美赛数模B题Finalist.docx
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美赛数模B题Finalist.docx
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美赛数模B题Finalist
TeamControlNumber
ForofficeuseonlyForofficeuseonly
T1________________F1________________
T2________________F2________________
T3________________F3________________
ProblemChosen
B
2014MathematicalContestinModeling(MCM)SummarySheet
Summary
Inordertoestimatetheexcellenceofdifferentsportscoachesandtogivearankingresult,
twodistinctmodelsaredeveloped.Thefirstmodelisacomprehensiveevaluationmethod.
AndthesecondmodelisarankingalgorithmanalogoustotheJournalInfluenceAlgorithm.
Inthefirstmodel,wetakeintoaccountavarietyofmetrics,anddividethemintotwo
categories:
ObjectiveMetricsandSubjectiveMetrics.IntheObjectiveMetrics,weconsider
fourfactors,thenumberofwins,winningpercentage,championsandfinalfours.Allthese
factorshavecontributionstotheexcellenceofacoach.Wedeemthatthetotalnumberof
gamesinayearcouldaffectthenumberofwins,andtheunevennessofteamqualitycould
affectthewinningpercentage.Byemployingstatisticalregressionmethodtoprocess
collecteddata,weestablishtwofunctionsofinfluencecoefficienttoeliminatethe
discrepancycausedbythetwokindsofeffect.IntheSubjectiveMetrics:
weconsidertwo
factors,mediapopularityandtenure.WeemployFuzzyAnalysisMethodtoquantifythese
twosubjectivefactors.WefurtherincorporateAnalyticHierarchyProcess(AHP)andGray
RelationalAnalysisGradeMethod(GRAP)todeterminetheweightallocationtodifferent
metrics.Thefinalrankinggivesacomprehensiveresultbyweighingresultsreturnedby
thesetwomethods.UsingdatafromSportsReferenceandotherwebsites,therankingsin
basketball,footballandbaseballaccordwithpreviousmediacommentaries.
Inthesecondmodel,wedeemthattheexcellenceofacertaincoachcanbereflectedfrom
themediaimpactoverthespanofhistoryandthattheinteractionsbetweentwocoachescan
reflectthedisparityofskilllevelbetweenthem.WeusesearchresultsreturnedbyGoogle
toquantifytheimpactofonecoachonanother.Basedonthesearchresults,webuilda
cross-referencematrixtorepresentrelationshipsbetweencoaches.Inviewthatthedifferent
timeperiodsthattwocoacheswereinmaylargelyaffecttheinteractionbetweenthem,and
thepersonalreputationmayinfluencethenumberofsearchresults,wedevelopaweight
functionoftwovariablestocompensatetheinfluenceoftimeandtoruleouttheredundant
information.
Inconsiderationofthesimilaritybetweenpersonalinfluenceandjournalinfluence,werefer
totheJournalInfluenceAlgorithmintroducedbyEigenfactorandestablishanewranking
algorithm.Thebasicideaofthealgorithmissubtle:
usingweightfunctiontomodifythe
cross-referencematrix,andtakingintoconsiderationofindividualinfluence,thealgorithm
givesanevaluationvectortorankdifferentcoaches.Totestthevalidityofthisalgorithm,
weapplythealgorithmintobasketball,footballandbaseball.Thealgorithmgivesaresult
thatissimilartotheresultobtainedinthefirstmodel.Therankingalsoagreeswith
previousmediacommentaries.Furthermore,byslightlyadjustingthecoefficients,wecan
applythealgorithmintovarioussports.
感谢作者分享
2014-B-Finalist杨杰,刘瞳葳,郑博⽅
24270
T4________________
F4________________
校苑数模⽹
“DreamTeam”ofCollegeCoaches
#Team24270
感谢作者分享
2014-B-Finalist杨杰,刘瞳葳,郑博⽅
校苑数模⽹
Team#24270Page2of26
Contents
1.Introduction......................................................................................................................3
1.1.RestatementoftheProblem.....................................................................................3
1.2.ModelOverview......................................................................................................3
2.Assumptions......................................................................................................................3
3.ModelⅠ...........................................................................................................................4
3.1.Additionalassumptions...........................................................................................4
3.2.Notations.................................................................................................................4
3.3.EvaluationSystem...................................................................................................5
3.3.1.Theinfluenceoftimeonthetotalnumberofwins........................................................6
3.3.2.Theinfluenceoftimeonthewinning-percentage..........................................................6
3.3.3.FuzzyAnalysis...............................................................................................................7
3.3.4.Nondimensionalizationprocess.....................................................................................8
3.3.5.Finalresult.....................................................................................................................8
3.4.SolutionstoModelⅠ............................................................................................10
3.4.1.Basketball.....................................................................................................................10
3.4.2.Football........................................................................................................................11
3.4.3.Baseball........................................................................................................................12
3.4.4.Sensitivityanalysis.......................................................................................................13
4.ModelⅡ.........................................................................................................................13
4.1.Additionalassumptions.........................................................................................14
4.2.Notations...............................................................................................................14
4.3.TheIndividualInfluenceVector............................................................................14
4.3.1.Originaldata.................................................................................................................15
4.3.2.Theinfluencecoefficientoftime.................................................................................15
4.3.3.Theinfluencecoefficientofreputation........................................................................16
4.3.3.Theindividualinfluencevector...................................................................................16
4.4.TheCross-ReferenceMatrix.................................................................................16
4.4.1.Theweightfunction.....................................................................................................17
4.4.2.Thefinalcross-referencematrix..................................................................................17
4.5.TheEvaluationVector...........................................................................................18
4.6.SolutionstoModelII.............................................................................................18
4.6.1.Basketball.....................................................................................................................18
4.6.2.Football........................................................................................................................19
4.6.3.Baseball........................................................................................................................19
4.6.4.Sensitivityanalysis.......................................................................................................19
5.Applicability....................................................................................................................20
6.StrengthsandLimitations.............................................................................................21
6.1.ModelⅠ.................................................................................................................21
6.2.ModelII.................................................................................................................21
7.Conclusions.....................................................................................................................21
8.TheArticleforSportsIllustrated...................................................................................22
References..............................................................................................................................23
Appendix................................................................................................................................24
感谢作者分享
2014-B-Finalist杨杰,刘瞳葳,郑博⽅
校苑数模⽹
Team#24270Page3of26
1.Introduction
1.1.RestatementoftheProblem
Sports,bydefinition,isallformsofusuallycompetitivephysicalactivitywhichaimtouse
physicalabilitywhileprovidingentertainmenttoparticipantsandspectators[1].Nowonderthe
word“sports”givesusafirstimpressionoffiercecompetition,agitatedspectators,sweating
ontherunningtrack,combinedwithajoyofvictory.Itistheuncertaintythatmakesthe
sportsgamesointriguing.However,wherethereiscompetition,therewillalwaysbevictory,
defeat,andranking.Loyalsportfanscoulddebatedayandnightoverthequestionwhoisthe
bestplayero
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