Quantifying incentive (in)compatibility: A case study from sports

The existence of home advantage has been established for all major professional team sports in England and North America. The advantage was found to be greatest in soccer, with the home team currently obtaining about 64% of all points gained in the English Football League. Home advantage has changed very little since the formation of the League in 1888 and there are only small variations between the four Divisions of the League. The advantage is less marked in local derbies, in the FA Cup and in nonprofessional competitions. It is greater in the European Cup and increases as the stages of the competition progress. The allocation of three points, instead of two, for a win in the Football League has not changed home advantage, but its effect has been greatly reduced in the GM Vauxhall Conference where an away win gains more points than a home win. The statistical evidence suggests that crowd support and travel fatigue contribute less to home advantage in soccer than do the less easily quantifiable benefits of familiarity with conditions when playing at home. Further possible explanations for the advantage are discussed in the light of findings in other sports.

Officiating bias is thought to contribute to home advantage. Recent research has shown that sports with subjective officiating tend to experience greater home advantage and that referees' decisions can be influenced by crowd noise, but little work has been done to examine whether individual referees vary in their home bias or whether biased decisions contribute to overall home advantage. We develop an ordinal regression model to determine whether various measures of home advantage are affected by the official for the match and by crowd size while controlling for team ability. We examine 5244 English Premier League (EPL) match results involving 50 referees and find that home bias differs between referees. Individual referees give significantly different levels of home advantage, measured as goal differential between the home and away teams, although the significance of this result depends on one referee with a particularly high home advantage (an outlier). Referees vary significantly and robustly in their yellow card and penalty differentials even excluding the outlier. These results confirm that referees are responsible for some of the observed home advantage in the EPL and suggest that home advantage is dependent on the subjective decisions of referees that vary between individuals. We hypothesize that individual referees respond differently to factors such as crowd noise and suggest further research looking at referees' psychological and behavioural responses to biased crowds.