. It is obvious that there are advantages as follows.
In the definition of a formula to measure how the low level indicator affects the timeline, we hope to fit multivariate data with timeline includes the intense level of competition, people’s attention on the events, state’s financial investment in sports and data on media, and other technology development so that we can optimize the timeline overall.
Because of the lack of data, we selected the most important indicator-intense level of competition to optimize data through the definition of new formulas.
In the promotion of football, we obtain that
Although we cannot come up with a certain answer to the evaluation results of the best college coach through the use of the mathematical model described in this paper to select the best coach, we can generally conclude accurate result which matches the results online largely. Thus, we can consider that the model has a strong practicality. We consider that evaluating coaches in different aspects helps select the best coach for the team, making the team more competitive and excellent.
The authors declare that there is no conflict of interests regarding the publication of this paper.