Farewell, El Capitan

All We're Left With Is Memories and Dreams of What-Might-Have-Been

When I went to bed Sunday night I was planning on spending this evening writing about the 2011-12 EPL season outlook using my input to the Transfer Price Index's season predictions.  I thought I had come to terms with the departure of of Cesc Fabregas over the summer, and certainly in the last week as it became abundantly clear that Barcelona were going to have their man no matter what.  All of that changed on Monday morning, as I woke to the inevitable news of his sale and for some strange reason I felt emotional loss.  It's odd for me, as I've only been following the Gunners for 2+ seasons now.  I certainly have come to love them because of their beautiful play, rich history, and their intention to not buy championships but build teams from the (relative) ground up to win them as a club and not a rich man's toy.  But I've never seen them in person, and certainly have avoided buying any player's jersey in anticipation of the inevitable transfer they will leave upon.  I've intentionally avoided making any emotional attachments knowing the brutal business realities within which a club must work.

At the same time, I've probably never typed "I <3..." for any other player except Cesc.  Those unfortunate enough to listen to my Twitter feed during a match certainly saw that phrase on occasion the last two seasons.  For some reason I was magnetically attracted to Cesc, and loved him for what he embodied and what he stood for the last 5-6 years.  It was the realization Monday morning - the fact that I will likely NEVER type "I <3 Cesc" ever again - that made me think about why such a forgone conclusion seemed to affect me so much.  This blog post is an attempt to explain the thoughts I've had in the last 24 hours.

The Emotional: Breaking Up Is Hard To Do

During the drive in to work on Monday I had a flood of emotions come over me.  Cesc's departure was the first big loss by the club in my brief fandom, so I wondered why this one seemed to bother me so much.  Sure, losing a captain is never easy for club, especially when it seems as if he just might be coming in to his prime.  But as I thought about those emotions, I concluded it was something deeper.  I finally realized what was bothering me- these are some of the same emotions I felt when I went through my divorce from my first wife.  Certainly this was nowhere near as personal, nowhere near as intense, but the feelings were similar nonetheless.

• Betrayal of promises of a commitment to the club and its goals.  


• The finality of it all after such a long transfer process.


• Even the issue of seeing someone you considered committed to you (or your club) kiss the suitor to which you lost them.  

And that's how I choose to view Cesc's departure: a divorce, or at least an end to a long-term relationship where the two involved in the relationship made life-altering plans around each other.

Marriage Counseling, Arsene Style

Most relationships fail because those involved in them mistakenly believe love is all they need.  Marriages don't survive on love alone - they survive because that love allows for the couple in the marriage to become more than the sum of their parts.  Different marriages judge that sum by different measures - some desire money, some desire possessions, others desire spiritual growth, others find a higher purpose for their marriage in the rearing of their children.  There are a millions of motivations for being married, but the most durable marriages rely on the concept of a "sum is greater than its parts" and then utilize love to realize that sum.

In the case of Cesc and Arsenal, that's where the relationship broke down.  It wasn't about the money - he's paying €1M a year to Arsenal for five years for the privilege of going to Barcelona.  It wasn't about the love - he reiterated his love for the club and its supporters even as he was introduced at Camp Nou.  It wasn't really about going home, that was just a side benefit.  Does anyone really think he would return to Barcelona if they weren't a more prestigious club than Arsenal at the moment?  It was about the sum not being greater than its parts.  In being introduced at the Camp Nou, Cesc said of his reason for the departure:

"It wasn't really the losing, it was the routine. Year after year, it was always the same story.  Fighting until the end only to see we didn't have the energy, in the semifinals, the finals, to arrive in the final sprint."

Cesc knows he's a great player.  What he was looking for in departing for Arsenal eight years ago was a chance to contribute to a world class club's already rich history.  He could have done that at Barcelona, but he chose to take his talents to London and attempt to build upon what Henry, Bergkamp, and others had already started under Arsene Wenger.  He soon found himself being the centerpiece the team was built around, both tactically and leadership-wise.  Yet season after season, he saw his own club falter in the business end of the season while his former club became one of the best club sides of all time.  He was brought in to a great club that was winning championships, was told the entire team was being (re-)built around him, and the rebuilding project had yet to bear fruit over six seasons of its implementation.  Cesc had enough of the promises of something better that went continuously

None of this makes Cesc's departure any easier - not for him, not for the club, and not its supporters.  No matter how rational the move might seem, we supporters felt he was our captain.  During a particularly challenging time in the club's history, we were looking to him to lead rather than leave.  We wanted him to recommit to the club, just as we wanted the club to recommit itself to spend the funds to build the championship team he deserved.  In some ways, we entered "counseling" last summer and agreed to work on things - compete strongly in 2010/11, win a cup or two, and perhaps we could patch things up after five years of nothing.  That clearly wasn't the case, and Wenger saw the writing on the wall.  The counseling failed, and the divorce proceeded with Wenger reluctantly granting his captain the divorce he desired.

But did it make logical sense from Cesc's perspective, or was he making a decision as emotional as the supporters' reactions to it?

The Analytical: Cesc is Justified in Leaving

Let's look at what Cesc arrived to and what he left behind, and judge his decision in the totality of the data.  As you know, I've spent much digital ink demonstrating that championship caliber teams are built upon transfers via my work in the Transfer Price Index (TPI) database.  It is that outlook I carry over in to the analysis below.

Note: All transfer figures are in 2011 TPI numbers

• Player Purchases: After spending big money on players like Dennis Bergkamp (£25.1M), Thierry Henry (£29.9M), Marc Overmars (£21.5M), and Sylvain Wiltord (£29.5M) during the championship years, Arsenal would only buy two players during the trophyless years for more than £20M - Alexander Hleb (£26M) and Theo Walcott (£27.9M).


• Squad Cost: The total squad cost (Sq£) was £252M in 2003-04, but by the end of the 2010-11 season it had been reduced to £155M (a 38% reduction). This has led Arsenal to fall from a solid third position within the Big Six (and nearly on par with Manchester United in 2nd position) in 2003-04 to a clear sixth position in squad cost by 2010-11 (click on graph below to enlarge).

• Starting XI Cost: When Fabregas arrived at the start of the 2003-2004 season, Arsenal had an average starting XI cost (£XI) of £120M.  By the time of his final season at Arsenal, the average £XI had fallen to £71.5M (a 40% reduction). Arsenal's slide in the £XI metric versus the other Big Six clubs is similar to that seen for the Sq£ metric (click on graphic to enlarge).

• Performance vs. Transfer Expectations: During the Invincibles run, Arsenal earned an astonishing 0.96 PPG above what was predicted by the m£XIR model.  That had decreased to a more pedestrian 0.38 PPG by last season, with each of the last four seasons seeing a steady erosion from 0.63 PPG over performance in 2007/08 to the 0.38 PPG experienced last season.  This suggests that Wenger's youth project that has focused on reducing squad costs and preserving performance clearly is not working, even given the reduced transfer costs of the assembled team.  Especially troubling to Cesc must have been the championship caliber performances over the first half of the last two seasons (0.69 PPG in 2009-10, 0.53 PPG in 2010-11) that was followed up with poor second halves both years (regression to a season long average of 0.50 and 0.38 PPG, respectively).


• Trophies:  In Cesc's first three seasons with Arsenal, the club won the Premiership (2004), the FA Cup (2005), and made it to the Champions League final in 2006 where they lost to Barcelona.  After that run, they featured in two League Cup Finals (2007, 2011), and were otherwise knocked out in semi-final or earlier rounds of every other competition in the five years.


• Premier League Table: After finishing first in 2003-04 and second a year later, Arsenal averaged a table position of 3.67 and never finished higher than third in the final six years Cesc was at the club.

Conclusions

It's clear that while Arsene's management of the team finances has prevented the club from going into debt like other clubs, it has also put a glass ceiling on the club's table position and trophy case.  Cesc's observation relating to "the routine" of late season failure was spot on.  Frustrated with a lack of investment and results that were progressively worse, especially when he gave the club one final chance in 2010-11, he decided it was time to end the relationship.  I can't blame him for doing so - six years of rebuilding is certainly long enough to judge a team and its level of commitment to its world class captain.

We Gooners can only hope that Arsene and the club take the lessons from the divorce and apply them to making the club better - invest the funds wisely, and sign a big name player or two.  Much like the well wishes one might have for an ex that ended a relationship amicably, I hope that Cesc also gains from this breakup.  He certainly seems to have made a tough decision, and faces an even tougher task of breaking in to Barcelona's crowded starting XI.  I just hope his continued development doesn't come at our expense in Champions League - if we even make it that far in the next few seasons.

One of my Twitter followers, who is an LFC fan, made the following observation regarding how Fernando Torres' time at Anfield and his departure played out in the press and wider public.  There is some coarse language in the quote, but I've chosen to preserve it to communicate the emotion.

"It's really weird, but I always say that Torres with LFC was that partner who everyone around you said "how the hell did you land him/her?", making the suggestion that the person was too good for us. Then the papers would continually link Torres away from us trying to fuck it up, and fans kept saying to themselves "it's not true, it's not true". Then, when we least expected it, Torres requested to leave for that one club everyone kept linking him to, but that we all fucking hated with a passion. I'll be honest, fans were prepared for Torres to leave, but the surrounding circumstances (timing, destination, hours after we brought in Suarez, team was winning, etc.) was just the perfect storm in the creation of the shit sandwich that was."

Cesc's departure was more drawn out and less sudden.  Perhaps that made it worse than Torres' move to Chelsea, perhaps better given we Gunners won't be seeing Cesc winning games on a weekly basis at a league rival.  What does sting more about Cesc's departure is that no one ever questioned how we got him.  He came in to a team that was just embarking on its most successful season of league football in the history of England's top flight.  We got him on the cheap, and he represented the finest example of Wenger's forthcoming youth policy.  He was the embodiment of the Arsenal-of-the-future, and a team was built around him.  The reality in him leaving is that our club, at least in its current vision, has failed and the experiment is over.  We're no longer the attractive young man or woman that has others fawning all over us.  We're now that club that will be greeted with raised eyebrows when we land that "great catch" with which we have no business being seen.

How the club in general, and Wenger specifically, react to this departure over the season will say a lot.  Arsenal is facing the real possibility of rebuilding after a failed rebuilding project, and struggling to maintain their Champions League spot in seasons to come (and the important revenue and prestige that comes with it).  They may not be a selling club yet, but they certainly are in trouble.  Youth Policy 1.0 is effectively dead with Cesc's departure.  It's tombstone will read, "Consistently 4th, but highly profitable".  Where the club goes from here is any one's guess, but I can guarantee it will be a bumpier ride than in season's past.

Fabregas says, I am very happy at Arsenal

Arsenal captain Cesc Fabregas said on Wednesday he was happy at the Premier League club and no decision had been made about a possible move.

"I am an Arsenal player. I have been very happy for eight years and I am very happy".Fabregas said at promotional event, when asked about the prospect of return to Barcelona. "I am not thinking about football right now,just about my holidays," there have been no decisions".

"I am very happy where I am . You can never say never in this life as so many thing happen that you can never predict"

Arsenal Samir Nasri Latest News Rumour

There is always one transfer story in the summer windows that drag on and grabs everyone's attention for a few long months of rumours and gossip.

This year, it is Samir Nasri, as he teases everyone about his Arsenal future and the outlook of joining rivals Manchester United, and while Wenger has recently stated that Arsenal "will do everything to keep Nasri at the club", reports have emerged claiming that Arsenal would be "willing to listen" to offers for the player.

Reporedly Bayern Munich have joined the trail for Arsenal midfielder Nasri.
The Mail on Sunday claims Bayern are prepared to battle it out with Manchester United, Manchester City and Chelsea to land the Gunners playmaker.

It is understood the German club has a £200 million transfer kitty and are looking at Nasri to play with, and sooner replacing 28-year-old countryman Franck Ribery.

Barcelona wants to get Cesc Fabregas

Barcelona are all set of signing Spanish talent Cesc Fabregas ,Arsenal’s top goalscorer this  season and is also their captain and therefore set to meet Arsenal chief for the discussion.

 Barcelona have established their trail for old boy Fabregas is now on, but at well below Arsenal’s £54million asking price.

Quantifying the Bias of Arsenal’s Referees vs. The Rest of the League’s Clubs

This post can also be found at Untold Arsenal.

Author’s Note: Special thanks to DogFace for his co-authorship on this post.  His voluminous data set, unending patience, invaluable insight and contribution, and constant editorial feedback throughout the creation of this article was invaluable. He’s a wonderful blogging partner with whom any Gooner or statistician would be lucky to work.

In my first post in this series I used DogFace’s match data to explain how Phil Dowd is the least desirable referee for Arsenal as he not only shows the most biased officiating in terms of fouls, yellow cards, and red cards, but he also shows the largest effect on Arsenal’s likelihood of winning a match. That analysis focused on the effects of all of Arsenal’s referees, but did not quantify how those referees officiated other teams’ matches. This post contains such an analysis, and the results are very interesting.

To aid in such an analysis, a binary logistic regression (BLR) model was created for each team’s likelihood of winning a match based upon a number of factors. Each BLR model includes terms that capture the effects of venue (home/away) and differentials of shots, shots-on-goal, corners, fouls, and fantasy points for yellow and red cards. Not every term was significant for each team – terms that had a p-value of 0.10 or less were eliminated from the team’s BLR and their coefficient for that term is set to zero. I know that may upset some stats geeks who would prefer p-values of <= 0.05, but the reduced sample size requires a lower p-value threshold or very few teams would have any significant terms. The resultant BLR’s allow a construction of each team’s odds of winning each match, and a study was constructed as to how each official impacts the odds of winning each match based upon their officiating versus the expected average officiating from the club’s total number of matches.

Background on the Data Used in the Analysis

Before diving in to any analysis, a few statements on the types of data used are in order.

The intuitive way to model bias in a referee would be from the fouls per booking and bookings per match figures – although DogFace has often found these to be counter intuitive in that, if a bias exists, it can be expressed within the game in different ways – these often depend on the styles of play of the teams involved.

The noise in these figures is further increased by the fact that the official statistics only reflect what the referee deemed to be a foul rather than the reality of a foul (according to the laws) and/or the consistency of the referee’s interpretation thereof. “Sins of omission”, where a referee should have called a foul but for some reason or another did not, are tough to quantify in an analysis that uses such statistics.

To combat this effect, Untold Arsenal utilises a professional referee (Walter Broeckx) to analyse matches and it is clear that what is recorded in the official statistics is often way off the mark. DogFace’s own data sets confirm this effect. The rise in popularity of statistical analysis in football has led him to notice a trend for parity in the fouls per booking figures that suggests that the referee is aware of his statistics in game – it could be said that this ‘trial by media’ has created the bias we see in these figures and that a referee himself has a conflict of interest in every call he makes or indeed does not make.

The ideal situation would be an independent body to record/analyse referee performance and provide an open source database for us to comb through though - this data would include the most important data of all i.e. the standard ‘human’ error. Alas, we do not have such research based on an independent body, and instead you will have to make do with the work of humble bloggers like Walter Broeckx, DogFace and me.

Quantifying How Arsenal’s Referees Officiate the Rest of the League

Just like the last post, each team’s average foul and fantasy point total was calculated. These variables represent the match attributes directly controlled by the referee. Each team’s actual odds of winning each match were compared to the odds that would be realized if the referee had given the team’s average foul or fantasy point differentials (different values were used based upon the team’s averages for home and away matches). This allows a calculation of an odds differential for each match.

Matches were then grouped by referee to allow an analysis of each referee’s overall bias vs. the average odds. In this case, the same referees as the first post were examined – Atkinson, Bennett, Dean, Dowd, Foy, Halsey, Webb, and Wiley – as they had officiated the greatest number of Arsenal matches and in general a large number of matches overall. Most importantly, they have officiated a range of home and away matches so the impact of home/away bias is minimized. Unfortunately, the limitations of the number of matches in a season and the availability of each of the referees prevents an analysis where each referee officiates an equal number of home and away matches, but the statistics used in the analysis take the effect of venue into account to minimize its effect on match outcome. The data used for this analysis was also isolated to the 2006/07 through 2009/10 seasons to ensure an adequate number of samples were available from each referee.

It should be noted that for the first part of the analysis, referee data from all four seasons was grouped together. This allows us to look at gross bias throughout the seasons, and keeps a pretty high sample size for the analysis. Later in the post key referees' data is broken out across seasons to show the effects of referee by season. Such a study by season helps us see any bias that may be dependent on club’s objectives (Premier League title, European competition qualification, avoiding relegation) and current quality of play (above, at, or below form). Inevitably, such seasonal analysis suffers from limited sample size and is saved for those referees whose overall bias is the most noteworthy.

One further adjustment to the data set had to be made. When creating BLR’s for each team, several of them showed no impact to their odds of winning a match due to foul or fantasy point differentials. That is to say that none of the two coefficients for those terms in a team’s BLR were statistically significant – the coefficient’s p-value was greater than 0.10. This means that we can’t evaluate the impact of officiating on those teams’ likelihoods of winning a match. Thus, teams that did not have a significant BLR term from the two associated with officiating bias – fouls or fantasy points – were eliminated from the analysis as they’d provide a zero impact and generate misleading results.

A general linear model (GLM) using referee and team officiated (Arsenal vs. not Arsenal) was created from the reduced data set to observe the resultant interactions. The results of the analysis are represented in the graph below which shows each referee’s average odds differential for Arsenal and the rest of the teams. The two plots in the graph show the same data in two different manners. The key plot is the one in the lower left (click to enlarge).

Before diving in to the plot, readers with a keen eye will note that the red line, which represents Arsenal’s average odds differential by referee, is a bit different from a similar line plotted in my previous post. This is due to the two different ways the data is analyzed. In the previous case, I was looking at the referee’s performance as a function of just Arsenal’s matches by year. That led to the grouping and averaging to be a bit different than this analysis, which simply looked at Arsenal versus the rest of the league regardless of season within the four analyzed. This latest analysis essentially ignores the effects of time.

Looking at the lower left hand corner of the plot, it’s clear that Dowd shows the largest gap between how he officiates the average match and how he calls an Arsenal match - about a 1.5% penalty for Arsenal. However, what’s different about this analysis is that it also clearly shows that Howard Webb is pretty biased too – also nearly a 1.5% penalty for Arsenal. Rounding out the top three are Wiley, Halsey, and Bennett each with a nearly 1% penalty for Arsenal. Atkinson and Foy seem to show the smallest gaps.

Another way to look at in-match bias is to look for odd patterns in fouls-per-booking. A plot of four factors – Referee, Arsenal/Not Arsenal, Season, and Home/Away – and their impact on fouls-per-booking is shown below. Values on the left or right side of the plot represent the fouls per booking for the plots across that row. Values above and below the graph represent different levels of each factor expressed as text in one of the boxes in each column. The legends to the right of the graph explain what each color/shape combination represents in each row. Thus, if one wants to understand how each referee’s average fouls per booking for Arsenal compares to their fouls per booking for the rest of the league, one can look to the square in the 2nd row/1st column or the 1st row/2nd column. Each of those two plots shows the same data, but each is plotted in a different manner.  Click on the image below to enlarge it.

Looking at the plot of data in the 2nd row/1st column, one sees there is only one referee that has a higher fouls per booking for Arsenal than the rest of the league – Steve Bennett. Yet again, Howard Webb and Phil Dowd lead the pack with their differential of fouls per booking for Arsenal versus the greater numbers of fouls-per-booking they allow for the rest of the league. Surprisingly, the favorable Chris Foy also has a large gap between how he calls Arsenal matches vs. the rest of the league.

What’s especially disturbing is the fact that Dowd ends up with such a bias against Arsenal in fouls-per-booking given his disproportionate number of home matches he’s officiated for Arsenal (7 home matches to 2 away matches). Take a look at the plot in the lower left, which shows home (red) and away (black) fouls-per-booking by referee. Overall, Phil Dowd shows one of the largest gaps in favor of a higher fouls-per-booking average home versus away – nearly two fouls per booking. Yet such an advantage is not showing up in Arsenal’s numbers when Dowd is officiating their home matches. In fact, when looking for statistically significant factors in the GLM of fouls-per-booking vs. referee, club, season, and venue, the interaction of referee and venue is the only statistically significant term! Some referees are being consistent between home and away matches, while others are showing large gaps.

Comparison with Pre-Match Expectations via the Asian Handicap Swing

Does this comport with pre-match expectations? One loose measure of such expectations is the Asian Handicap assigned to a match. Luckily, DogFace has also been recording this statistic for each match. DogFace has also introduced the concept of the Asian Handicap Swing (AH swing) to readers of Untold Arsenal. The AH Swing is computed via the following equation:

AH Swing = Actual Goal Differential – Asian Handicap

The AH Swing represents the performance or deviation against the handicap in actual goal difference. The betting line data (or Asian Handicap) is an average calculated from around 30-50 bookmakers across Europe and Asia. We assume the average bookie handicap does not use corruption/bias as a significant factor in the markets – not only for the reasons stated below but also because referee driven match fixing would only affect the markets significantly in terms of an ‘upset’ against the odds.

If we were to take the stance that the betting line reflects referee corruption/bias then any deviation from that line in terms of an over/under performance would be understated i.e. we could say that any ‘noise’ in the original handicap from the bookies would actually understate the bias we are attempting to model. Luckily previous research does not indicate this case, but rather indicates that on the whole bookmakers may be creating a market that is essentially based on efficiency and competition. At the least, they are essentially hedging a gestalt metaphysical abstraction based on media disinformation and the credulous belief that “it all evens out at the end of the day”. However it is worth considering that, as perception of bias in referee performance becomes more ‘main stream’ and paradigms shift, we will see this effect in reflected in the markets of the future.

This post will instead focus on the reality of the results as it is a far more revealing stance to take. The Asian Handicap line is one that reflects, more or less, the illusion of an uncorrupted market. The swing from that line allows for an examination that a corrupted, or biased, market exists.

Just like odds differential, the AH swing has been calculated for each and every match in the database. A plot of four factors – Referee, Arsenal/Not Arsenal, Season, and Home/Away is shown below. Values on the left or right side of the plot represent the Asian Swing for the plots across that row; values above and below the graph represent different levels of each factor expressed as text in one of the boxes in each column. The legends to the right of the graph explain what each colour/shape combination represents in each row. Thus, if one wants to understand how each referee’s average AH swing for Arsenal compares to their AH swing for the rest of the league, one can look to the square in the 2nd row/1st column or the 1st row/2nd column. Each of those two plots shows the same data, but plotted in a different manner.  Click on the image to enlarge.

Looking at the plot in the 2nd row/1st column, it is shown that Mike Dean, Howard Webb, and Phil Dowd have the lowest average values for Arsenal’s AH Swing. This means they are consistently officiating Arsenal’s matches tighter than the other referee’s. Unlike the analysis of fouls-per-booking, the interaction between referee and venue is not statistically significant. Referees consistently provide a significant AH swing advantage to home teams compared to away teams.

It has now become clear that on multiple fronts that Dean, Dowd, and Webb appear to be the most biased against Arsenal. To get an even better understanding we must look at how each of the three officials impact each team and compare those matches to how bookies might expect them to turn out.

Quantifying How Arsenal’s Referees Officiate the Rest of the League

One way to visualize whether or not Arsenal is the most penalized when it comes to the officiating of Dean, Dowd, and Webb is to look at how each team’s average odds differential compares to their average Asian handicap swing when these three officials are present. The three graphs below represent just such a comparison for each referee. The x-axis represents the average Asian handicap swing. The y-axis represents the average odds differential.

The key to the graph is the lower left hand quadrant. Teams that end up there, especially those that end up further away from both of the lines along an imaginary diagonal line extending from the origin of the graph, are likely experiencing a higher amount of bias in officiating than the other teams the referee has officiated. The three graphs below show such plots for each team against each of the three referees. A summary of conclusions is found after the third graph.  Click on any of the graphs to enlarge.

Here are some conclusions that can be drawn from the three graphs:

• There is clearly a band around the ± 2% region of the odds differential where most teams cluster.
• It’s also clear that the top teams – Arsenal, Chelsea, Liverpool, and Manchester United – tend to do better on the AH swing than other teams. Indeed, teams that would generally have a more positive Asian Handicap tend to be to the positive on the swing.
• While Arsenal do seem to be experiencing some bias at the hands of the three referees, they don’t seem to be the worst off. Liverpool clearly pays a bigger penalty under these three referees.
• Of Arsenal’s main competition for league trophies the last half decade, Manchester United and Chelsea get a much better shake from the referees. Each has a vastly superior AH swing, while each of the two teams finishes much better in terms of odd differential than Arsenal for two out of the three referees. These advantages translate to an average of a 0.73 goal benefit in AH swing and a 1.6% benefit in odds of winning a match.
• Chelsea’s average odds differential is 1.6% better than Arsenal’s, while their average AH swing advantage is 0.78 goals.
• Manchester United’s average odds differential is 1.5% better than Arsenal’s, while their average AH swing advantage is 0.68 goals.
• Mike Dean is the only referee of the three to put both Chelsea and Manchester United to the positive. He’s also the referee demonstrating the highest bias against Arsenal in AH swing, both nominally and when compared to Chelsea and Manchester United (a 1.52 swing deficit to both).
• Perhaps Ryan Babel’s tweet with Howard Webb wearing a Manchester United jersey wasn’t too far off. It Manchester United is his most favored team by a mile both in terms of swing and odd differential.
• Of any referee who has officiated the Big Six, Mike Dean gives the most favorable treatment to Chelsea. Their average odds of winning a match are improved by nearly 1% when he officiates one of their matches, and they experience their best AH swing under him.
• Of Arsenal’s North London rivals, Spurs are treated about even by Dean and worse by Dowd and Webb.

There are some interesting interactions that go on between referees and managers as well. One could be referred to the Dean-Redknapp effect. When looking at matches where Dean is the official in matches involving Portsmouth and Tottenham, both teams do better in terms of AH swing with Redknapp at the helm than when he is not, bordering on statistically significant effects (odds differential was a wash). Interestingly enough, the interaction of manager and team is not significant, so Redknapp’s record under Dean is not unduly boosted or penalized by his record from either of the clubs. It stands on its own. Such a detailed analysis would have to be the focus of a subsequent post, and deserves a wider treatment of referees, to ensure that it’s not simply an effect of Redknapp’s superior coaching. Nonetheless, it provides intrigue when studying the effects of officiating.

A Comparison of The Big Six By Season

It has been shown that over the 2006/07 through 2009/10 seasons that Dean, Dowd, and Webb have given Arsenal a bit of the short end of the stick when it comes to fouls-per-booking, AH swing, and odds differential. One last bit of examination remains – what happens if we open up the examination to the entire six years of data in DogFace’s database, isolate for the Big Six for these three referees, and examine how a few of the trends may be changing over time?

The graph below provides a plot of such data. The solid lines represent the teams’ average AH swings under the three referees, the value of which can be found on the right hand side of the graph. The dashed lines represent the team’s average odds differentials under each of the referees, the value of which can be found on the left hand side of the graph (click to enlarge).

A few general trends can be observed:

• All teams except Manchester City have been on a general downward trend over time in terms of AH swing.
• Manchester City also is also the only team to demonstrate a steadily increasing odds differential over time.
• Arsenal started out with the third lowest swing in 2005/2006, and their decline has been consistent to the point of falling below 0 this season with the three referees. They are the only team of the Big Six to experience a negative swing.
• The dashed set of lines shows Chelsea and Manchester United hanging around neutral (i.e. 0%) odds differential over time.
• Again, Arsenal is on a steady downward trend to the point that their average odds differential under the three referees is on track to be greater than -2% this season. Only Tottenham has a worse odds differential.

So who’s driving this downward trend for Arsenal? The plot below shows the same data as the plot above, but it eliminates the other three teams and instead focuses on Arsenal’s referees (click to enlarge).

On the AH swing front, there’s been a steady erosion the last year. However, before that Mike Dean’s officiating showed a distinct downward path compared to the rest of the referees. His AH swing went negative in the 2009/10 season, and Webb has joined him now in 2010/11. It appears it’s a case of Dean pulling the rest of the average down with him, and the other two referees joining him this season.

As for odds differential, it’s Dean again that leads the pack. He started out as a neutral referee in 2005/2006, but then has steadily eroded that neutrality to a -2% differential by last season. Dean’s low average and the recent degradation in Phil Dowd’s officiating are what are leading to Arsenal’s precipitous drop in 2010/11.

Conclusions

Whether it’s actually poor form generating a higher number of fouls and cards or actual referee bias, it is clear that Arsenal pay a bigger referee penalty than all of the teams they’re competing against for the Premier League championship save for Liverpool. This might be combated by having the three highlighted referees – Dean, Dowd, and Webb – officiate fewer Arsenal matches. They officiated an average of ten matches, or 26% of Arsenal’s season, each of the last four years. Statistics would suggest that having a fewer number of referees officiate a greater number of matches for each squad would lessen the chance of a poorly officiated match impacting a team’s season point total. Such an assumption is based upon the idea that the official’s errors or bias are randomly distributed. The data above suggests otherwise.

Arsene Can Only Blame Himself, But He Can Fix It

"Ah, piss off!"

There was a time on Sunday when "King Kenny" and #PissOffWenger were trending on Twitter, demonstrating the reach of the global soccer community and the power of the Kop. Surely there are a lot of Wenger haters not aligned with Liverpool that jumped on the trend once it got going, but the phrase is symbolic of where the two clubs and their managers may be at this late point of the season. All the more fitting because of the fact that they started the season, literally, each at a different place. What a difference eight months makes.

The Match Statistics

Before diving into some thoughts on what ails my Gunners, I'll start with a statistical breakdown of each match - the first of the season at Anfield and this latest one at the Emirates. It provides some insight into what each side should have expected out of both matches, and provides some grounding in my later criticism of Wenger.

Just like this post, the tables below represent the odds of winning a match based upon a binary logistic regression (BLR) that looks at venue and differentials of shots, shots-on-goal, corners, fouls, and fantasy points for yellow and red cards. I've generated summaries of each match's statistics and the resultant odds based upon those statistics. Click on either table to enlarge it.

It wasn't just your eyes that told you Liverpool should have won the match at Anfield - the match statistics bear this out as well. Liverpool had the statistical advantage in every category - shots-on-goal, fouls, and fantasy points were in their favor, while total shots and corners were not (note: it turns out that teams want to have fewer corners and shots versus the opposition, a concept I will explain in a later post). Reina's muffing of Chamakh's shot truly was a gift of a point for the Gunners. Liverpool should have come away with a full three points that day.

Fast forward eight months, and the match at the Emirates was a little more even but still in favor of the Reds again. Arsene Wenger highlighted his team's "difficulty at creating chances" at his post-match news conference. Indeed! Even though Arsenal took 60% more shots than Liverpool, the Gunners had no advantage in shots-on-goal and had 7 more corners than the Reds - all adding up to a huge knock on the Gunners' chances of winning the match. All of this results in dropping Arsenal's odds of winning the match, which are only slightly raised by the two fewer yellow cards. Liverpool's oddity of being only one of three teams in the Premier League from 2005/06 through 2009/10 with a statistically insignificant constant term in their BLR model means that all of those statistical advantages added up to a 69% chance of winning the match, while Arsenal had a 34% chance of winning with such form. The odds were much closer than the first match, and perhaps a draw was warranted based on the statistics and what we all saw with our own eyes.

The bigger problem for Arsenal in the second match was their inability, yet again, to close out a match and take advantage of a lucky break. Statistically they may have been at a disadvantage for a win, but fortune broke their way late and they were a few minutes away from keeping pace with Manchester United. Instead, they walked away with what was a disappointing draw. Such collapses that snatch a loss or a draw from the jaws of victory has been all too common this season.

The Common Denominator - The Defense

What became immediately clear upon replay of the foul that enabled Dirk Kuyt's tying goal was the softness with which Lucas went down. Good for him, as drawing a foul is part of the game. What's more frustrating is how Emanuel Eboue put himself in position to have a foul called. This is symptomatic of wider defensive woes this season that have cost the Gunners a total of what should have been nine additional easy points that would have them top-of-the table right now, as well as the Carling Cup. Recall the following:

• Way back in September Arsenal drew Sunderland 1-1 at the Stadium of Light after leading for nearly 80 minutes. The stoppage time equalizer from Darren Bent came literally on the last play of the match, which was set up by a poor clearance from Gael Clichy.
• In November the Gunners conceded a two goal lead in the final 40 minutes of the match. I recounted here how rare an event that was. It was Tottenham's first win at Arsenal in 17 years.
• It was Abou Diaby providing the exact response for which Newcastle United were looking when they implemented their second half kick-them-off-the-pitch strategy while down by four goals in February. Diaby's sending off began Newcastle's comeback from four goals down, which was a first in the history of the Premier League and perhaps the best example of how Arsenal's defense can both make boneheaded mistakes and crumble under pressure at the same time.
• In the Carling Cup final, it was defensive miscommunication between Laurent Koscielny and Wojciech Szczesny that led the heavily favored Gunners to lose to Birmingham City. This loss, combined with the loss against Newcastle earlier in the month, set up an awful run in March and now April that has seen the Gunners fail to capitalize on any Manchester United stumble and now find them six points adrift of the Premiership title and only two points ahead of Chelsea.

In some cases, it's been a lack of killer instinct (TottenhamSunderland, Birmingham, and Liverpool). Either way, it's clear that the defense has major holes when it comes to protecting leads. I agree with Tim at 7AM Kickoff - I think the goal keeper problem is largely solved via Szczesny. What we Gooners want to see is better play from the defense in front of him, and we want to see it next season.

The Transfer Policy Needs to Be Adapted, Arsene

I've written here and here about the impacts the squad and starting XI transfer cost can have on a team's likely finish position. I've also heaped praise on Wenger for grossly outperforming such a model - averaging a third place finish over the last six seasons when his transfer expenditures suggest he should finish 10th. What's also become clear over that time frame is that consistently finishing third isn't meeting the supporters' expectations.

The Swiss Ramble made an excellent post in September 2010 that provides an great summary to Arsenal's financial quandary. Their strategy of not taking on debt to finance transfers has generated tidy annual profits in the transfer market, which helps compensate for their lower commercial income when compared to Chelsea, Liverpool, and Manchester United. They also have match day income that is the envy of Chelsea and Liverpool, and surpassed only by Manchester United. However, they do have the third highest payroll in the Premier League, outstrip their next closest competitor (Liverpool) by £21M, and have a wage-to-turnover ratio (50%) the envy of everyone else but Manchester United. They may not be paying for transfers in the open market, but they are paying their players wages that are in line with winning championships. And that's the rub.

It's time for Arsene and the Arsenal board to admit the plan has failed. I know that they don't set out to finish third every year, have steadily earlier exits each year in Champions League, and go trophyless in FA Cup and Carling Cup. They set out to win, and they've tried to win in an anti-Chelsea manner. They've had a squad, transfer-wise, that barely maintains the league average transfer cost yet competes with the big boys every year. It also consistently fails to win a trophy. Arsenal has made some good deals (Walcott, Szczesny, Cesc, etc.) along the way, and have a few great academy players in the first team as well (Wilshere and Djourou being the brightest). Save for Djourou, none of those great deals and academy players starts between the goal and the midfield. The Gunners simply need a few more top quality defenders, and they'll have to pay to get them.

Which brings me back to the start of my post and #PissOffWenger. The man elicits such a response partly because he has been around so long, partly because he has been so successful in the past, partly because he's not English, partly because he's been in everyone else's face trying to explain that he's building a team differently, and partly because lately he's been a bit of an insufferable whiner. He may have a few legitimate gripes, but the sheer number of gaffes this season suggests there's more than bad officiating or a league conspiracy at work here. The public manner in which he has vented his frustrations during and after matches makes him seem like a sore loser, and plays right into the role within which the press want him to fit. If you're a defender looking to join a club fighting for the Premiership title, and you perceive that the manager is a bit of a complainer who seems to not be totally in touch with reality, do you take a pass on such a club? If you're Cesc Fabregas and looking at your manager's behavior and comparing it to the fun your Spanish national team squadmates are having playing for Barcelona, is their even a comparison? There's a time to get angry and harass the officials and opposite manager when officiating is biased or play is dirty. But when it seems to become your MO after each loss in the eyes of the public, you have to stop and wonder if that's the best way to build a positive atmosphere at a club expecting to compete for trophies each year.

Wenger is clearly a managerial and financial genius. Of that there is no doubt. Perhaps he needs to hear more people say it before he feels his approach vindicated. Whatever he feels, he needs to move on. He doesn't need to bust the bank and become a £300M transfer cost behemoth like Chelsea. The future of Financial Fair Play will prevent that. What he does need to do is stop having such an aversion to spending ANY money in the transfer market, and look to upgrade the defense this offseason. Finishing third with the cheapest squad to ever do so is no longer good enough. Only championships matter now.  This Arsenal team is his team - he owns it lock, stock, and barrel. It will be interesting to see if the old man can adapt his ways enough to get one more championship before he enjoys a well deserved retirement. As Tim at 7AM Kickoff said back in February,

"Wenger made this mess, and only Wenger can sort it out."