Who_is_the_best_coach论文.docx

Page 37 of 37Control#27447SummaryTo select “the best coaches in the history”, this paper develop the evaluation method of college coaches. Several elements that can reflect the level of coaches are analyzed, firstly. The calculating methods of these elements are given. According to these elements, the rules of selection are set and the candidates are listed. Several factors into account, we receive the calculating formula of these coaches grades. These scores were just based on some original data which included coaches annual games played times, category of competitions and win-lost records to calculate. Because the difference of different ages competed environment and the level of competitions are considered, we use the degree of coaches score beyond the ages average level as the basis of judgment to do the final sorting. The comprehensive information and other aspects of well-known coaches and various events on the web can be also used to constitute the competence evaluation model of coaches based on AHP. For example to the basketball, football, and hockey of American University, two methods are used to rank the well-known coaches based on the overall level. According to the American College coaches grades on the web, 18, 12 and 8 candidates are selected to do the final sorting. The first five coaches are as followed:Basketball：John Wooden, Bob knight, Dean Smith, Adolph Rupp, Mike Krzyzewski；Football：Tom Osborne, Knute Rockne, Bo Schembechler, Fielding Yost, Bud Wilkinson；Hochey：Toe Blake, Scotty Bowman, Al Arbour, Dick Irvin, Hap Day. At last, this paper analyze the impact of gender on the level of coaching. The analysis of the three sports results shows that our evaluation methods are effective and can be chosen to use according to the type of data source. These methods and the perspective of the considering problems can also be used to deal with the other sports.Who is the best coach?AbstractTo select “the best coaches in the history”, this paper develop the evaluation method of college coaches. Several elements that can reflect the level of coaches are analyzed, firstly. Calculating methods of these elements are given. According to these elements, the rules of selection are set and the candidates are listed. Several factors into account, we receive the calculating formula of these coaches grades. These grades are just based on some original data which include coaches annual games played times, category of competitions and win-lost records to calculate. Because the difference of different ages competed environment and the level of competitions are considered, we use the degree of coaches grade beyond the ages average level as the basis of judgment to do the final sorting. The comprehensive informations and other aspects of well-known coaches and various events on the web can be also used to constitute the competence evaluation model of coaches based on AHP. For example to the basketball, football, and hockey of American University, two methods are used to rank the well-known coaches based on the overall level. By comparison, there is minimal difference between the two results. And the results are basically consistent with the public evaluation. This shows that our evaluation methods are effective and can be chosen to use according to the type of data source. At last, this paper analyze the impact of gender on the level of coaching. These methods and the perspective of the considering problems can be also used to deal with the other sports.Key words:Analytic Hierarchy Process Competence Evaluation Basketball Football Hockey Ages GenderContents1. Introduction41.1 Outline of Our Approach42. Analysis of the questions43. Assumptions44. Constructing the models54.1 Selecting the data of coaches 1 based on the significant competitions scores initially54.2 Sorting model (considering the ages)54.3 The examination of the models: Analytic Hierarchy Model 264.2.1 The basic methods and procedures of AHP:64.2.2 The achieving methods of four steps:64.3 Constitution of Competence Evaluation Model of coaches based on AHP. 3105. Solution of the models135.1 Selecting the data of coaches based on the significant competitions scores initially135.1.1 Basketball135.1.2 Football155.1.3 Hockey155.2 Sorting the levels of coaches165.2.1 Basketball165.2.2 Football185.2.3 Hockey205.3 Examine: Solve the Constitution of Competence Evaluation Model of coaches based on AHP.225.3.1 Basketball225.2.2 Football275.2.3 Hockey315.4The effects of gender346. References347. Memo351. IntroductionSports Illustrated, a magazine for sports enthusiasts, is looking for the “best all time college coach” male or female for the previous century. This paper need construct models to rank the coaches and discuss the different effects on the sex of the coaches and ages. At last, this paper need give a 1-2 page article forSports Illustratedthat explains the results and includes a non-technical explanation of our mathematical model thatsports fanswill understand.1.1 Outline of Our Approach Our aim is to rank the coaches of last century to attain the first five coaches. Then our aim is considering the sex of coaches and the different ages to discuss the different effects of indexes. In this paper, we will1. Establish assumptions.2. Develop an algorithm to deal with the data of coaches games scores.3. Build models to rank the coaches (Consider the effects of ages).4. Consider the effects of sex of coaches.5. Examine our results: Using Analytical Hierarchy Model (AHP) to build the Competence Evaluation Model6. Write a 1-2 page article forSports illustrated.2. Analysis of the questionsTo select the famous coaches of 20th century in large numbers, we base on the score. We predigest the data at first, and the point is narrowing the scope of selection. According to key factors about the score, we choose good coaches to second step. In detailed selection, rule out the influence of extra factors, like time. Getting rid of time, we can compare the coach in different times by considering degree of ability over the times level. Finally discharge the order. So we get the conclusion of one coachs excellence degree in his time. Coaching in 1913 will be not different in coaching in 2013. 3. Assumptions(1) Famous coaches led the team that had the same overall strength.(2) Famous coaches led the team that had the same basic strength.(3) In the 20th century, the coaches who didnt have more than 5 years of coaching are not famous coaches.4. Constructing the models4.1 Selecting the data of coaches 1 based on the significant competitions scores initially The selection of famous coaches in 20th century, ruling out this centurys coach. Deleting less than 5 years of coaching in the last century, the coach with the winning rate less than 0.5 also ignore. Famous coach means the team is outstanding, which the numbers of the field, total win rate and performance in competition playing the main work. The ability of coachF(X) =a0*n+a1*X1+a2*X2+.1=a0+a1+a2+F(X) means the ability of coach，Xi is the score in large competition，at the same time ai representative the importance in all competition。Calculating F(X)，we select the coach in list with descending order. Sometimes the major competitions begin in the middle of century. Dividing the years into three groups according to these competitions, we establish ai in each time group.4.2 Sorting model (considering the ages)In order to judge the ability of coaches, we consider three factors: the experience value, contribution and competitive advantage. There are five related data: coaching time, competitions times, the total average of the win-loss percentage, annual average of the win-loss percentage, the age of the coaches and time. We consider these factors in order. Firstly, we consider the factor: time.The function about the coachs ability in every year: fx=ax-AvAv+G1G a=1 normal year0 the year of war or the year having catastrophe Av=i=1nxin fx：the coachs ability this year x：the win-loss percentage of team Av：the average of total coaches the win-loss percentage n：the total number of coaches G1：the competition number that team attends G：the allowed maximum times to attend large competition a：Natural backgroundThe function about the coachs ability during his/her teaching time: Fx=i=1Yaixi-AviAv*Gi*YG+xSTDEV Fx: the coachs ability x：the total win-loss percentage during his time Avi：the win-loss percentage average of total coach in year i Y：the years of teaching G：the number of attending competitions Gi：the number of attending competitions in year I STDEV：standard deviation of xi ai：nature background in year i xi：the win-loss percentage average in year I 4.3 The examination of the models: Analytic Hierarchy Model 2 Analytic Hierarchy Process (AHP) is a combination of quantitative and qualitative. It is a method which is used to transform peoples subjective judgment to numbers to express and deal with. Essentially it is a way of thinking. AHP decomposes complex problems into component factors, then groups these factors according to relations of domination to form hierarchical structure. 4.2.1 The basic methods and procedures of AHP:（1）Anglicizing the relationship between the factors of the system, Creating the hierarchical structure of the system;（2）Making each element which is on the same level pairwisie comparison based on one standards importance on the previous level, constructing pairwise comparison judgment matrixes;（3）Calculating the relative weights of the compared elements about the standard according to the judgment matrixes;（4）Calculating the synthesized weight of each layers elements about the target of the system.4.2.2 The achieving methods of four steps:（1）Creating a hierarchical structure: Level can be divided into three categories:（a）Top: There is only one element. It is the intended target or desired outcome of the issues, so it also be called target layer;（b）The middle layer: This level includes intermediate links which are involved by the target goal and standards which are needed to consider. This layer may consist of several levels , hence there are criteria and sub- criteria. This layer is also called criteria layer;（c）Bottom: This level includes various measures and decision-making programs to achieve the goal, so it is also called measures layer or program layer.We call the structure which is confirmed by the relationship of upper elements dominating the lower elements as hierarchical structure. Apparently, the upper elements can dominate the all lower elements, and can only dominate the part of lower elements.The basic hierarchy is shown (Figure 1 ): Coach 1Coach 2 Coach t Figure 1:Basic hierarchy(2) Constructing pairwise comparison judgment matrixes:In the hierarchical structure, setting up that upper element B is the standard. The next layer elements P1,P2,Pm are controlled by B. We want to determine importance of elements P1,P2,Pm relative to B. The importance is also called weight. If we cant get the importance directly, there are some qualitative descriptions. Use the method of pairwise comparison to determine the weight. The method is that relative to B, element Pi and Pj which is more important? And how much it is more important? Assign the degree of importance according to 1 to 9 proportional scales. The following table lists the meaning of the scale from 1 to 9 (Table 1):ScaleMeaning1Said two elements compared with the same importance3Said two elements compared to the former is slightly more important than the latter 5Said two elements compared to the former than the latter important obviously 7Said two elements compared to the former than the latter important strongly9Said two elements compared to the former than the latter is important extremely2，4,6,8Said the intermediate value of adjacent judgments ReciprocalThe ratio of the importance between Pi and Pj is aij,so the ratio of the importance between Pj and Pi is aji=1aijTable 1:The meaning of nine scalesFor standard B, the comparison of relative importance between the n elements to get a pairwise comparison judgment matrix A=aijnn . A has the following properties: aij0 aji=1aij aii=1 .We call A as Reciprocal matrix. If the all elements of A have the following properties: aijajk=aik .We call A as consistency matrix.（3）Consistency test of relative weights and judgment matrixes of elements under a single criterionWe have known the judgment matrix A of P1,P2,Pm relative to standard B, asking: the relative weights w1,w2,wn of P1,P2,Pm relative to B. Vector form is w=w1,w2,wnT.（a）Using legitimate to calculate weights: Calculate the arithmetic mean of the n column vectors of A normalized. Then use the arithmetic mean as the vector of weights, approximately.wi=1nj=1naijk=1nakj i=1,2,nCalculated steps as followed:Step 1: normalizing the elements of A according to the column;Step 2: adding each column which had been normalized;Step 3: using the sum dividing n to get the weights vectors; (b) Consistency testSteps as followed:. Calculating the consistency index: C.I.C.I.=max-nn-1. Finding the corresponding average random consistency index: R.I.1-15 Order reciprocal matrixes calculate 1000 times to obtain the average random consistency index (Table 2) Order12345678R.I.000.520.891.121.261.361.41Order9101112131415R.I.1.461.491.521.541.561.581.59Table 2:R.I. of Order reciprocal matrixes. Calculating the consistency ratio: C.R.;C.R.=C.I.R.I.When C.R.0.1, Consistency of judgment matrixes is considered acceptable.When C.R.0.1, Should correct the matrix appropriately. . Calculating the weights of total sort of each layer relative to target layer.The weights of total sort need to synthesis the weights which are under the single standard from top to bottom. And determine the overall consistency test Layer by layer. Setting Wk-1=w1k-1,wnk-1k-1 represents the vector of sort weight of the nk-1 element which is on the k-1 layer relative to the total target. Pjk=p1jk,pnjkT represents the vector of sort weight of the nk element which is on the k layer relative to the j element which is on the k-1 layer. Whats more, the weighs of these elements which are not dominated by element j are zero.Pk=p1k,pnk-1k is a matrix with nknk-1 elements. It represents the sort of the elements which are on the k layer relative to each element which is on the k-1 layer. So, the total sort Wk of the elements which are on the k layer isWk=w1k,wnkkT=PkWk ;Or wi(k)=j=1nk-1pij(k)wj(k-1) i=1,2,nAnd the general formula isw(k)=p(k)p(k-1)p(3)p(2)Among:W2 is the sort vector of the elements which are on the second layer, and is also the sort vector under the single standard. We need to do consistency test from top to bottom. If we have gotten the consistency index C.I.jk of the element j which is on the k-1 layer, average random consistency index R.I.jk and consistency ratio C.R.jk, j=1,2,nk-1, the consistency index of the k layer C.I.k=C.I.1k,C.I.nk-1kWK-1 , R.I.k=R.I.1k,R.I.nk-1kWK-1, C.R.K=C.I.kR.I.k .When C.R.K0.1 , we believe all of the judgments whose hierarchical structures are above the level of k layer with the overall satisfacted consistency.4.3 Constitution of Competence Evaluation Model of coaches based on AHP. 3 This paper chose 18 assuming characteristic indexes of college coaches, Specific indicators are as follows: (Table 3)123456Knowledge baseaccumulated experienceInductions, deductive thinkingTrainingPlayers character creationInnovation789101112SpecializationFrontier trackSpot commandCaringTeamworkExcitation131415161718DedicationPursuing the sportsmanshipSelf-confidence, self-discipline,AppealingIndependent studyCommunicationTable 3:18 assuming characteristic indexesClassified the 18 indexes to get three main categories and nine indexes (Table 4):Providing effective guidance for athletes training, development and learning B1Self-confidence, self-discipline, dedication, self-learning P1Appealing P2Caring, communication, team character creation P4Training, innovation P5 Using an effective incentive skills to encourage athletes to pursue athletic spirit B2Excitation P3Pursuing the sportsmanship P9Using appropriate competitive strategies and tactics B3Spot command P6Frontier track P7Induction, deductive thinking, specialized knowledge reserves ,accumulated experience P8Table 4:Index classesStep 1: Building the hierarchical model of the coaches evaluation based on the model of coaches competency (Figure 1)Model of Coaches comprehensive evaluation B2B3B1 P3P8P7P6P1P2P4P5 P9 Coach 2Coach nCoach 3Coach 1 Figure 1: Basic hierarchyStep 2: Collecting the following information of Candidates. We can get a smaller number of coaches finally. Then collect the following information of coaches once coached.Step 3: According to AHP, assign the degree of importance according to 1 to 9 proportional scales. Then establish the positive and negative criteria matrix of c