Judges Bias in Football: Judge` Influence on Bets

The result of a football match depends on a number of factors. Among them is the personality of the arbitrator. In particular, his interpretation of the key events of the match can play a decisive role in the fate of individual confrontations.

As in the case of football players, the judges’ abilities and experience differ, and they are also prone to make mistakes, although they are extremely rare.

Thus, there are inevitable situations where team fans or coaches have a feeling that their team is judged unfairly, and sometimes there are complaints that a particular judge is constantly demonstrating a prejudiced attitude toward a particular team.

If this were the case, then it would entail obvious shifts in the coefficients to be presented for matches involving these teams, when a particular judge is assigned to them. But do we have any statistical data that support these widely held beliefs?

The English Premier League uses about twenty referees for 380 games of the season, but most of these matches are served by about half of this number of arbitrators. During the 2013/2014 season, twelve judges served twenty or more matches. Therefore, it is inevitable that the team will meet with the same judge on a regular basis. For many referees, it is not uncommon for the whole career to judge matches of a certain team more than 20 times. For example, Mike Dean started his career in the Premier League from the season 2000/2001 and successfully worked 350 first-class matches.

Mike Dean vs. Arsenal

Dean was assigned to more than 30 Premier League matches with Arsenal, and a specific interval from 2009 to 2013 led the fans to the assumption that Dean is an extremely “terrible” judge for the “Gunners”.

One win and five draws and a success bet of 0. 23 over 15 matches are eloquent figures, even given the high status of many matches, where Arsenal played against their opponents in the fight for the title. P OTE editor: to calculate the success bet is equal to 1 draw 0.5 victory. That is, 1 victory and 5 draws is 3.5 (three and a half) wins, which is 23% of 15 matches.

The estimated probability of the outcome of the match, which can be calculated based on pre-match factors, predicted an average of 6 Arsenal wins and 4 draws in these 15 matches. That is, the expected success bet was more than 0. 5 per game, while in reality it was significantly lower – 0. 23.

If you simulate the results of these 15 games a thousand times, then the success bet of 0. 23 or lower will be extremely rare – about every 250th attempt.

So it’s hard not to conclude that the unusually low performance for Arsenal is really related to the work of Mike Dean as a referee in these matches. And although the correlation should not imply a causal condition, many fans of Arsenal are convinced that there is a connection. Nevertheless, they are mistaken.

First, the sample is biased. It begins with the unsuccessful stretch for Arsenal. For 21 games that preceded this sample, the “Gunners” lost just one Premier League match of those that served Mike Dean.

In general, the statistics of “Arsenal” in matches with Mike Dean as the main referee is not noticeable. The team won 15 times and 12 tied, while on pre-match expectations it was 18 times to win and draw 8 times. Small sample sizes often give sensational results, and similar deviations are quite expected, even in samples in which there are more than 15 matches.

Headlines of newspapers with the participation of “Arsenal” and Mike Dean arise just because of an unsuccessful sample. A series of victories or defeats arise in a truly random sequence.

Also, the odds of 1 to 250 apply only to those 15 games. Games “Arsenal”, for 15 pieces or more, judged among the referee is not the only Mike Dean. Therefore, if each of these judges is subjected to such an imitation to calculate the success of Arsenal’s performances, the chances that at least one of these referees will show very bad results for Arsenal are very high.

And if we go further, we will see that each of the top teams of the English Premier League has arbitrators who have served its matches a large number of times, so that the chances that when the same judge is working, one of the teams will show terrible results, even more. It so happened that such a team was Arsenal.

In short, Mike Dean’s relationship with Arsenal is almost certainly an accidental one, and such an event should have happened sooner or later, given the large number of matches in the Premier League.

And, consequently, Mike Dean’s personality should not affect our bets when he and Arsenal meet again.

The destruction of the myth about the bias of judges

To finally make sure that the referees do not show prejudices or preferences with respect to individual teams, we took sequences of matches when the team played poorly when servicing the games by a particular referee, and compared with subsequent games where he was scurrying judged. That is, they studied the possibility that the “black streak” with this judge will continue, beyond the general statistics.

To do this, we took sequences of 10 matches in which the team performed worse than expected, if you focus on the odds of the bookmaker, with the work of a single arbitrator. We did this for the 50 “blackest” bands in four English top clubs – Liverpool, Chelsea, Arsenal and Manchester United – between 2000 and 2013. After that, we studied the result of the match following each series of 10 bad games for the team, with the same referee judging.

Expectations based on the coefficients for these matches were such that teams in total were to win in 25 of 50 games and 12 times to draw, with a success bet of 0. 62. In fact, the team won 26 times and 11 times in a draw in these 50 games, which almost coincided with expectations.

In short, bad results do not go beyond the scope of statistics and are fully reflected in pre-match expectations. Almost certainly the sequence of bad performances is just a random set of results, and not the influence of the referee’s personality, contrary to the general opinion.

Sometimes the referees can make mistakes. However, the Premier League referees are not biased, and for a player at football betting it will be foolish to bet on the outcome of a match based on the identity of the referee.