Home advantage of European major football leagues under COVID-19 pandemic

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Home advantage of European major football leagues under COVID-19 pandemic EIJI KONAKA (MEIJO UNIVERSITY, JAPAN) MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Outline ⚫Home advantage in football ⚫Closed match under COVID-19 pandemic ⚫Home advantage under COVID-19 pandemic ⚫Analysis method ⚫Results and discussions MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Home advantage in football ⚫“Home advantage” in sports ⚫“… the benefit that induces home teams to consistently win more than 50 percent of the games under a balanced home-and- away schedule.” [Courneya and Carron, 1992] ⚫Statistical survey over 120 football leagues over the world ⚫Source: https://www.worldfootball.net/ ⚫Summary (2010-2019) ⚫Matches: 173492 ⚫Home W/D/L 79648/43957/49887 ⚫Home GF/GA 260159/197531 ⚫Five major European leagues (ENG/GER/ITA/FRA/ESP) ⚫Matches: 16434 ⚫Home W/D/L 7550/4154/4730 ⚫Home GF/GA 25475/19151 MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Home advantage in football ⚫“Home advantage” in sports ⚫“… the benefit that induces home teams to consistently win more than 50 percent of the games under a balanced home-and- away schedule.” [Courneya and Carron, 1992] ⚫Statistical survey over 120 football leagues over the world ⚫Source: https://www.worldfootball.net/ ⚫Summary (2010-2019) ⚫Matches: 173492 ⚫Home W/D/L ratio 0.4591/0.2534/0.2875 ⚫Home GF/GA ratio 0.5684/0.4316 ⚫Five major European leagues (ENG/GER/ITA/FRA/ESP) ⚫Matches: 16434 ⚫Home W/D/L ratio 0.4594/0.2528/0.2878 ⚫Home GF/GA ratio 0.5709/0.4291 MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) Home advantage of five major European leagues is similar to the average all over the world

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Home advantage in football: worldwide survey ⚫Statistical survey over 120 football leagues over the world ⚫Source: https://www.worldfootball. net/ ⚫2010-2019 ⚫Win prob. difference MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) World average

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Home advantage in football: European major leagues ⚫Statistical survey ⚫Source: https://www.worldfootball. net/ ⚫2010-2019 ⚫Goals diff. per match ⚫Win prob. diff. ⚫Five major European leagues MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) World average World average

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Explanations of home advantage ⚫Home advantage clearly exists in professional football. ⚫Possible causes of home advantage[Pollard 2008] ⚫Crowd effects, travel effects, familiarity, referee bias, territoriality, special tactics, rule factors, and their interactions. ⚫Key data ⚫Number of goals, yellow/red cards ⚫Most previous studies assumes a balanced schedule MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Closed match COVID-19 pandemic ⚫COVID-19 pandemic ⚫Suspension: from March 2020 ⚫France: Ligue 1 was cancelled in April ⚫England, Germany, Italy, and Spain: Resumed by late June and finished by early August ⚫Resumed matches were “closed.” ⚫“Closed match”=match without spectators MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Closed match COVID-19 pandemic ⚫COVID-19 pandemic ⚫Suspension: from March 2020 ⚫France: Ligue 1 was cancelled in April ⚫England, Germany, Italy, and Spain: Resumed by late June and finished by early August ⚫Resumed matches were “unbalanced.” ⚫The leagues were already approximately two-thirds completed by the mid- March suspension. MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Closed match COVID-19 pandemic ⚫COVID-19 pandemic ⚫Suspension: from March 2020 ⚫France: Ligue 1 was cancelled in April ⚫England, Germany, Italy, and Spain: Resumed by late June and finished by early August ⚫Resumed matches were “unbalanced.” ⚫The leagues were already approximately two-thirds completed by the mid- March suspension. MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) Unbalanced schedule bias should be separetad from home advantage

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Objective ⚫Analysis home advantage under COVID-19 pandemic ⚫Is the “crowd effect” vanished? ⚫Separate unbalanced schedule bias ⚫Outline of the analysis method ⚫Pairwise comparison ⚫Short-term rating method ⚫Compare the time series of the home advantage between normal and closed periods. MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Closed matches under the COVID-19 pandemic ⚫Number of normal and closed matches ⚫“Closed” means “Without spectators” MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) Country League Teams Matches (10/11-18/19) Matches Normal, 19/20 Matches Closed 19/20 England Premier League 20 3420 290 90 France Ligue 1 20 3420 279 0 Germany Bundesliga 18 2754 216 90 Italy Serie A 20 3420 240 140 Spain LaLiga 20 3420 270 110 Total 16434 1295 430

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Basic stats ⚫2010-2020 ⚫Goals diff. per match ⚫Win prob. diff. MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Basic stats ⚫2010-2020 ⚫2019/20 season ⚫Goals diff. per match ⚫Win prob. diff. MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Basic stats ⚫2010-2020 ⚫2019/20 season ⚫Goals diff. per match ⚫Win prob. diff. ⚫In the closed period, the home advantages were reduced MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Basic stats ⚫2010-2020 ⚫2019/20 season ⚫Goals diff. per match ⚫Win prob. diff. ⚫In the closed period, the home advantages were reduced ⚫“Home disadvantage” in Germany MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Home advantage analysis: the method ⚫Logistic regression model ⚫Team i played at its home against team j ⚫The rating values are calculated so as to minimize σ 𝜖𝑖,𝑗 2 MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) 𝑠𝑖,𝑗 = ൗ 1 1 + exp − 𝑟𝑖 + 𝑟homeAdv,𝑘 − 𝑟 𝑗 − 𝜖𝑖,𝑗 𝑠𝑖,𝑗 = Τ (𝑠𝑖 + 1) 𝑠𝑖 + 𝑠𝑗 + 2 , 𝑠𝑖 : goals of team 𝑖 𝑟𝑖 : rating of team 𝑖 𝑟homeAdv,𝑘 : home advange of the league 𝑘

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Home advantage analysis: the method ⚫Rating on scoring ratio ⚫Conversion to winning ratio ⚫𝐷𝑘 are calculated so as to minimize σ 𝜖𝑖,𝑗 2 MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) 𝑠𝑖,𝑗 = ൗ 1 1 + exp − 𝑟𝑖 + 𝑟homeAdv,𝑘 − 𝑟 𝑗 − 𝜖𝑖,𝑗 𝑟𝑖 : rating of team 𝑖 𝑟homeAdv : common home advange of the league 𝑤𝑖,𝑗 = ൗ 1 1 + exp −𝐷𝑘 𝑟𝑖 + 𝑟homeAdv,𝑘 − 𝑟 𝑗 − 𝜖𝑖,𝑗 = ෝ 𝑤𝑖,𝑗 − 𝜖𝑖,𝑗

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Home advantage analysis: short-term estimation ⚫Proposed model: Estimate the rating of each team and the home advantage of the league simultaneously. ⚫Separate team strength from home advantage ⚫Useful under the unbalanced schedule ⚫Short-team estimation: follow the change of the home advantage ⚫Five matchweeks ⚫Classification of the periods: Normal, Mixed, and Closed ⚫Example: Premier league MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) Matchweek 25 26 27 28 29 30 31 32 33 34 35 Spectator N N N N N C C C C C C Period N N N N N M M M M C C

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Calculation example ⚫Fit result ⚫EPL. Matchweeks from 21 to 25 ⚫𝑟homeAdv is positive (red vertical dashed line) MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Main result ⚫Boxplot of distributions of 𝑟homeAdv ⚫Wilcoxon’s rank sum test ⚫Null hypothesis: The home advantage from two different categories were the samples from continuous distributions with equal medians. MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Main result ⚫Boxplot of distributions of 𝑟homeAdv ⚫No significant difference between Past and Normal periods MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Main result ⚫Boxplot of distributions of 𝑟homeAdv ⚫No significant difference between Past and Normal periods ⚫A significant difference between normal and closed periods ⚫Median in closed period is smaller than normal period MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Analysis for each league: England Sample X Sample Y 𝑵𝑿 𝑵𝒀 p-value Past Normal 306 25 0.223 Past Closed 606 5 0.213 Normal Closed 25 5 0.578 ⚫The home advantage in the closed period has no significant difference from the past and the normal periods. MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Unbalanced schedule in England’s closed period ⚫ In the closed period, in England, weaker teams played more home games than stronger teams. MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Unbalanced schedule in England ⚫ In the closed period, in England, weaker teams played more home games than stronger teams. ⚫Weak correlation (𝒓 ≃ 𝟎. 𝟒) between the final standings and the number of home matches in the closed period. ⚫No correlation in other leagues. Germany(0.2863), Italy(0.0867), and Spain(−0.1561). MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)

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Estimated 𝑟homeAdv : England MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) Sample X Sample Y 𝑵𝑿 𝑵𝒀 p-value Past Normal 306 25 0.223 Past Closed 306 5 0.213 Normal Closed 25 5 0.578

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Estimated 𝑟homeAdv : Germany MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) Sample X Sample Y 𝑵𝑿 𝑵𝒀 p-value Past Normal 270 20 0.163 Past Closed 270 6 <0.001 Normal Closed 20 6 <0.01

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Estimated 𝑟homeAdv : Italy MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) Sample X Sample Y 𝑵𝑿 𝑵𝒀 p-value Past Normal 306 20 0.029 Past Closed 306 10 0.065 Normal Closed 20 10 0.775

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Estimated 𝑟homeAdv : Spain MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25) Sample X Sample Y 𝑵𝑿 𝑵𝒀 p-value Past Normal 306 23 0.020 Past Closed 306 7 <0.001 Normal Closed 23 7 <0.001

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Summary ⚫The home advantage under COVID-19 pandemic was analyzed. ⚫Outline of the analysis method ⚫Pairwise comparison ⚫Short-term rating method ⚫Separate unbalanced schedule bias ⚫Compare the time series of the home advantage between normal and closed periods. ⚫Conclusion ⚫The home advantage was reduced in closed situation. ⚫Reduction amount was different between leagues. MATHSPORT INTERNATIONAL CONFERENCE 2021 (6/24-25)