美赛特等奖论文资料下载.pdf
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美赛特等奖论文资料下载.pdf
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AbrahamLincoln,GeorgeWashington,FranklinD.Roosevelt.Atlast,thestrengthandweaknessofourmodearediscussed,non-technicalexplanationispresentedandthefutureworkispointedaswell.Team#28414Page2of33I.Introduction.31.1ProblemBackground.31.2PreviousResearch.31.3OurWork.3II.Symbols,DefinitionsandAssumptions.42.1SymbolsandDefinitions.42.2GeneralAssumptions.5III.Articulateourmetrics.53.1Specifyevaluationnorms.53.2Collectdata.83.3Preprocessdata.9IV.Twomodelsforcoachranking.104.1ModelI:
AnalyticHierarchyProcess(AHP).104.1.1Thethree-hierarchystructure.104.1.2Obtaintheindexweight.104.1.3Results&
analysis.114.2ModelII:
FuzzySyntheticEvaluation(FSE).124.2.1Quantifygradesinthefiveaspects.124.2.2Determinemembershipfunctions.134.2.3Determinetheweightsusingentropymethod.144.2.4Results&
analysis.15V.ModelsCombination.155.1Evaluationofindividualmodel.155.2AggregationModel.175.3Results&
analysis.17VI.ExtendOurModels.186.1Gendersdonotmatter.186.2Timefactordoesmakeadifference.196.2.1Whytimefactormatters?
.196.2.2Howtimefactormatters?
.196.2.3Whatisthevariationtendency?
.236.3Modelalsoworksinothersports.23VII.Furtherdiscussion.257.1SensitiveAnalysisonFSE.257.1.1VaryMembershipfunction.257.1.2Varycalculationrule.277.2SensitiveAnalysisonAggregationweight.287.3Explore:
EvaluatingBestPresident.29VIII.StrengthandWeakness.30IX.Non-technicalExplanation.30X.Futurework.32XI.References.32Team#28414Page3of33I.Introduction1.1ProblemBackgroundSportsIllustratedisanAmericansportsmediafranchiseownedbymediaconglomerateTimeWarner1.Thismagazineislookingforthe“bestalltimecollegecoach”maleorfemaleforthepreviouscentury.Thebestcollegecoachorcoachescanbefromamongeithermaleorfemalecoachesindifferentfields,suchascollegehockeyorfieldhockey,football,baseballorsoftball,basketball,orsoccer.Wefacemainlyfourproblems:
Articulateourownmetricsandbuildamathematicalmodel;
Setuptheevaluationsystemfortheperformanceofthemodel.Discusshowourmodelcanbeappliedwithtimefactororacrossbothgendersandallpossiblesports;
Analyzetheinfluencesoftheparameters,thendiscusswhetheryourmodelcouldbeappliedintowidefields.1.2PreviousResearchSomemagazinesorwebsitesthatfocusmainlyoncollegesportshaverankedthetopcollegecoachesofdifferentsports.Forexample,hasmadeabasket-ballpowerrankings2whichshowsthetop25coachesofcollegebasketball.Consideringthebestcollegecoachesisanevaluationproblem.Therearesomemodelswhichcansolvesuchproblem.OneistheAnalytichierarchyprocess(AHP),whichwasdevelopedbyThomasL.Saaty3inthe1970s.TheAHPprovidesacomprehensiveandrationalframeworkforstructuringadecisionproblem,forrepresentingandquantifyingitselements,forrelatingthoseelementstooverallgoals,andforevaluatingalternativesolutions4.AnotheristheFuzzySyntheticEvaluationModel.Fuzzymathematicsformsabranchofmathematicsrelatedtofuzzysettheoryandfuzzylogic5.Itstartedin1965afterthepublicationofLotfiAskerZadehsseminalworkFuzzysets6.1.3OurWorkInthispaperwedeterminethebestcollegecoachesfromamongeithermaleorfemalecoachesindifferentsports.InSection2,weprovidetheterminologydefinitionsandassumptionsthatwillbeutilizedintherestofthepaper.InSection3,wegivethedefinitionsofevaluationstandardandspecificevaluationnormswhichweusedinourTeam#28414Page4of33models,andshowsomeofthedatawehavecollected.InSection4,webuildtwomathematicalmodelstochoosethebestcollegecoaches,andSection5considerscombinationofthetwomodelsmentionedabove.InSection6weextendourmodelsandtaketime,gendersandtypesofsportsintoconsideration.Section7providesfurtherdiscussofourmodels.InSection8,weprovideanoverviewofourapproachandgiveanon-technicalexplanationofourmodelsthatsportsfanswillunderstand.Section9showssomeworkwecandointhefuture.II.Symbols,DefinitionsandAssumptions2.1SymbolsandDefinitionsSymbolsforevaluationnorms:
SymbolDefinitionwinsfortheyearlossesfortheyeartheaverageSRStheaverageSOSthetimesforeachclassofplayofftheweightofeachawardpointforeachaspectofcontributionSymbolsforAnalyticHierarchyProcess:
SymbolDefinitionthejudgingmatrixthegreatesteigenvalueofmatrixAtheindicatorofconsistencychecktheconsistencyratiotherandomconsistencyindextheweightvectorforcriterialeveltheweightvectorforalternativesleveltheevaluationgradeformodelISymbolsforFuzzySyntheticEvaluation:
SymbolDefinitionthegradesforeachaspectthemembershipfunctionTeam#28414Page5of33thefuzzymatrixthecharacteristicweighttheentropyfortheevaluationgradetheweightvectorinentropymethodtheevaluationgradeformodelIISymbolsforAggregationModel:
SymbolDefinitiontheaverageoffsetdistancetheweightformodelItheevaluationgradeforaggregationmodel2.2GeneralAssumptionsTheelementsthatwealreadyhavetakenintoconsiderationplayavitalroleintheevaluation.Theignoredelementsofcoachdonotinfluencetheranking.Thedatathatwehavecollectedisenoughandaccurateandthequantificationiscorrect.Thereexistsobjectiveandaccuraterankingforcoaches,andtherankingsfromselectedmediacouldreflecttheaccuraterankingtosomeextent.III.Articulateourmetrics3.1SpecifyevaluationnormsAsfortheevaluationstandardforplayers,therearemainlyfiveaspects9thatcount:
strength,speed,skill,defenseandattack.Similarlyacoachcouldbeevaluatedfromfollowingfiveaspects:
historicalrecord,gamegoldcontent,play-offperformance,honorsandcontributiontothesports.Whatfollowsinthechapterwillhammerataccountingforthefiveaspects.Historicalrecord:
Theteamsrecordundoubtedlyaccountsforthelargestproportioninthecoachevaluation.Accordingtothemainstreamstatisticindexesfortheteamrecord,winsandlossesaremostnotable.Theteamshistoricalrecordcoulddirectlyreflectsthecoachingability.Thetotalwinsacouldbecalculatedasfollows:
a=(3.1)Team#28414Page6of33-Wheredenoteswinsfortheyear.Thetotallosesbcouldbecalculatedasfollows:
b=(3.2)-Wheredenoteslossesfortheyear.Gamegoldcontent:
Ifallwinsareproducedduringthefightswithweakteams,apparentlythewinscouldnotillustratetherealcoachingability.Atthesametime,theaveragepointdifferencealsomakesadifference.Itreflectsthecoachingstylethatwhetheracoachisconservativeorradical.Toillustratetheupontwopoints,wechoosethefollowingtwonorms:
SimpleRatingSystem(SRS)8:
Thesimpleratingsystemworksbyfirstfindinghowmanypoints,onaverage,ateamwins/losesby.Foreachgame,thepointdifferentialisthenweightedbasedonhowmuchbetterorworsethanaveragetheiropponentspointdifferentialis.LetRdenotethetotalSRS,thenitcouldbecalculatedasfollows:
R=(3.3)-WheredenotestheSRSvaluefortheyear,tdenotesthenumberoftheyears.StrengthofSchedule(SOS)8:
Insports,strengthofschedule(SOS)referstothedifficultyoreaseofateams/personsopponentascomparedtootherteams/persons.Thisisespeciallyimportantifteamsinaleaguedonotplayeachotherthesamenumberoftimes.LetOdenotethetotalSOS,thenitcouldbecalculatedasfollows:
O=(3.4)-WheredenotestheSOSvalu
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