{"id":"https://openalex.org/W3209966001","doi":"https://doi.org/10.1142/s0219525921500077","title":"STATISTICAL PROPERTIES OF RANKINGS IN SPORTS AND GAMES","display_name":"STATISTICAL PROPERTIES OF RANKINGS IN SPORTS AND GAMES","publication_year":2021,"publication_date":"2021-03-01","ids":{"openalex":"https://openalex.org/W3209966001","doi":"https://doi.org/10.1142/s0219525921500077","mag":"3209966001"},"language":"en","primary_location":{"id":"doi:10.1142/s0219525921500077","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219525921500077","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Complex Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2111.03599","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"JOS\u00c9 ANTONIO MORALES","orcid":null},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"JOS\u00c9 ANTONIO MORALES","raw_affiliation_strings":["Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, 04510, Mexico"],"affiliations":[{"raw_affiliation_string":"Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, 04510, Mexico","institution_ids":["https://openalex.org/I8961855"]}]},{"author_position":"middle","author":{"id":null,"display_name":"JORGE FLORES","orcid":null},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"JORGE FLORES","raw_affiliation_strings":["Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, 04510, Mexico"],"affiliations":[{"raw_affiliation_string":"Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, 04510, Mexico","institution_ids":["https://openalex.org/I8961855"]}]},{"author_position":"middle","author":{"id":null,"display_name":"CARLOS GERSHENSON","orcid":"https://orcid.org/0000-0003-0193-3067"},"institutions":[{"id":"https://openalex.org/I4210107358","display_name":"Lakeside Labs","ror":"https://ror.org/01w08b546","country_code":"AT","type":"nonprofit","lineage":["https://openalex.org/I4210107358"]},{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["AT","MX"],"is_corresponding":false,"raw_author_name":"CARLOS GERSHENSON","raw_affiliation_strings":["Centro de Ciencias de la Complejidad, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, 04510, Mexico","Instituto de Investigaciones en Matem\u00e1ticas Aplicadas y Sistemas, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, 04510, Mexico","Lakeside Labs GmbH, Lakeside Park B04, 9020 Klagenfurt am W\u00f6rthersee, Austria"],"affiliations":[{"raw_affiliation_string":"Centro de Ciencias de la Complejidad, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, 04510, Mexico","institution_ids":["https://openalex.org/I8961855"]},{"raw_affiliation_string":"Instituto de Investigaciones en Matem\u00e1ticas Aplicadas y Sistemas, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, 04510, Mexico","institution_ids":["https://openalex.org/I8961855"]},{"raw_affiliation_string":"Lakeside Labs GmbH, Lakeside Park B04, 9020 Klagenfurt am W\u00f6rthersee, Austria","institution_ids":["https://openalex.org/I4210107358"]}]},{"author_position":"last","author":{"id":null,"display_name":"CARLOS PINEDA","orcid":null},"institutions":[{"id":"https://openalex.org/I8961855","display_name":"Universidad Nacional Aut\u00f3noma de M\u00e9xico","ror":"https://ror.org/01tmp8f25","country_code":"MX","type":"education","lineage":["https://openalex.org/I8961855"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"CARLOS PINEDA","raw_affiliation_strings":["Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, 04510, Mexico"],"affiliations":[{"raw_affiliation_string":"Instituto de F\u00edsica, Universidad Nacional Aut\u00f3noma de M\u00e9xico, Mexico City, 04510, Mexico","institution_ids":["https://openalex.org/I8961855"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I8961855"],"apc_list":null,"apc_paid":null,"fwci":0.5911,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.82443076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"24","issue":"02","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.30809998512268066,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.30809998512268066,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11674","display_name":"Sports Analytics and Performance","score":0.2493000030517578,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.07959999889135361,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.9194999933242798},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.852400004863739},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5561000108718872},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5544999837875366},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.3743000030517578},{"id":"https://openalex.org/keywords/rank-correlation","display_name":"Rank correlation","score":0.35910001397132874},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.33730000257492065}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.9194999933242798},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.852400004863739},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5561000108718872},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5544999837875366},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.453000009059906},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.3743000030517578},{"id":"https://openalex.org/C101601086","wikidata":"https://www.wikidata.org/wiki/Q3753228","display_name":"Rank correlation","level":2,"score":0.35910001397132874},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3506999909877777},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34439998865127563},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.33730000257492065},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.32429999113082886},{"id":"https://openalex.org/C2986587452","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical analysis","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C86037889","wikidata":"https://www.wikidata.org/wiki/Q4330127","display_name":"Learning to rank","level":3,"score":0.29170000553131104},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.2531999945640564},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.25119999051094055},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0219525921500077","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219525921500077","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Complex Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2111.03599","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2111.03599","pdf_url":"https://arxiv.org/pdf/2111.03599","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:RePEc:wsi:acsxxx:v:24:y:2021:i:02:n:s0219525921500077","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0219525921500077","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2111.03599","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2111.03599","pdf_url":"https://arxiv.org/pdf/2111.03599","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1830855051","https://openalex.org/W2000042664","https://openalex.org/W2037959956","https://openalex.org/W2072271719","https://openalex.org/W2085314032","https://openalex.org/W2091203480","https://openalex.org/W2143902672","https://openalex.org/W2170210105","https://openalex.org/W2189259429","https://openalex.org/W2440298909","https://openalex.org/W2610394548","https://openalex.org/W2787893209","https://openalex.org/W2788432705","https://openalex.org/W2908727066","https://openalex.org/W2993383518","https://openalex.org/W2994907129","https://openalex.org/W3032200391","https://openalex.org/W4235752132"],"related_works":[],"abstract_inverted_index":{"Any":[0],"collection":[1],"can":[2,137],"be":[3],"ranked.":[4],"Sports":[5],"and":[6,15,65,74,94,170,177,193],"games":[7],"are":[8,17,191],"common":[9],"examples":[10],"of":[11,26,38,53,68,167,172,188,198],"ranked":[12,19],"systems:":[13],"players":[14],"teams":[16],"constantly":[18],"using":[20],"different":[21,72,159,199],"methods.":[22],"The":[23],"statistical":[24,140],"properties":[25,141],"rankings":[27,117],"have":[28,85,163],"been":[29],"studied":[30],"for":[31,158,195],"almost":[32],"a":[33,36,54,100,122,134],"century":[34],"in":[35,57,118,146],"variety":[37],"fields.":[39],"More":[40],"recently,":[41],"data":[42],"availability":[43],"has":[44],"allowed":[45],"us":[46],"to":[47,126],"study":[48,61,77],"rank":[49,63,66,78,88,92,95,130,154,161,189],"dynamics:":[50],"how":[51,110],"elements":[52,112],"ranking":[55,179],"change":[56,90],"time.":[58,119],"Here,":[59],"we":[60,80,84,104],"the":[62,116,128,143,147,168,173],"distributions":[64,155],"dynamics":[67,162,190],"12":[69],"datasets":[70],"from":[71],"sports":[73],"games.":[75],"To":[76],"dynamics,":[79,131],"consider":[81],"measures":[82,187],"that":[83,103,108,133,152,185],"defined":[86],"previously:":[87],"diversity,":[89],"probability,":[91],"entropy,":[93],"complexity.":[96],"We":[97,120],"also":[98,183],"introduce":[99],"new":[101],"measure":[102],"call":[105],"\u201csystem":[106],"closure\u201d":[107],"reflects":[109],"many":[111],"enter":[113],"or":[114,175],"leave":[115],"use":[121],"random":[123],"walk":[124],"model":[125],"reproduce":[127],"observed":[129,145],"showing":[132],"simple":[135],"mechanism":[136],"generate":[138],"similar":[139,164],"as":[142],"ones":[144],"datasets.":[148],"Our":[149,181],"results":[150,182],"show":[151],"while":[153],"vary":[156],"considerably":[157],"rankings,":[160],"behaviors,":[165],"independently":[166],"nature":[169],"competitiveness":[171],"sport":[174],"game":[176],"its":[178],"method.":[180],"suggest":[184],"our":[186],"general":[192],"applicable":[194],"complex":[196],"systems":[197],"natures.":[200]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-03-24T08:02:53.985720","created_date":"2021-11-08T00:00:00"}