Note: Special thanks to Tim at 7AM Kickoff for supplying his spreadsheet of referees and their disciplinary record during Arsenal matches.
"I know you're no longer with Arsenal, but that's too obvious
of a bad call to make, William. Give me a few minutes and I'll
make sure you guys get a chance to get back into this match."
make sure you guys get a chance to get back into this match."
If someone had told Arsenal fans on Friday that by Saturday evening they would have closed the gap to Manchester United to four points and that the Invincibles would continue to stand as the only undefeated team in the history of the Premier League, most Gooners would have been happy. Then Saturday's action unfolded, and the manner by which the Gunners arrived at such an outcome did not please a single fan. Instead of being happy, we feel cheated of an additional two points.
Arsenal's Contribution To The Newcastle Meltdown
Arsenal's Contribution To The Newcastle Meltdown
Before I explain the feelings of being cheated, I must admit a few deficiencies in the team itself. I am not usually one to moan about Arsenal constantly facing teams who seem intent to push the boundaries of fair play rules and employ a strategy of "kick them off the pitch". Facing different strategies is part of the game, and sometimes those rough strategies can be very effective at disrupting pass oriented teams. Perhaps there is an element of truth in James Martin's analysis of yesterday's action:
Quantifying Referee's Disciplinary Records
When it comes to consistency, Dowd ranks in the top third. The other three officials above him - Wiley, Clattenburg, and Jones - all have average disciplinary scores that indicate they favor Arsenal. Dowd ends up being as consistent as Howard Webb in dispensing more discipline Arsenal's way, although Webb's average of 0.8 is much lower than Dowd's. Dean ranks in the bottom half in terms of consistency, which is due to the evenhandedness he displays in most Arsenal matches that is distorted by the Manchester United match highlighted earlier.
Determining Statistical Significance
A Mann-Whitney test was used to determine if Dowd's disciplinary record against Arsenal is statistically significant compared to the rest of the referees in the league. Dowd's record was extracted from the total data set, and the two populations were compared via the test. The results of the test are shown below.
To simplify the statistical language, Dowd's calls against Arsenal are indeed statistically significant when compared to the rest of the referees who have officiated Arsenal matches - Dowd's calls result in Arsenal consistently receiving more discipline than the opposition. There is less than a 3% chance in making the incorrect conclusion (that there is bias when none is actually present). The beauty of sport is that it should have some random nature to it, and that officiating should be balanced. There must be great concern whenever such a statistically significant relationship is present, as it can ruin the balance and fairness of a match.
Conclusions
Griping about officiating after a lost opportunity can often make one sound like a sore loser. I am not one to indulge in it often. However, in some cases it might be warranted. There is a reason teams have not drawn or lost a match when up by three goals or more at the half - it's a statistical outlier. Outliers typically indicate special circumstances that help create the outlying behavior. On one hand, it might be argued that Arsenal's soft play and hot heads in the second half cost them three points against Newcastle. On the other, their hot-headedness may be due to perceived biased officiating - if a team is getting "kicked off the pitch" and feels the official isn't keeping control of things they might take matters into their own hand. It seems that with Phil Dowd it is less perceived and more actual bias.
You knew going into the second half that Barton and Nolan, experienced players who can drive opponents nuts with tough (and sometimes cheap) tackles, were going to try to provoke the Gunners. It should have been up to Arsene Wenger's men to keep their cool and see the game out. Instead, a lack of discipline cost them dearly.
Once Barton and Nolan got going, we Gooners knew it wasn't going to end well. It's too bad Zonal Marking wasn't watching the match, because we could have clear analysis of how the eventual booking of Abou Diaby changed the flow of the match. His departure, along with Johan Djourou's injury, exposed our thin back line that was not upgraded during the transfer window. At that point, the match turned and the rest was history.
While some can fairly criticize Arsenal for losing such a lead, one must keep one fact in mind - the resultant draw for a team with a four goal lead was an outlier. It had never happened in the history of the Premier League. In fact, no team with a three goal lead at the half from the 05/06 to 09/10 seasons had lost or tied a match. Also, recall that earlier this season Arsenal lost at home to Tottenham after being up 2-0 at the half, an event that has only happened 2% of the time when a team has a two goal lead at the half. The common denominator in both matches, besides Arsenal choking in the second half, was referee Phil Dowd. That's why we feel cheated.
Luckily, Tim at 7AM Kickoff blog has been keeping track of the discipline record of each Arsenal match for the last two seasons, as well as the referee who dispenses such discipline. He was gracious enough to supply me with his spreadsheet with the intent of examining which referees consistently give more cards to Arsenal over the last two years.
Quantifying Referee's Disciplinary Records
As card count, like goals scored, can be a bit low and not provide the resolution needed for statistical analysis, I converted the cards given in each match to points against each team following the Premier League Fantasy Football rules for disciplinary cards:
- 1 point for every yellow card
- 3 points for every red card (includes any yellow card points)
I then calculated the difference between the disciplinary points acquired by Arsenal and the points acquired by the opponent in each match. A positive differential indicates Arsenal is penalized more, while a negative differential indicates greater disciplinary action against the opponent. Totaling up the disciplinary differences from each match officiated by a referee gives us a good idea of that referee's bias. The tables below yield some interesting insights. The first shows the number of matches officiated by each referee, the second table displays the average disciplinary difference for each referee, while the third quantifies the consistency of their disciplinary difference by using the standard deviation of their differences. The last two tables isolate for referees who have officiated at least three matches, as three samples are the minimum needed to calculate a standard deviation.
From the average difference table, we can see that Phil Dowd is the referee that, on average, penalizes Arsenal the most compared to their opposition. Sitting a close second is Mike Dean. While we're familiar with Dowd's refereeing of the Spurs and Newcastle matches this season, Dean deserves special mention for awarding Wayne Rooney a penalty in the 2-1 loss at Old Trafford last season. In that same match, Dean gave Arsenal six yellow cards to Manchester United's two. Ironically, Dean officiated the Newcastle match at the Emirates earlier this season that ended in a 1-0 loss for Arsenal, although his officiating was pretty even that day.
When it comes to consistency, Dowd ranks in the top third. The other three officials above him - Wiley, Clattenburg, and Jones - all have average disciplinary scores that indicate they favor Arsenal. Dowd ends up being as consistent as Howard Webb in dispensing more discipline Arsenal's way, although Webb's average of 0.8 is much lower than Dowd's. Dean ranks in the bottom half in terms of consistency, which is due to the evenhandedness he displays in most Arsenal matches that is distorted by the Manchester United match highlighted earlier.
Determining Statistical Significance
A Mann-Whitney test was used to determine if Dowd's disciplinary record against Arsenal is statistically significant compared to the rest of the referees in the league. Dowd's record was extracted from the total data set, and the two populations were compared via the test. The results of the test are shown below.
To simplify the statistical language, Dowd's calls against Arsenal are indeed statistically significant when compared to the rest of the referees who have officiated Arsenal matches - Dowd's calls result in Arsenal consistently receiving more discipline than the opposition. There is less than a 3% chance in making the incorrect conclusion (that there is bias when none is actually present). The beauty of sport is that it should have some random nature to it, and that officiating should be balanced. There must be great concern whenever such a statistically significant relationship is present, as it can ruin the balance and fairness of a match.
Conclusions
Griping about officiating after a lost opportunity can often make one sound like a sore loser. I am not one to indulge in it often. However, in some cases it might be warranted. There is a reason teams have not drawn or lost a match when up by three goals or more at the half - it's a statistical outlier. Outliers typically indicate special circumstances that help create the outlying behavior. On one hand, it might be argued that Arsenal's soft play and hot heads in the second half cost them three points against Newcastle. On the other, their hot-headedness may be due to perceived biased officiating - if a team is getting "kicked off the pitch" and feels the official isn't keeping control of things they might take matters into their own hand. It seems that with Phil Dowd it is less perceived and more actual bias.
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