We all know the feeling well. You are sitting in your lounge room, watching a match you have spent all week waiting for. Your model found an amazing value bet, in fact you couldn’t believe your eyes when you read the opening prices for the weekend. You confidently put down your hard earned dollars, and agonise through every kick, every tackle, and more importantly every referee decision.
Or you could be sitting in the stands of your local stadium at an important crunch match. Your team desperately needs the three points, and the match is poised at a crucial moment when either team could grab the win. And then it happens, a crucial call goes against the home team, the crowd rise as one to voice their disapproval. You can’t believe yet another call has gone against your team. It must be the referee, he’s been out for your team all day.
But is that the case? Do we just see the referee’s performance through our own bias glasses, or are some referees just out to get the home team? Or more simply put, does the referee influence the outcome of football matches, and if so, how, and towards which team?
Luckily for us there has been quite a bit of academic research into the impact of referees in football matches, and as a long suffering fan, the result might just surprise you.
Measuring the impact of a referee on a match is in itself quite difficult. Unless you are a qualified referee assessor, and watch every game to mark each decision individually as correct or incorrect, you are never going to have a full picture of exactly how much of an influence a referee has on the final result of a match. However there are some key statistical indicators which can be used to measure a referee’s leaning towards one team or another. These are fouls awarded, penalties awarded, yellow cards issued, red cards issued, and the length of injury time. Of course knowing how a referee can influence these different part of the game is not only important for the outright result of the game, but with a multitude of proposition bets now available on every match it may pay to make adjustments to your standard possion distribution model if you plan on making any sort of wager on cards issued, the awarding of a penalty, or a player being sent off.
Firstly we will start our investigation into the impact of referee bias on a match with one of the most mysterious and often contentious parts of any match, injury time. Law 7 of the world famous FIFA Laws of the Game relates to the duration of matches. As well all know football is played in two equal 45 minute halves, but there is one kicker, the referee may add additional time onto the end of a half for “time lost”. This additional period of extra time is more often known as “injury time”, and makes up for any lost time throughout the half through substitutions, player injuries, and time wasting. This allowance for time lost is “at the discretion of the referee”, who is the sole judge of time for the match.
Injury time is often a point of contention for many fans due to its sometimes seemingly random nature, and bias towards certain teams. But do referees really shorten or extend injury time to help teams have a chance of scoring a crucial goal, or deny a team by having a shorter period?
In a study of 750 Spanish professional football matches, we looked at the amount of injury time added to a match related to the score at the completion of the 90 minutes of normal time. On average referees added a further three minutes to the end of the second half, but it is when the score at the 90 minute mark is considered that their results get interesting.
On occasions when the home team were losing by one goal, the injury time was 35% longer than average, and conversely when the home team was leading by one goal the injury time was 29% shorter than average. However this change is only seen when a match is close, if either team is winning by two or more goals, there is little or no change from the average three minutes.
But what is it exactly that is influencing referees to be bias towards the home side? We believe that it could simply be the pressure of the home crowd through social pressure. They found that for every 1 standard deviation increase (17,780), on the average crowd of 27,840, referees became 20% more bias towards the home team.
But they are not alone in this theory, there have been many studies conducted on the phenomenon of social pressure and its influence on football referee. In a study of 5244 English Premier League matches, we found that not only does crowd size effect the bias of referees towards the home team, but that experienced referees tend to be less bias towards the home team than inexperienced referees.
This study also provides us with some valuable data surrounding the differences seen for home and away teams regarding different aspects of play affected by referees. Covering seasons 2015-2019, home teams score 1.5 goals compared to 1.1 for the away team, but given the well documented “home ground advantage” in football this is hardly a surprising result. What is more surprising is when you look at cautions and dismissals. On average home teams receive 1.171 cautions per match compared to the away teams 1.621, an amazing 38% increase. Dismissals? On average there are 0.056 dismissals per match for the home side and 0.094 for the away team, a difference of 68%!
Do teams really play that differently when they are away from home? It is difficult to believe that a team is collectively behaves that much worse, or intentionally alter their play to such an extent simply because they are playing away from home. It makes sense that there are other factors at play, and put simply it is the effect of the crowd on the referee.
Need more proof? We again looked at the social pressure on referees from home fans using the unique opportunity provided when in response to crowd violence the Italian Government ordered that 24 Serie A and Serie B matches be played at empty stadiums. Comparing these matches to those with fans in the stands, referees were found to give 2.6 fewer fouls per game, a number made more significant by the fact that home teams were given 1.7 more fouls per game! In terms of cards, both the home and away teams received less cautions, with the away team being issued 1.16 less cautions per game, and yes you guessed it, they also received less red cards.
Through this unique study where “control” matches could be assessed compared to matches with a crowd, the overall bias effect from the referee was thought to be 4.56 for fouls, 0.61 for cautions and 0.07 for red cards. Studies have also been conducted with referees watching video replays of matches and being asked to make decisions on fouls with a home crowd sound effect being played. Sure enough, the louder and more vocal the crowd, the more the referee made decisions favouring the home team.
In another study using the English Premier League, we found that not only do away teams receive more cautions in matches, but also that underdogs in matches receive more cautions than favourites. This may be explained by the need for a lesser team to foul opposition players as the stronger opponent has more scoring opportunities. Not surprisingly they also found that the closer the two teams are in ability, and the higher the stakes of the game, the more cautions are given.
So we have now established that home teams certainly do receive favourable circumstances when it comes to injury time, and that away teams receive more cautions and dismissals than home teams. We also know that the larger the home crowd, the larger the bias towards the home crowd tends to be, and that the more experienced a referee is, the less he is influenced by the crowd. But can even the architecture of the stadium influence the match?
We again looked that the influence of the referee bias on football matches. An once more he discovered that there is a home bias in regards to the addition of injury time, but also that referees tend to favour the home team in decisions to award goals and penalty kicks. However this influence reduced with higher percentage of away supporters in the stadium, and that the referee bias was higher inside rectangular stadiums compared to those with running tracks.
Again it was found that there was a bias towards home teams as seen in previous studies, as well as against underdog teams. Interestingly in comparing stadiums, we discovered that rectangular stadiums in the Bundesliga had fewer cautions for the home team, again displaying the influence of “social pressure” placed on the man in the middle.
So there it is, there certainly can be referee bias towards football teams. If your team is an away underdog, playing at a large rectangular stadium with a sold out partisan crowd they are more likely to receive more cautions, have a higher probability of having a player sent off, is less likely to have a penalty awarded, and if the match is close have injury time in favour of a home team result.