Watching Premier League football, you frequently hear claims by away team managers that they have been short-changed by a weak/incompetent ref, more often than not concerning penalties given or not given. Are these managers ever right or are they just suffering from a confirmation bias?
While it is true that opposition teams get far fewer penalties at Old Trafford, Anfield and Stamford Bridge, it is very difficult to determine whether this represents a big-team/home team bias. Man Utd playing at home will normally have more of the play and more penalty box action than their opponents and, as such, would be expected to win more penalties.
This very clever paper seeks to provide an answer by focusing on something that is completely at the referee’s discretion, the amount of time added on at the end of a game. In the authors’ words:
Referees have discretion over the addition of extra time at the end of a soccer game to compensate for lost time due to unusual stoppages. We find that referees systematically favor home teams by shortening close games where the home team is ahead, and lengthening close games where the home team is behind. They show no such bias for games that are not close. We further find that when the rewards for winning games increase, referees change their bias accordingly.
The data is from matches in Spain's La Liga and the authors find that the relevant mechanism is the size of the home crowd. In other words, the more fans a team has at a game, the more they will be favoured by the ref. The authors see this as evidence that social pressure affects referees' decision making. However, it is unclear why this should be the case. It is unlikely that the refs have been bribed (this is Spain, not Italy) and unlikely that refs are afraid of physical harm (again, this is Spain, not Bulgaria). So where is the benefit? Are referees being influenced without realising it, or are Spanish refs all utilitarians, seeking to maximise the welfare of the largest number of people in the stadium? Suggestions in the comments section please.