Are football referees really biased and inconsistent?

In professional football disciplinary transgressions by players and sanctions taken by referees provide a rich source of subject material for debate among pundits, journalists and the general public. Although newspaper and television pundits routinely and piously deplore incidents involving foul play or physical confrontation, there is no doubt that a violent incident, immediately followed by the referee’s theatrical action of brandishing a yellow or red card in the direction of the miscreant, makes an important contribution to the popular appeal of the football match as a spectacle. Due to the ever-increasing scope of television coverage of football especially at the highest level, together with improvements in video technology, the actions of players and referees have never been more keenly and intensely scrutinized than they are in the modern-day game.

Here you have performance analysis in football the margins separating success from failure can be slender, and often depend ultimately on split-second decisions taken by referees and players in the heat of battle. Yet the financial implications of success or failure for individual football clubs and their players can be huge. The football authorities are under intense pressure from all sides to take steps to ensure that refereeing decisions are as fair, consistent and accurate as is humanly possible. In an attempt to learn more about disciplinary sanction we carried out a statistical analysis of patterns in the incidence (or frequency) of disciplinary sanction using data on the 4,940 matches played in the English Premier League between the 1996-97 and 2008-09 seasons, inclusive.

The statistical analysis allows for tests of several hypotheses concerning patterns in the incidence of disciplinary sanction, including:

• A home advantage hypothesis: the tendency for away teams to incur more disciplinary points than home teams is solely a corollary of home advantage, or the tendency for home teams to win more often than away teams
• A refereeing consistency hypothesis: the propensity to take disciplinary action does not vary between referees
• A time consistency hypothesis: the overall incidence of disciplinary sanction is stable over time and unaffected by changes to the content or interpretation of the rules

The following questions are also examined in the analysis:

• Does the average rate of disciplinary sanction against each team depend upon which team is the favorite and which is the underdog?
• Does it depend upon whether the match itself is competitive (between two evenly balanced teams) or noncompetitive?
• Does it depend upon whether end-of-season outcomes are at stake for either team?
• Is it affected by the stadium audience?

The incidence of disciplinary sanction and variation across referees

We attempt to explain the variation in the total number of disciplinary ‘points’ incurred by the home and away teams in each match. The disciplinary points are calculated by awarding one point for a yellow card and two points for a red card. Table 1 (below) shows the frequency distribution for the number of disciplinary points incurred by the home and away teams in the 4,940 matches during the sample period. For example, there were 340 matches where neither side incurred disciplinary points, 443 matches in which the home team received no disciplinary points but the away team incurred one point, and so on. In our statistical models, the number of disciplinary points that the home and away teams can expect to incur in each match is conditional upon a number of factors that vary from match to match (and these relate to the hypotheses and questions of interest mentioned above).

Inconsistency in the standards applied by different referees is among the most frequent causes of complaint from football managers, players, supporters and media pundits. Table 2 summarises the average numbers of disciplinary points per match awarded against the home and away teams and against both teams combined, by each referee who officiated at least 30 Premier League matches during the study period. There appears to be considerable variation between the propensities for individual referees to take disciplinary action. For example, the most lenient referee (Keith Burge) averaged 2.526 disciplinary points per match over 57 matches, and the most prolific (Mike Reed) averaged 4.541 points over 85 matches.

Are referees inconsistent?

Does the variation in refereeing standards suggested by Table 2 constitute statistical evidence of inconsistency in refereeing standards? Our results say it does. In other words, individual referee effects make a significant contribution to the expected number of disciplinary points incurred by the home and away teams in each match, indicating that there are inconsistencies between referees in the interpretation or application of the rules. There is also evidence of variation between referees in the degree of home team bias and this variation contributes to the overall pattern of refereeing inconsistency.

Our research also found:

• The tendency for away teams to incur more disciplinary points than home teams cannot be explained solely by the home advantage effect on match results. Even after controlling for team quality, a (relatively strong) away team can expect to collect more disciplinary points than a (relatively weak) home team with the same win probability.
• The incidence of disciplinary sanction tends to be higher in matches between evenly balanced teams, in matches with end-of-season outcomes at stake, and in matches that attract high attendances.
• Home teams appear to play more aggressively in front of larger crowds, but perhaps surprisingly crowd size does not influence the incidence of disciplinary sanction against the away team.
• Despite an increase over time in the number of offences subject to disciplinary sanction, there is no consistent time-trend in the data: players and officials appear to have adjusted to changes in the rules so that in the long run the rate of disciplinary sanction remained approximately constant.

Conclusion

By providing a comprehensive statistical analysis of patterns in the award of yellow and red cards, this study has given the English football authorities and other interested parties a firm factual basis for policy decisions and debate concerning the interpretation and implementation by referees of the rules governing disciplinary sanction.

References

P Dawson, SM Dobson, JA Goddard and J Wilson (2007), Are football referees really biased and inconsistent? Evidence on the incidence of disciplinary sanction in the English Premier League. Journal of the Royal Statistical Society, Series A, 170 No.1 pp 231-250.

SM Dobson and JA Goddard (2011), The Economics of Football, Cambridge University Press (2nd edition).

Table 1 Frequency distribution for home team and away team disciplinary points

Source: The Football Association

Table 2 Average number of disciplinary points awarded per match by referee