By Daniel Silberwasser
Home field advantage has become a crucial element of professional soccer. The final matches of major tournaments such as the UEFA Champions League are played in predetermined third party stadiums, and unlike other professional sports in the US, in order to establish strength of schedule parity across teams, during the regular season, each team plays every other team both at home and away. Studies have found that home field advantage certainly exists when it comes to winning percentage. However, few studies have compared foul and booking differences between teams playing at home and away. HSAC has already delved into questions of fouls in derbies, but I wanted to look at foul rates from a slightly different angle.
Looking at around 4,000 games from the previous eleven Premier League seasons made available online by football.data.co.uk, I found that at a 99% significance level, away teams on average earn more fouls and more bookings (yellow cards + red cards). The home and away team averages for both fouls and bookings are visualized below.
In order to determine statistical significance, I ran two paired t tests on the differences of home and away averages per team, one for fouls and one for bookings. This test found that teams on average commit approximately 0.50 more fouls when playing away than at home and receive an additional 0.40 bookings. The p-value for the study comparing the difference in mean fouls was 3.24×10-5 and the p-value for the study comparing the difference in mean bookings was 3.50×10-14, indicating the differences in means is strongly significant. If the p-values aren’t convincing enough, the differences in fouls and bookings when a team is home as opposed to away are visible in the chart above.
Although I think it’s pretty interesting in itself that teams are called for fouls and are booked significantly more when playing away than when playing at home, what I found particularly surprising was that the home and away effect was much stronger for bookings than for fouls.
Although both t tests were significant, the test for the difference in mean bookings was dramatically more significant than the test for the difference in mean fouls. This is confirmed in the figure above. There are some teams that foul more at home than away. Blackpool and Blackburn are notable in that regard. However, the majority of teams foul more when away than home and significantly so.
In contrast, when it comes to bookings, there isn’t a single team that is booked more at home than away. This is reflected in the fact that a team’s away fouling is more highly correlated with its away bookings (0.36) than a team’s home fouling is correlated with its home bookings (0.29). A t test comparing the cards given to the home team per foul to the cards given to the away team per foul confirms this finding as well. The test, with a p-value of 2.2×10-16, finds that teams earn an additional 0.036 cards per foul when playing away. Considering away teams commit about 12 fouls a game, this seemingly minuscule effect has real impact over the course of a season. Over the course of ten seasons, away teams have been booked almost 2,000 times more than home teams.
I can think of two possible explanations for this phenomenon, which aren’t mutually exclusive. First, the bad guest hypothesis: even though teams might not be fouling that much more when playing away, they are fouling more ruthlessly when away, leading to more bookings. One can imagine that playing in enemy territory with thousands of unruly fans hurling insults might goad teams into playing more aggressively. Second, the bad host hypothesis: referees are biased, booking away teams more regardless of whether they’re actually playing more aggressively and not booking home teams when they are playing aggressively. Studies looking at other sports have shown referee biases towards home teams.
In order to disentangle whether a team’s increased likelihood for being called for fouls and for being booked when playing away is due to a change in team strategy (the bad guest hypothesis), ref bias (the bad host hypothesis), or other factors, further studies could look at possession and other advanced game statistics to determine whether a team does change the aggressiveness of its play when competing away.
Until then, we can sleep soundly knowing that we have additional statistical reasons for hating our opponents.
The data used for this post can be found here.