The evaluation of the university coach.docx
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The evaluation of the university coach.docx
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Theevaluationoftheuniversitycoach
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2015
MathematicalContestinModeling(MCM/ICM)SummarySheet
Theevaluationoftheuniversitycoach
Abstract
Withthedevelopmentoftimesandinformationtechnology,theevaluationmetricsofcollegecoachesarebecomingincreasinglydiverseandtheevaluationofcollegecoachesisgettingincreasinglyobjectiveandscientific.Wedevisesomemodelstoevaluatecollegecoachesandtogetarankingofcollegecoaches.
Afteranalyzingtherelevantliterature,weobtainthemainevaluationmetrics:
thecareeraccomplishmentsandcoachingexperience.Andthenweobtainapreliminaryrankingofcollegecoaches.Afterthat,webuiltamulti-metricmodel.combinedwiththeopinionsfromDelphipanelandsportsfans,weobtainthreecomprehensivemetrics-theprofessionalachievements,thecoachingexperienceandinfluenceofcoaches.WeuseAHPtodeterminetheweightsofdifferentmetrics.Finally,weuseacomprehensiveTOPSISevaluationmodeltogetafurtherrankingofcollegecoaches.
Furthermore,weconductsensitivityanalysisonAHP.Throughanalysis,wefindthatthecoach’sinfluenceisanincreasinglycriticalevaluationmetricandwefindthatModelcanevaluatecollegecoachesinthelastcentury.Throughmodeltestofdifferentgendersandsportsonourmodel,weconcludethatthemodelisrelativelyaccurate.
Finally,thestrengthsandweaknessesofmodelsarediscussed,andthefutureworkispointedout.
Keywords:
AnalyticHierarchyProcess,Sensitivity,coach,evaluation.
Contents
Theevaluationoftheuniversitycoach1
Abstract1
1Introduction3
2TheDescriptionofProblem3
3BasicAssumptions4
4Models4
4.1Asimpledual-metricevaluationmodel4
4.1.1DataDisposal5
4.1.2AHPforWeightsofEvaluationMetrics5
4.1.3TOPSISmethod8
4.1.4Thesolutiontothemodel9
4.2Theevaluationofmodels10
4.2.1Sensitivityanalysis10
4.2.2Localsensitivityanalysis10
4.2.3Globalsensitivityanalysis11
4.3EvaluationofSensitivityAnalysis13
4.3.1Theinfluenceofthetimelinehorizon13
4.3.2ModelTest:
Theinfluenceofotherfactors14
5AnarticletosportsfansandreadersofSportsIllustrated15
6Strengths,WeaknessesandImprove16
6.1Strengths16
6.2Weaknesses16
6.3Improve17
7References17
8Appendix17
1
Introduction
Inrecentyears,thedevelopmentofmoderncompetitivesportshasbeengrowingrapidly.Asstrongpromotersofthedevelopmentofcompetitivesports,coachesalsoplayanincreasinglyimportantrole.Muchoftheliteratureconcernedwithcollegecoaching-inparticular,thearticlesandcommentarieswrittenbycoachesforcoaches-stressthecoach'sroleasateacherandexemplar.
Inordertoattractstudentswithhigherlevelsandtomaketheschoolteamnotedalloverthecountryandtheworldatlarge,alargenumberofcollegesarecompetingforthebestcoaches.Aparticularlychallengingproblemisstrategizingtoidentifythebestcoachesasaccurateaspossible.However,nomatterhowdifficulttheproblemis,therearealwayswaystoevaluateacoach’scomprehensiveability.Oneofthemosteffectivewaystoidentifythebestcoachesisthroughcomprehensiveanalysisofvariousmetricsforassessment—thethemeofthispaper.
Inthisproblem,SportsIllustratedislookingforthe“bestalltimecollegecoach”maleorfemaleforthepreviouscentury.Theobjectiveofusismodelingtoidentifythebestcollegecoachesindifferentkindsofsports.Thisproblemencompassesthefollowingfivequestions:
●Whetherthemodelissuitablebothinthepastandatpresent.
●Clearlyarticulateyourmetricsforassessment.
●Discusshowyourmodelcanbeappliedingeneralacrossbothgendersandallpossiblesports.
●Presentyourmodel’stop5coachesineachof3differentsports.
●Preparea1-2pagearticleforSportsIllustratedthatexplainsyourresultsandincludesanon-technicalexplanationofyourmathematicalmodelthatsportsfanswillunderstand.
2TheDescriptionofProblem
SportsIllustrated,amagazineforsportsenthusiasts,islookingforthe“bestalltimecollegecoach”maleorfemaleforthepreviouscentury.Buildamathematicalmodeltochoosethebestcollegecoachorcoaches(pastorpresent)fromamongeithermaleorfemalecoachesinsuchsportsascollegehockeyorfieldhockey,football,baseballorsoftball,basketball,orsoccer.Doesitmakeadifferencewhichtimelinehorizonthatyouuseinyouranalysis,i.e.,doescoachingin1913differfromcoachingin2013?
Clearlyarticulateyourmetricsforassessment.Discusshowyourmodelcanbeappliedingeneralacrossbothgendersandallpossiblesports.Presentyourmodel’stop5coachesineachof3differentsports.
InadditiontotheMCMformatandrequirements,preparea1-2pagearticleforSportsIllustratedthatexplainsyourresultsandincludesanon-technicalexplanationofyourmathematicalmodelthatsportsfanswillunderstand.
3BasicAssumptions
Thefollowingassumptionswereusedinourmodels:
●ThedataweusedfromtheInternetshouldbereliableandcorrect.
●Wedonottakeintoaccounttheimpactofdifferentschoolsorteamsonthesamecoach.
●WeonlyconsiderthecollegecoachintheAmericaasthebasisofthemodelwhichwillbeestablished.
●Thelongerlengthofcoachingaddsacoach’sopportunitytobealeaderinthegames.
●Wedonottakeintoaccountthepossibilitythatnon-naturaldeathsleadingtotheabruptterminationofcoaching.
4Models
4.1Asimpledual-metricevaluationmodel
Agoodcoachoftenbringsasatisfactoryresult,sotheevaluationofacoach'scareeraccomplishmentsisoftendirectlylinkedtothewinningpercentageofthegame.Withtheincreasingageofthecoach,hiscoachingexperienceoftenrevealsatrendofsteadyrise.Therefore,thecoachingexperienceofcollegecoachesisalsoarelativelyimportantfactor.Sothewinningpercentageofthegameandthecoachinglifeofcollegecoachesarechosentobethemainevaluationmetrics.Figure1displaysthesimpledual-metricevaluationModel’sexplanationgraphically.
Inordertohaveamorereliableresult,wesearchthedataofcollegecoachesofbasketball,Rugbyandfieldhockey-thethreemostpopularsportsintheUS.Webegintoevaluatethecollegecoachesbasedonthesedata.
Figure1.Evaluation.
4.1.1DataDisposal
Sincethemetricsaredifferentbetweenvarioussports,wecannotdirectlycomparethembetweendifferentsports.Therefore,wefirstlynormalizethedataofdifferentsports.
Forthesakeofconsistency,weneedtoprocesstheoriginaldata,whichwedenoteas
.Findthemaximumandminimumvaluesinthewholetable,denotedby
and
.Theadjustedvalueis
.
(1)
Throughtheevaluationofsurveydataandsportscoachstandard,wesettheweightsoftwometricstobe0.6and0.4respectively.
Theoverallevaluationofcollegecoachesiscalculatedusingthefollowingequation,(where
and
areweightingfactors)
.
(2)
Where,
istheprofessionalachievement,
isthebasicresults.
Thebasicresultsareshowninfigure2.
Figure2.Thebasicresults.
4.1.2AHPforWeightsofEvaluationMetrics
Inordertodeterminetheweightsofdifferentmetrics,wedecidetocarryouttheanalytichierarchyprocessmethod(AHP).
1.TheCombinationofMetrics.
Wedeviseacompositemeasureofthethreemainmetrics:
Theprofessionalachievements,ThecoachingexperienceandInfluence.
WedividethemetricsintoseverallayersasFigure3shows:
Figure3.SchematicdiagramofAPH.
2.Analytichierarchyprocess.
AnalytichierarchyprocesswasintroducedbySaatyin1971andhasbecomeoneofthemostextensivelyusedmultipleattributesdecision-makingmethods(MCDM/MADM).Inthispart,theweightsofmetricsaredeterminedbyAHP.
Step1:
ImportanceAnalysisbetweenMetrics.
ConsideringthegeneralsituationofthesportsintheUS,wecomprehensivelyanalyzetheabilityofcoacheswhichvarywidelybetweensports.Wecomparetherelativeimportancebetweeneachmetricusingtable1.
Table1.Constructthejudgmentscale.
Grade
Relativeimportance
1
EquallyImportant
3
GenerallymoreImportant
5
FarmoreImportant
7
MoreImportantatthesecondhighestdegree
9
MoreImportantatthehighest
2,4,6,8representstheimportance
levelisinbetweenaccordingtotheabove
Thereciprocalvalue(1/2,1/3,…,1/9)
express‘Lessimportant’
WeplacethesegeneralvaluesthatbasicallysuitedtoeverysportinTables2-5.
Table2.JudgmentMatrix1.
T
1
3
1/4
1/3
1
1/2
4
2
1
Table3.JudgmentMatrix2.
1
5
5
1/5
1
1
1/5
1
1
Table4.JudgmentMatrix3.
1
6
1/6
1
Table5.JudgmentMatrix4.
1
5
5
1/5
1
1
1/5
1
1
Step2:
Estimatetherelativeweightsofthemetrics.
Wespecifythecalculationofthefirstlayer;theotherscanbecalculatedinthesameway.Aftercomparingtheeffectoftwocriteriainthesamelayertothehigherlayer,wecanconstructtheconjugated-comparativematrixwithSaaty’sRule.Forexample,
canindicatethedifferenceoftheeffectbetweentheprofessionalachievementsandthecoachingexperience.LetAbetheconjugated-comparativematrixofthefirstlayer.
Wedeterminetheweightsofotherdifferentmetricsbyusingthesamemethod.Fromformula
(1),combinedwiththeweightsofthecomprehensivemetrics,weobtainthecomprehensiveweightofeachsub-metric.
Table6.Weights.
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