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1、Primacy&RankingofUEFASoccerTeamsfromBiasingOrganizingRulesMarcelAusloos1;;2;,AdamGadomski3,NikolayK.Vitanov41;RoyalNetherlandsAcademyofArtsandSciences,JoanMuyskenweg25,1096CJAmsterdam,TheNetherlands2GRAPES,ruedelaBelleJardiniere483,B-4031Liege,FederationWallonie-Bruxe
2、lles,Belgiumemail:marcel.ausloos@ulg.ac.be3UniversityofTechnologyandLifeSciences,DepartmentofPhysics,InstituteofMathematicsandPhysics,PL-85-796Bydgoszcz,Polandemail:agad@utp.edu.pl;agad@atr.bydgoszcz.pl4InstituteofMechanics,BulgarianAcademyofSciences,Acad.G.BonchevStr.,Bl.
3、4,BG-1113So a,Bulgariaemail:vitanov@imbm.bas.bgMay7,2018AbstractAquestionisraisedonwhethersomeimpliedregularityorstructure,asfoundinsoccerteamrankingbytheUnionofEuropeanFootballAs-sociations(UEFA),isduetoimplicitgameresultvalueorscorecompe-titionconditions.Theanalysisisbas
4、edonconsiderationsaboutcomplexsystems,i.e.searchingwhetherpowerorothersimplelaw tsareappro-priatetodescribesomeinternaldynamics.Itisobservedthattherankingisspeci callyorganized:amajorclassmadeofafewteamsemergesaftereachgameseason.Otherclasseswhichapparentlyhaveregularsizes
5、sub-sequentlyoccur.Thus,thenotionofSheppardprimacyindexisenvisagedtodescribethe ndings.Additionalprimacyindicesarediscussedforen-hancingthefeatures.ThesemeasurescanbeusedtosortoutpeerclassesarXiv:1406.4644v1[physics.soc-ph]18Jun2014inmoregeneralterms.Averysimpli edtoymodel
6、containingingredientsoftheUEFArankingrulessuggeststhatsuchpeerclassesareanextrinsicpropertyoftheranking,asobtainedinmanynonlinearsystemsunderboundaryconditionconstraints.Associateresearcher11IntroductionNonlinearityandcomplexity[1]-[3]arecommonfeaturesofalargenumberofsyst
7、emsstudiedinmodernscience[4]-[6].Theyareofteninvestigatedbynon-lineardynamicsmethods[7]-[9].Inthelastdecadeorso,thesemethodshavebeenappliedtomanysocial,economic,and nancialsystems[10].Inmanycomplexsystems,researchershavedetectedtheexistenceofpowerlaws,foralargevarietyofcha
8、racteristicquantities.Suchpowerlawshavebecomeveryusefultoolsforstudyingcomplexsystemsbeca
