Modelling home advantage for individual teams in UEFA Champions League football

Abstract

Background

Home advantage (HA) is well documented in a wide range of team sports including association football (soccer). Although much attention has been paid to differences in the overall magnitude of HA between football competitions and across time, few studies have investigated HA at the team level.

Methods

A novel method of estimating HA for individual teams, based solely on home performance, was used to compare HA between the highest performing teams and countries in the Union of European Football Associations (UEFA) Champions League over a 10-year period (2003/2004 to 2012/2013). Away disadvantage (AD) was also estimated based on each team's performance away from home. Poisson regression analysis was used to estimate covariate adjusted HA and AD in terms of the percentage of goals scored at home (HA) and conceded away from home (AD).

Results

When controlling for differences in team ability, HA did not vary significantly between the 13 selected teams. There was evidence (p < 0.1), however, of between-team variation in AD, ranging from 45% (away advantage) to 68% (away disadvantage). When teams were grouped into the 11 selected countries, both HA and AD varied significantly (p < 0.02) between countries: HA ranged from 52% for Turkish teams to 70% for English teams, while AD ranged from 52% (France) to 67% (Turkey).

Conclusion

Differences in style of play and tactical approaches to home and away matches may explain some of the variation in HA and AD between teams from different countries.

1. Introduction

Home advantage (HA) is the tendency for sporting teams to perform better at their home ground than away from home, and its existence has been well established in a wide range of team sports including association football.1, 2 Although much attention has been paid to differences in the overall magnitude of HA between football competitions3, 4, 5 and across time,² relatively few studies have investigated HA at the individual team level, and this is the focus of the present study.

In a sporting competition where each team plays each other the same number of times both home and away, differences in team ability balance out over the season and therefore do not bias calculations of total HA across the whole competition.⁶ HA for an individual team, however, will be largely determined by its ability relative to other teams in the competition; that is, a stronger team will be expected to win more matches at home than a weaker team. Team ability therefore needs to be controlled for when estimating HA for individual teams.

In the first comprehensive investigation into HA at the team level in football, Clarke and Norman⁶ compiled 10 years of match data for 94 teams across 4 divisions of English football. HA for individual teams was calculated as a function of home and away goal difference and total HA across the whole division. Although this results in each team's HA being influenced by the HAs of all the other teams in the competition, the authors showed that this method controls for differences in team ability. A regression analysis found some evidence of variation in HA between teams, as well as for London teams having lower HA. There was strong evidence, however, for HA being higher for teams playing on artificial pitches, suggesting that home ground familiarity was playing a role.

Another method of estimating HA for individual sporting teams was developed by Pollard and Gomez,⁷ originally for basketball, and subsequently applied to football teams in 4 countries in South-West Europe.⁸ To control for team ability, the raw calculated HA—based on both home and away performance—for each team was regressed on a measure of that team's ability. The residual value for each team (i.e., the difference between its observed HA and the expected HA for a team of that ability) was then added or subtracted from the total HA for all teams in the competition. Like the Clarke and Norman⁶ method described above, this approach produces HA estimates which are influenced by the HAs of other teams. Highly significant differences in HA between teams were observed in France, Italy, and Portugal, although there was little evidence of variation in HA between Spanish teams. Teams from ethnically and/or culturally distinct locations in France and Italy had greater HA than the rest of the teams in those countries, suggesting that territoriality and/or travel factors may be playing a role. However, such regional effects were not observed for teams in Portugal or Spain. Teams from capital cities in each country except Italy had significantly lower HA than teams from other areas.

The Pollard and Gomez⁷ method of estimating HA for individual teams has also been used in studies of Brazilian and Greek football. In the First Division of the Brazilian football league, significant variation in HA between teams was observed.⁹ In particular, teams in the north and south of Brazil had significantly higher HA than those from the central region; effects of travel and change in climate were suggested as possible explanations. Significant between-team variation in HA was also observed in the Greek Superleague,¹⁰ with teams based in Athens showing less HA than those in the rest of Greece; the authors suggested that the sense of territorial protection may be less for teams in capital cities.

The present study introduces a novel method of estimating HA for individual teams, based solely on home performance and hence independent of the HAs of other teams in the competition. Away disadvantage (AD) is also estimated, based on a team's performance away from home. Multivariate regression techniques are used to control for team ability. Ten years of match data from the Union of European Football Associations (UEFA) Champions League—an international club competition featuring the best teams from over 25 European countries—were used to estimate HA and AD for a selection of the highest performing teams and countries over this period. This is the first study to investigate HA for individual teams in the UEFA Champions League.

2. Materials and methods

2.1. Data

The data used in this study were matches from the 2003/2004 to 2012/2013 seasons of the UEFA Champions League. Entry into this competition is based on a team's performance in their domestic league the previous season. The Champions League consists of a round-robin group stage, followed by a knock-out finals stage. All matches except the final are played in pairs, 1 at each team's home ground. Each of the group stage matches is decided on its own, whereas matches in the finals stage (except the final) are decided over 2 “legs”. The final match in each season was excluded from the analysis as it was played at a neutral venue where there is no HA to be gained. Matches between AC Milan and Inter Milan (n = 2) were also excluded as these teams share the same home ground. Teams playing at least 50 matches over the 10-year study period (13 teams; 1058 matches) and countries whose teams played at least 75 matches between them (11 countries; 2028 matches) were chosen for the analysis. This selection method maximises the statistical power of the analysis, and results in the highest performing teams and countries being chosen. All match data were downloaded from the official UEFA website (www.uefa.com).

2.2. Analysis

HA for each individual team was estimated as the percentage of goals scored in home matches by that team. For example, if a team scored 50 goals in their home matches and conceded 30, then their unadjusted HA would be 50/(50 + 30) × 100% = 62.5%. Correspondingly, AD for each team was estimated as the percentage of goals conceded in away matches. HA greater than 50% represents superior performance in home matches, whereas AD greater than 50% represents inferior performance in away matches. Since crude calculations of HA and AD are influenced by differences in team ability, multivariate regression analysis was used to control for its confounding effect.

To model HA a paired design was used whereby each match contributed 2 observations, 1 for the home team and 1 for the away team. A repeated measures regression analysis using log-link Generalised Estimating Equations¹¹ in STATA Version 11 (STATA Corp., College Station, TX, USA) was used to estimate the mean number of goals scored by home and away teams. Repeated measures analysis is used when observations occur in pairs or groups and the outcome of interest is likely to be correlated within each group. In the present study the “groups” were the individual matches and the “observations” were the number of goals scored by each of the 2 opposing teams. As this outcome is a discrete count Poisson errors were specified for the regression model. Robust estimation of variance was used, as this produces valid standard errors even if the within-group correlations deviate from the correlation structure specified in the model.¹² An additional advantage of robust variance is that it prevents under-estimation of standard errors when count data are over-dispersed. This modelling strategy has previously been used to investigate HA in terms of goals scored¹³ and disciplinary sanctions issued by referees¹⁴ in football, and is described in greater detail by Goumas.¹⁵

To determine places and seedings in its club competitions, UEFA allocates points to each European football team based on previous performance in these competitions (www.uefa.com/memberassociations/uefarankings). To control for difference in home and away team ability a linear term for the number of points allocated to each team in each season of the Champions League was added to the regression model described above. Departure from linearity was tested for using quadratic and logarithmic terms; none were evident. Team ability was also fit as an interaction with match location (0 = Away, 1 = Home) to allow for the fact that ability may express itself differently in home and away matches. Variation in HA and AD across seasons and stages of competition (group, round of 16, quarter-finals, and semi-finals) was controlled for by adding indicator variables for each of these covariates to the regression model as a main effect and interaction with match location. Due to the relatively small number of quarter-final and semi-final matches in the analysis, these 2 categories were combined.

To estimate HA and AD for individual teams the data were separated into 2 sets: an “HA” dataset including each of the selected team's home matches; and an “AD” dataset including their away matches. A unique team ID value was assigned to both the home team and away team observations for each home (HA dataset) and away (AD dataset) match played by the selected teams. Table 1 shows sample data for 2 matches played between Chelsea (1 of the selected teams) and Lazio (a non-selected team), 1 at each team's home ground. An indicator variable for each selected team was added to the regression model as a main effect and interaction with match location, with 1 team arbitrarily chosen as the reference. The regression coefficient for these interaction terms is therefore interpreted as the difference in HA or AD (on the log scale) relative to the reference team.

Table 1.

Sample observations from the Union of European Football Associations (UEFA) Champions League home advantage (HA) and away disadvantage (AD) datasets.

Dataset	Observation	Match ID	Team ID	Location	Team	Ability	Goals
HA	1	234	1	Home	Chelsea	27	2
	2	234	1	Away	Lazio	8	1
AD	1	236	1	Home	Lazio	8	0
	2	236	1	Away	Chelsea	27	4

Linear combinations of equations (“lincom” command in STATA) were used to estimate covariate adjusted HA and AD in terms of the percentage of goals scored in home matches by each team (HA) and the percentage of goals conceded in away matches by each team (AD). Use of the “lincom” command is described in detail in Goumas.1, 15 HA and AD were derived from the “lincom” regression coefficient (β) for match location (0 = Away, 1 = Home) for each team using the following equation:

$$\text{HA}\text{and}\text{AD}=\frac{\exp \left(\beta \right)}{\exp \left(\beta \right)+1}\times 100\%$$

To test for variation in HA and AD between teams, a χ² test of the joint effect of the interaction terms between match location and each team's indicator variable was carried out. p values less than 0.05 were considered to be significant.

HA and AD datasets for countries were created in the same way as that for teams. However, matches played between teams from the same country were excluded, as the purpose of this part of the analysis was to compare home and away performance between different countries. Covariate adjusted HA and AD were estimated for each country, and tests for variation between countries carried out, in the same way as described above for individual teams.

3. Results

3.1. Teams

Thirteen teams met the inclusion criteria of playing at least 50 matches during the 2003/2004 to 2012/2013 seasons of the UEFA Champions League. Table 2 shows the number of home matches played by each team, goals scored for and against, and crude and adjusted HA. Teams are listed in descending order of HA after adjusting for team ability, season, and stage of competition. This can be interpreted as the level of HA expected to be gained by each team when playing an opponent of equal ability, and eliminates any between-team variation due to confounding effects of season and stage of competition. All teams except Olympiacos and Inter Milan had a significant (p < 0.05) adjusted HA over the period of study. Although HA ranged from 58% (Inter Milan) to 73% (Arsenal), there was no statistical evidence of between-team variation (${\chi }_{12}^2=12.6;p=0.40$).

Table 2.

Home advantage (%) for individual teams in the Union of European Football Associations (UEFA) Champions League in 2003/2004 to 2012/2013 seasons.

Teama	Country	Home matches	Goals for	Goals against	Home advantage (%)
					Crude	Adjustedb (SE)	pc
Arsenal	England	47	95	29	77	73 (3.9)	<0.001
Juventus	Italy	26	44	17	72	71 (4.8)	<0.001
Barcelona	Spain	50	120	38	76	70 (3.3)	<0.001
Bayern Munich	Germany	45	103	36	74	69 (3.2)	<0.001
Real Madrid	Spain	46	108	42	72	68 (2.8)	<0.001
Chelsea	England	52	100	37	73	68 (3.1)	<0.001
Manchester United	England	47	99	39	72	67 (3.1)	<0.001
Liverpool	England	30	56	22	72	65 (4.9)	0.002
Porto	Portugal	37	49	25	66	64 (3.9)	<0.001
AC Milan	Italy	43	75	37	67	62 (3.9)	0.002
Lyon	France	41	75	41	65	61 (3.8)	0.004
Olympiacos	Greece	26	36	28	56	59 (4.7)	0.07
Inter Milan	Italy	39	64	38	63	58 (4.1)	0.06

^aTeams are listed in descending order of adjusted home advantage.

^bAdjusted for team ability, season, and stage of competition.

^cChi-square p value for adjusted home advantage being greater or less than 50%.

Table 3 presents AD for each of the selected teams. Teams are listed in ascending order of AD after adjusting for team ability, season, and stage of competition. Unlike HA, adjusted AD showed evidence (${\chi }_{12}^2=19.6;p=0.09$) of between-team variation, ranging from 45% (away advantage) for Barcelona to 68% (AD) for Olympiacos. Porto and Olympiacos were the only teams to have a significant (p < 0.05) AD, and no team had a significant away advantage. Teams with higher HA tended to have lower AD; exceptions include Arsenal who had the highest HA but also relatively high AD, and Lyon who had both low HA and AD.

Table 3.

Away disadvantage (%) for individual teams in the Union of European Football Associations (UEFA) Champions League in 2003/2004 to 2012/2013 seasons.

Teama	Country	Away matches	Goals for	Goals against	Away disadvantage (%)
					Crude	Adjustedb (SE)	pc
Barcelona	Spain	50	77	47	38	45 (4.0)	0.19
Liverpool	England	30	38	27	42	48 (4.8)	0.69
Manchester United	England	47	54	38	41	48 (4.1)	0.62
Lyon	France	41	64	54	46	49 (4.1)	0.84
Chelsea	England	52	71	54	43	49 (3.9)	0.76
Bayern Munich	Germany	45	71	56	44	50 (4.1)	0.99
Real Madrid	Spain	46	69	63	48	53 (3.6)	0.41
Juventus	Italy	26	26	27	51	54 (4.9)	0.42
Inter Milan	Italy	39	46	48	51	56 (4.4)	0.16
Arsenal	England	47	57	63	53	58 (4.1)	0.06
AC Milan	Italy	43	44	50	53	58 (4.3)	0.07
Porto	Portugal	37	43	56	57	60 (3.7)	0.007
Olympiacos	Greece	26	21	47	69	68 (4.5)	<0.001

^aTeams are listed in ascending order of adjusted away disadvantage.

^bAdjusted for team ability, season, and stage of competition.

^cChi-square p value for adjusted away disadvantage being greater or less than 50%.

3.2. Countries

Eleven countries met the inclusion criteria of their teams having played at least 75 matches in the Champions League during the period of study. Table 4 presents results of the home match analysis for each of these countries. All countries except Greece, Netherlands, Russia, and Turkey had a significant (p < 0.05) adjusted HA over the period of study. HA varied significantly (${\chi }_{10}^2=21.5;p=0.02$) between countries, ranging from 52% (Turkish teams) to 70% (English teams).

Table 4.

Home advantage (%) for individual countries in the Union of European Football Associations (UEFA) Champions League in 2003/2004 to 2012/2013 seasons.

Countrya	No. of teams	Home matches	Goals for	Goals against	Home advantage (%)
					Crude	Adjustedb (SE)	pc
England	6	169	346	115	75	70 (2.1)	<0.001
Spain	11	170	335	154	69	65 (2.0)	<0.001
Germany	8	116	226	123	65	63 (2.3)	<0.001
Italy	8	147	246	137	64	62 (2.2)	<0.001
France	8	108	167	113	60	61 (2.6)	<0.001
Ukraine	2	45	66	59	53	60 (3.7)	0.007
Portugal	4	75	95	69	58	60 (3.3)	0.003
Greece	3	48	57	54	51	58 (4.0)	0.06
Netherlands	4	49	62	57	52	57 (3.9)	0.07
Russia	5	47	53	52	50	56 (4.1)	0.13
Turkey	5	40	48	56	46	52 (4.2)	0.62

^aCountries are listed in descending order of adjusted home advantage.

^bAdjusted for team ability, season, and stage of competition.

^cChi-square p value for adjusted home advantage being greater or less than 50%.

Table 5 shows AD for each of the selected countries. After adjustment all countries except England, France, and Spain had a significant (p < 0.05) AD. Adjusted AD varied significantly (${\chi }_{10}^2=22.7;p=0.01$) between countries, ranging from 52% (French teams) to 67% (Turkish and Greek teams).

Table 5.

Away disadvantage (%) for individual countries in the Union of European Football Associations (UEFA) Champions League in 2003/2004 to 2012/2013 seasons.

Countrya	No. of teams	Away matches	Goals for	Goals against	Away disadvantage (%)
					Crude	Adjustedb (SE)	pc
France	8	108	132	144	52	52 (2.7)	0.48
England	6	169	215	183	46	53 (2.3)	0.19
Spain	11	170	226	216	49	53 (2.2)	0.16
Italy	8	147	167	193	54	56 (2.3)	0.009
Germany	8	116	151	190	56	58 (2.4)	<0.001
Portugal	4	75	75	118	61	61 (3.0)	<0.001
Russia	5	47	43	79	65	61 (3.8)	0.004
Ukraine	2	45	44	88	67	62 (3.7)	0.001
Netherlands	4	49	37	81	69	64 (3.9)	<0.001
Greece	3	48	39	101	72	67 (3.6)	<0.001
Turkey	5	40	32	81	72	67 (3.8)	<0.001

^aCountries are listed in ascending order of adjusted away disadvantage.

^bAdjusted for team ability, season, and stage of competition.

^cChi-square p value for adjusted away disadvantage being greater or less than 50%.

4. Discussion

The aims of this study were 2-fold. First, to describe a novel method of estimating HA which is based solely on home performance yet still adequately controls for differences in team ability; and second, to use this method to compare HA and AD between the best performing teams and countries in the UEFA Champions League over a 10-year period.

When adjusting for team ability, season, and stage of competition, HA did not vary significantly between the 13 Champions League teams selected for the analysis, although it did range from 58% to 73%. The lack of statistical significance may be due to the relatively small number of home matches (50 or less) played by each team. The HA estimates for these teams can be (cautiously) compared with those of previous studies which controlled for team ability. Of the 4 English clubs represented in this study, Arsenal had the highest HA (73%), with that for Chelsea, Manchester United, and Liverpool at least 5 percentage points lower. In Clarke and Norman's⁶ analysis of individual teams in English domestic leagues, which calculated HA in terms of average goal advantage per match, the relative HAs for these 4 clubs were quite different: Manchester United had the highest HA (+0.6), followed closely by Arsenal (+0.5), but with Liverpool and Chelsea much further behind (+0.3). Of course, there are several reasons why relative HAs in the current and previous study may differ. First, there is a 10-year gap separating the 2 respective study periods, and teams are therefore likely to be composed of different players who may respond differently to the factors which contribute to HA (e.g., crowd support). Second, different competitions were investigated in the 2 studies, and teams may vary in their tactical approach to home and away matches in domestic⁶ and international (present study) competitions. Third, and perhaps most important, different methods of estimating HA were used: Clarke and Norman's⁶ was based on both home and away performance, whereas that in the present study was based on home performance only.

Of the 3 Italian teams selected in the present study, Juventus clearly had the greatest adjusted HA (71%), at least 9 percentage points higher than that for AC Milan and Inter Milan. In Pollard and Gomez's⁸ study of domestic leagues in South-West Europe, Juventus also had greater HA than the other 2 Italian teams, although the between-team differences were much less than that in the present study. The similar HA for the 2 Spanish teams in the present study (Barcelona: 70%; Real Madrid: 68%) was also shown in their domestic league, with only a one percentage point difference in HA between these teams. Again it should be pointed out that the South-West Europe study covered a much different time period (from the 1920s to 2000s) than the present study, and different methods of HA estimation were used.

Unlike HA, adjusted AD showed evidence of variation between the selected teams, ranging from 45% (away advantage) to 68% (away disadvantage). Teams with higher HA tended to have lower AD. An exception is Arsenal who had the highest HA but also relatively high AD, suggesting that this team is unusually dependent on home ground effects (e.g., crowd support) for its success in the UEFA Champions League. Lyon, on the other hand, who had both low HA and AD, appears to be less affected by home ground factors than most other teams.

Although adjusted HA did not vary significantly between teams, it did so between countries. English teams had clearly the highest HA (70%), at least 5 percentage points higher than teams from any other country, whereas Turkish teams had little or no HA (52%). AD also varied significantly between countries, ranging from 52% (France) to 67% (Turkey and Greece). As with individual teams, countries whose teams had higher HA also tended to have higher AD. The high HA and low AD amongst English teams suggest that there is something unique about football in this country. English football is faced paced and physically demanding compared with that in most other European nations; perhaps a more aggressive playing style combined with home-crowd support is more difficult for less aggressive away teams to adjust to than vice versa. Also, English football stadia tend to be designed in such a way that the crowd is much closer to the playing field than football stadia in other countries, which may increase the intensity of home-crowd support, resulting in higher HA.

Differences in tactics may also explain some of the observed variation in HA and AD between teams and countries, especially in the knock-out rounds of the Champions League where away goals can decide outcomes when aggregate scores are tied.16, 17 Some teams may adopt a cautious approach to away matches, in the hope of gaining most of their points/goals at home, whereas other teams may approach both home and away matches similarly.

A limitation of this study was the relatively small number of matches (100 or less) available for each of the teams selected for analysis. This was mainly because a team qualifying the UEFA Champions League is only guaranteed of playing 3 home and 3 away matches that season, with a maximum of 6 home and away matches played if that team reaches the semi-finals. Although no significant (p < 0.05) between-team variation in HA or AD was observed, the range across teams was similar to that across countries, which did show significant variation probably due to the larger number of matches in the country level analysis. This suggests that significant between-team differences would have been detected if more data were available.

The main advantage of the present method of estimating HA over previously used methods6, 7 is that it produces HA estimates that are not influenced by the HAs of the other teams in the competition. Previous methods have the effect of “regressing” each team's HA towards the mean HA for all teams combined, and therefore reduce the power to detect differences between teams.

5. Conclusion

The method used in this study to estimate HA for individual teams was based solely on a given team's performance at home, while effectively controlling for differences in team ability. This has the advantage over previously used methods6, 7 of not being influenced by the HAs of other teams in the competition, and therefore has more statistical power to detect variation between teams. When teams were grouped by country, significant between-country variation in both HA and AD was observed, which may be due to differences in style of play and tactical approaches to home and away matches.

Competing interests

The author declares that he has no competing interests.