Are some referees disproportionately biased towards home teams?

No football fan ever believes the referee is on their side. Most, however, will accept that officials are subconsciously swayed by home support; indeed the authors of Scorecasting believe almost all of home field advantage can be explained by involuntary refereeing biases.

But are some Premier League referees more susceptible to these biases than others?

The chart below illustrates home points per game by Premier League referees who have officiated at least 60 games since the start of the 2010-11 season. Also plotted is the expected home points per game by referee, according to odds set by bookmakers. A big assumption here is that bookmakers do not adjust their odds based specifically on who is refereeing the match.

Matches officiated by Michael Oliver or Martin Atkinson saw home teams collect 1.82 points per game in this period, but these teams were expected to collect only 1.60 points under Atkinson compared to 1.69 under Oliver. This difference is explained by the fact that Oliver has tended to officiate more home games for the traditional ‘big’ clubs. So whilst both would, on a very superficial level, appear to disproportionately favour home teams, Atkinson’s results are more extreme than Oliver’s.

What we want to know though is how extreme are some of the larger differences in points and expected points? How rare would it be to see a typical referee oversee 1.82 home points per game when expected to oversee 1.60 home points per game?

We can do this by simulating the matches thousands of times and seeing how many times the results were as in favour of the home or away team:

To explain some of the more extreme values:

• In just 3% of the simulations of Martin Atkinson’s matches did the home teams collect more than or equal to 222 or points in total. In other words, we would only expect to see home teams do so well under a typical referee just 3% of the time.
• In just 4% of the simulations of Neil Swarbrick’s matches did the home teams collect less than or equal to 86 points in total. In other words, we would only expect to see home teams do so poorly under a typical referee just 4% of the time.
• In just 2% of the simulations of Anthony Taylor’s matches did the home teams collect less than or equal to 121 points in total. In other words, we would only expect to see home teams do so poorly under a typical referee just 2% of the time.

This is potentially interesting, but only if we would expect to see such trends continue into the future. It’s not implausible that home teams have consistently managed to produce results on their own merit in matches that Atkinson just so happened to officiate.

I’ve therefore split the games refereed by each of the officials into three groups, and compared the home points per game above/below expectation in one period to the next. For example, in Martin Atkinson’s (MA on chart) first group of games, home teams won 0.3 points per game more than expected, followed by 0.3 points per game again in the second group. This level of repeatability, however, was scarce among the group as a whole.

Put simply, if you were thinking of placing a bet on the basis of a referee having particularly favoured home or away teams recently, you might want to think again.

Application

Having read this far, you might be disappointed to be learn that in general, there’s no real trend for referees to repeatably favour home or away teams above what we would expect.

However, that is not to say that the results of Atkinson, Swarbrick and Taylor should be dismissed as entirely freak occurrences. These statistics can be the starting point for a more detailed analysis of individuals, and may reveal certain traits or tendencies that lead to involuntarily favouritism of a certain type of team.