Factors that influence the outcome of a soccer game
Soccer outcomes can be influenced by a number of factors, such as the talent of the respective sides and luck. In addition the influence of the referee, particularly in his interpretation of key events can play a significant role in deciding individual contests.
As with players, the abilities and experience of the referees will vary and they are also prone to making errors, although they are extremely rare in number.
Therefore, it's inevitable that a partisan fan or a disgruntled manager will feel that his side is sometimes treated unfairly by the officials and occasionally claims are made that an official shows a persistent bias against a particular side.
The ref especially in his interpretation of key events can play a significant role in deciding individual contests
If this were the case, it would have obvious implications for the betting odds when these referees oversaw such sides. So does the data confirm these often widely held beliefs?
The Premier League uses around 20 referees over the course of a 380 game season, but the bulk of the matches are officiated by around half this number. During the 2013/14 season, twelve referees each took charge of twenty or more matches. So it is inevitable that a team will meet up with the same referee on a regular basis.
Over the course of their careers, it is not uncommon for a ref to take charge of the same side upwards of 20 times. Mike Dean, for example, began his Premier League career in 2000/01, and has refereed in excess of 350 top-flight matches.
Mike Dean vs. Arsenal
Dean has officiated in over 30 EPL games involving Arsenal and one particular stretch of matches between 2009 and 2013 has inevitably led to speculation that Dean had become a “bogey” ref for the Gunners.
One win and five draws, for a success rate of 0.23 from the 15 league games, does seem compelling evidence, even considering the high profile nature of many of the matches that were often against fellow title contenders.
The implied probabilities from the match odds quoted for the 15 games predict an average of around six wins and four draws as the most likely return for Arsenal over that run of games. This is consistent with a success rate of over 0.5 compared to the lowly 0.23 actually gained.
Similarly, simulating the likely outcomes of the 15 matches thousands of times, returns success rates of 0.23 or below are extremely rarely, occurring about once every 250 trials.
So it's difficult not to conclude that Arsenal’s unusually poor performance does appear to coincide with Mike Dean’s presence as the referee. And although correlation should not imply causation, many Arsenal fans appear convinced that the two are connected.
However, they are incorrect.
Firstly, the sample is a biased one. It has been selected so the sequence begins with an Arsenal loss. In the 21 games prior to the start of this sequence of poor results, stretching back to 2000, the Gunners had lost just one Premier League game refereed by Mike Dean.
Overall Arsenal’s record under Dean from 2000 to 2013 is unremarkable. They have won 15 and drawn 12, when implied betting odds suggest they should have won about 18 and drawn 8. This is below par, but is hardly significant. Small sample sizes often give slightly extreme results and so deviations of this size should be expected, even over 15 matches.
The poor sequence was merely a random set of results, rather than having a common, repeatable cause, namely the identity of the ref
The headlines regarding Dean and Arsenal only arise because the starting point of the sequence has been selectively cherry picked from part of a larger sequence. A run of consecutive wins or losses should be expected in a truly random sequence.
Also the 1 in 250 odds only apply to those specific 15 games. Arsenal has been refereed 15 or more times by more than just Mike Dean. So if each different referee had a similar likelihood of overseeing such an under performance, the chances of at least one ref partaking in a run of poor Arsenal result becomes more likely.
If we widen the net further, each of the top Premier league teams will have been refereed multiple times by numerous officials, so the chances that one top EPL team will have a rotten run of results under the same official becomes even more likely. In this case, Arsenal just happened to be that side.
In short, the Mike Dean/Arsenal interaction is almost certainly a random event that was bound to happen to someone sooner or later as more Premier league games were played. And therefore, is no help in gaining a betting edge when Arsenal and Dean meet up again.
Debunking the myth about biased referees
To satisfy ourselves that refs do not show a bias or preference for particular teams, we can look at sequences where a side has greatly under-performed when they have shared the pitch with a particular official, and then see the outcomes of the next match when the pair are reunited.
In short, test the assertion that the poor run will continue in “out of sample” data.
We took a sequence of 10 games where a side most under-performed against the expected results from the quoted odds when they had the same referee. We did this for the 50 most extreme sequences using the original Big Four teams, Liverpool, Chelsea, Manchester United and Arsenal from 2000 to 2013. And compared their results the next time they played under the apparent “bogey” ref, against the implied probabilities that they would win/draw or lose that subsequent match.
The expectation from the betting odds was that the sides as a group would win 25 of the 50 games and draw 12 for a success rate of 0.62. They actually won 26 and drew 11. This was virtually in full agreement with expectations.
In short, the under-performance is not seen in out of sample testing and this was also fully reflected in the match odds. Almost certainly the poor sequence was merely a random set of results, rather than having a common, repeatable cause, namely the identity of the ref.
They may occasionally make mistakes, but Premier League refs are not biased and soccer bettors would be unwise to bet on them being so.