Who_is_the_best_coach论文.docx

Page 42 of 42Control#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:矚慫润厲钐瘗睞枥庑赖。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.聞創沟燴鐺險爱氇谴净。 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.残骛楼諍锩瀨濟溆塹籟。Who is the best coach?AbstractTo select “the best coaches in the history”, this paper develop the evaluation method of college coaches. 酽锕极額閉镇桧猪訣锥。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. 彈贸摄尔霁毙攬砖卤庑。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.謀荞抟箧飆鐸怼类蒋薔。Key words:Analytic Hierarchy Process Competence Evaluation Basketball Football Hockey Ages Gender厦礴恳蹒骈時盡继價骚。Contents1. Introduction4茕桢广鳓鯡选块网羈泪。1.1 Outline of Our Approach4鹅娅尽損鹌惨歷茏鴛賴。2. Analysis of the questions4籟丛妈羥为贍偾蛏练淨。3. Assumptions4預頌圣鉉儐歲龈讶骅籴。4. Constructing the models5渗釤呛俨匀谔鱉调硯錦。4.1 Selecting the data of coaches 1 based on the significant competitions scores initially5铙誅卧泻噦圣骋贶頂廡。4.2 Sorting model (considering the ages)5擁締凤袜备訊顎轮烂蔷。4.3 The examination of the models: Analytic Hierarchy Model 26贓熱俣阃歲匱阊邺镓騷。4.2.1 The basic methods and procedures of AHP:6坛摶乡囂忏蒌鍥铃氈淚。4.2.2 The achieving methods of four steps:6蜡變黲癟報伥铉锚鈰赘。4.3 Constitution of Competence Evaluation Model of coaches based on AHP. 310買鲷鴯譖昙膚遙闫撷凄。5. Solution of the models13綾镝鯛駕櫬鹕踪韦辚糴。5.1 Selecting the data of coaches based on the significant competitions scores initially13驅踬髏彦浃绥譎饴憂锦。5.1.1 Basketball13猫虿驢绘燈鮒诛髅貺庑。5.1.2 Football15锹籁饗迳琐筆襖鸥娅薔。5.1.3 Hockey15構氽頑黉碩饨荠龈话骛。5.2 Sorting the levels of coaches16輒峄陽檉簖疖網儂號泶。5.2.1 Basketball16尧侧閆繭絳闕绚勵蜆贅。5.2.2 Football18识饒鎂錕缢灩筧嚌俨淒。5.2.3 Hockey20凍鈹鋨劳臘锴痫婦胫籴。5.3 Examine: Solve the Constitution of Competence Evaluation Model of coaches based on AHP.22恥諤銪灭萦欢煬鞏鹜錦。5.3.1 Basketball22鯊腎鑰诎褳鉀沩懼統庫。5.2.2 Football27硕癘鄴颃诌攆檸攜驤蔹。5.2.3 Hockey31阌擻輳嬪諫迁择楨秘騖。5.4The effects of gender34氬嚕躑竄贸恳彈瀘颔澩。6. References34釷鹆資贏車贖孙滅獅赘。7. Memo35怂阐譜鯪迳導嘯畫長凉。1. 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.谚辞調担鈧谄动禪泻類。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 will嘰觐詿缧铴嗫偽純铪锩。1. Establish assumptions.2. Develop an algorithm to deal with the data of coaches games scores.熒绐譏钲鏌觶鷹緇機库。3. Build models to rank the coaches (Consider the effects of ages).鶼渍螻偉阅劍鲰腎邏蘞。4. Consider the effects of sex of coaches.5. Examine our results: Using Analytical Hierarchy Model (AHP) to build the Competence Evaluation Model纣忧蔣氳頑莶驅藥悯骛。6. Write a 1-2 page article forSports illustrated.颖刍莖蛺饽亿顿裊赔泷。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. 濫驂膽閉驟羥闈詔寢賻。3. Assumptions(1) Famous coaches led the team that had the same overall strength.銚銻縵哜鳗鸿锓謎諏涼。(2) Famous coaches led the team that had the same basic strength.挤貼綬电麥结鈺贖哓类。(3) In the 20th century, the coaches who didnt have more than 5 years of coaching are not famous coaches.赔荊紳谘侖驟辽輩袜錈。4. Constructing the models4.1 Selecting the data of coaches 1 based on the significant competitions scores initially塤礙籟馐决穩賽釙冊庫。 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 coach裊樣祕廬廂颤谚鍘羋蔺。F(X) =a0*n+a1*X1+a2*X2+.仓嫗盤紲嘱珑詁鍬齊驁。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.绽萬璉轆娛閬蛏鬮绾瀧。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.骁顾燁鶚巯瀆蕪領鲡赙。The function about the coachs ability in every year:瑣钋濺暧惲锟缟馭篩凉。 fx：the coachs ability this year x：the win-loss percentage of team Av：the average of total coaches the win-loss percentage鎦诗涇艳损楼紲鯗餳類。 n：the total number of coaches G1：the competition number that team attends G：the allowed maximum times to attend large competition栉缏歐锄棗鈕种鵑瑶锬。 a：Natural backgroundThe function about the coachs ability during his/her teaching time:辔烨棟剛殓攬瑤丽阄应。 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峴扬斕滾澗辐滠兴渙藺。 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 詩叁撻訥烬忧毀厉鋨骜。4.3 The examination of the models: Analytic Hierarchy Model 2则鯤愜韋瘓賈晖园栋泷。 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. 胀鏝彈奥秘孫戶孪钇賻。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;鳃躋峽祷紉诵帮废掃減。（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;稟虛嬪赈维哜妝扩踴粜。（3）Calculating the relative weights of the compared elements about the standard according to the judgment matrixes;陽簍埡鲑罷規呜旧岿錟。（4）Calculating the synthesized weight of each layers elements about the target of the system.沩氣嘮戇苌鑿鑿槠谔應。4.2.2 The achieving methods of four steps:（1）Creating a hierarchical structure: Level can be divided into three categories:钡嵐縣緱虜荣产涛團蔺。（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;懨俠劑鈍触乐鹇烬觶騮。（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;謾饱兗争詣繚鮐癞别瀘。（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.呙铉們欤谦鸪饺竞荡赚。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.莹谐龌蕲賞组靄绉嚴减。The basic hierarchy is shown (Figure 1 ): Coach 1Coach 2 Coach t Figure 1:Basic hierarchy(2) Constructing pairwise comparison judgment matrixes:麸肃鹏镟轿騍镣缚縟糶。In the hierarchical structure, setting up that upper element B is the standard. The next layer elements are controlled by B. We want to determine importance of elements 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):納畴鳗吶鄖禎銣腻鰲锬。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=aijn脳n . 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: .We call A as consistency matrix.風撵鲔貓铁频钙蓟纠庙。（3）Consistency test of relative weights and judgment matrixes of elements under a single criterion灭嗳骇諗鋅猎輛觏馊藹。We have known the judgment matrix A of relative to standard B, asking: the relative weights of relative to B. Vector form is .铹鸝饷飾镡閌赀诨癱骝。（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.攙閿频嵘陣澇諗谴隴泸。Calculated steps as followed:Step 1: normalizing the elements of A according to the column;趕輾雏纨颗锊讨跃满賺。Step 2: adding each column which had been normalized;夹覡闾辁駁档驀迁锬減。Step 3: using the sum dividing n to get the weights vectors;视絀镘鸸鲚鐘脑钧欖粝。 (b) Consistency testSteps as followed:. Calculating the consistency index: C.I. Finding the corresponding average random consistency index: R.I.偽澀锟攢鴛擋緬铹鈞錠。1-15 Order reciprocal matrixes calculate 1000 times to obtain the average random consistency index (Table 2) 緦徑铫膾龋轿级镗挢廟。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.騅憑钶銘侥张礫阵轸蔼。When , Should correct the matrix appropriately. 疠骐錾农剎貯狱颢幗騮。. Calculating the weights of total sort of each layer relative to target layer.镞锊过润启婭澗骆讕瀘。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 represents the vector of sort weight of the element which is on the k-1 layer relative to the total target. 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.榿贰轲誊壟该槛鲻垲赛。 is a matrix with 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 is邁茑赚陉宾呗擷鹪讼凑。 ;Or And the general formula isAmong: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 of the element j which is on the k-1 layer, average random consistency index and consistency ratio C.R.jk, , the consistency index of the k layer , , 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.嵝硖贪塒廩袞悯倉華糲。4.3 Constitution of Competence Evaluation Model of coaches based on AHP. 3该栎谖碼戆沖巋鳧薩锭。 This paper chose 18 assuming characteristic indexes of college coaches, Specific indicators are as follows: (Table 3)劇妆诨貰攖苹埘呂仑庙。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):臠龍讹驄桠业變墊罗蘄。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)鰻順褛悦漚縫冁屜鸭骞。Model of Coaches comprehensive eva