2014年美赛数模B题-Finalist(5)

Team # 24270 Page 20 of 26

Table 14: The Amount of Change

Number 1 2 3 4 5 6 7 8 9 10

Change (in %) -3.73 -3.06 -1.31 -7.50 -5.61 -1.66 -2.13 -4.97 -1.48 -5.80 Number 11 12 13 14 15 16 17 18 19 20 Change (in %) -6.65 12.05 -7.09 -6.45 -5.73 15.23 -1.69 -6.25 14.74 -3.35

The ranking list of top five is:

1. John Wooden 2.Dean Smith 3.Mike Krzyzewski 4.Bob Knight 5.Rick Pitino

This list is closer to the list obtained in Model I(Table 3), in which four of the coaches are the same.

Secondly, we set the partial coefficient?? and?? to be 0.9 and 0.1, the returned evaluation vector changed in a moderate range. See Table 16.

Number 1 2 3 4 5 6 7 8 9 10

Change (in %) 3.03 2.12 0.29 7.23 5.21 0.5 1.3 4.38 0.99 4.99 Number 11 12 13 14 15 16 17 18 19 20 Change (in %) 6.3 -12.74 6.77 6.03 5.4 -16.02 1.45 5.64 -16.05 2.29 The ranking list of top 5 in this case is:

1. John Wooden 2.Mike Krzyzewski 3.Dean Smith 4.John Thompson 5.Rick Pitino Three of the coaches are listed in Model I.

As can be seen from above, with a slight change in the partial coefficient, the result

changed in a controllable range and remain close to the result in Model 1. The lager?? is, the more weight it is attributed to individual influence and vice versa.

Table 16: The Amount of Change

5. Applicability

? Genders

As for gender factors, we can employ two models to evaluate coaches with different genders due to the same evaluation indexes. Through the data collected by Internet[20], we use and modify model I to obtain the women basketball result. See Table 16.

Table 16: Top 5 Coaches of Women Basketball

No.1 No.2 No.3 No.4 No.5

Pat Summitt Tara VanDerveer Barbara Stevens C. Vivian Stringer Geno Auriemma

The ranking list of top coaches is agreement with the data from Internet. ? Other Sports

As for other sports，like Track and Field Events or Swimming Events, these evaluation systems of two models can be applied very well. For model I, we only need to change evaluation indexes and modify the data, while the analytical method is the same. For model II, because we do not need to consider other evaluation indexes but the data of search result, we also evaluate and rank top coaches of other sports conveniently.

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Team # 24270 Page 21 of 26 6. Strengths and Limitations

6.1. ModelⅠ

? Strengths

─ High accuracy. We combine objective and subjective indexes in modelⅠ, and

meanwhile, we employ subjective and objective methods to evaluate the rank of coaches in the previous century. Therefore, this evaluation system has a high accuracy and is accordance with reality.

─ Extendibility. With so many sports and fields, this model extracts the common

features of different sports so that it can be adapted to a large range of sports and fields via comparing the same metrics.

─ Easy to understand. This model is succinct and clear, which can be easily

understood.

? Limitations

─ The lack of data. When a game is not hot, the data are difficult to find, which may

result in the lack of data.

─ Difficult to determine weights. In order to obtain an accurate result, this model

needs to determine weights carefully. However, it is difficult to choose appropriate values of weights.

6.2. Model II

? Strengths

─ Efficient. Once the model has available data, the final result can be obtained

efficiently, which means that it do not rely largely on the work of human. ─ The lack of data do not occur. Since the data of model is based on the searching

number of Google, the needed data is always sufficient. ─ Simple. Information of coaches do not need to be specific. ? Limitations

─ The influence of media. Since this model is based on the degree of media attention,

it do not take comprehensive factors in consideration.

7. Conclusions

In model I, we have defined evaluation indexes and determined the weights of their importance. By searching and selecting needed data, we obtained the final amount of evaluation of each coach in a certain sport. Finally, we compared the evaluation amounts and listed top five coaches, which is accordant with widely accepted result. And in the sensitivity analysis, the result is satisfying and of robustness. Further work of model I should choose more evaluation indexes to rank coaches in a more fairly way.

In model II, the algorithm offers us a convenient way to evaluate the excellence of certain coach, without any need for detailed information. That is, by a series of repetitive search on the Internet, one can get a grasp of rankings in any given sports. Because of the simplicity of the search job, a program can be developed to perform the rote tasks. Given that the algorithm

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Team # 24270 Page 22 of 26

does not need any details, the method can be applied to any fields that need a ranking system. However, the partial coefficient in this algorithm must be determined on a mass of trail and

error adjustments, which we cannot adequately explain here.

8. The Article for Sports Illustrated

“Dream Team” of College Coaches

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