Monday, February 28, 2011

If You're Going to Trash Talk At Least Get Your Facts Straight

"Everyone is entitled to his own opinion, but not his own facts"
Daniel Patrick Moynihan
My Twitter timeline turned into a trash talk fest between Arsenal and Manchester United fans in the immediate aftermath of Arsenal's loss in the Carling Cup.  The two teams may not have been rivals for a Premier League championship for over half a decade, but the animosity from earlier clashes hasn't died down.  I've generally tried to stay above the fray because it often sounds like sore loser syndrome when one tries to defend the indefensibly poor play of their team - even if it was poor play for only a few seconds.  There is, however, a point where I reach my limit, and it is when opinions try to be passed off as facts.

I reached that point when I saw this tweet come across my timeline:
In 6yrs, Arsenal spent £107.9m on 30 players (0 Cups). United spent £123.7m on 21 Players (over 10 Cups)!
This is a patently false assertion, the expenditures listed are incorrect, and the goal really is to excuse Manchester United's position as consistently being in the Top 2 when it comes to transfer expenditures, year-in and year-out.  Let's review the actual expenditures by each team from the 05/06 season through the 10/11 season (all data is taken from the Transfer Price Index):
  • Arsenal: £130.2M at time of purchase for 24 players (£167M in 2010-2011 GBP per the TPI)
  • Manchester United: £196.9M at time of purchase for 24 players (£223.8M in 2010-2011 GBP per the TPI)
But that's not the real measure in disparity between what resources the two clubs have available to them.  The real difference is measured in their Sq£, which takes into account the cumulative costs of all transfers currently on the squad (like Wayne Rooney's 04/05 transfer that would cost £49.1M if executed today).  The average Sq£ (in 10/11 GBP per the TPI) for the two teams from 05/06 to 10/11 is shown below.
  • Arsenal 10/11 Sq£: £140.9M
  • Manchester United 10/11 Sq£: £284.1M
Over those years, Manchester United has had a more than two to one advantage in the terms of the cost of players it can put on the pitch.  Compare that to the suppossed 14% advantage that United enjoyed in the tweet, and you see that the estimates aren't even close.  As was demonstrated in this series of posts, it is that ever increasing amount expended on transfer fees that has allowed Manchester United (and to a certain degree Chelsea) to maintain their high finish position in the league.  Frankly, what Arsene Wenger has been able to do with such a meager budget - average finish of 2nd when his financial resources should have put him 6th - is nothing short of amazing.  In recent years it's become even more magical, where his 10/11 expenditures have him finishing 10th when in reality he's challenging for the Premier League title.  I'd like to see how well Alex Ferguson would do if he were actually constrained by such a budget that refuses to take on debt.

Yes, Manchester United fans should rightfully crow about their cups.  They won them, and Arsenal hasn't over the last six years.  However, no one should kid themselves that the clubs have two different expectations based upon their financial commitment in the transfer market.  To compare the two as equals is a bit absurd - whether its a Manchester United or an Arsenal fan doing the comparisons.

One could also argue that Chelsea's, Manchester United's, and Manchester City's of buying players at any cost to win championships is EXACTLY why the EPL has the highest debt load of any UEFA league and why UEFA is having to institute financial fair play rules.  But that's a discussion for another time...

Book Review: Gaming the World

Perhaps US soccer and MLS would have a brighter future if we could see more images like this.

I have always maintained numbers are just a means-to-and-end in understanding the beautiful game. They provide a semblance of order and understanding to what is a chaotically beautiful game with relatively simple rules. As such, I balance my statistical blogs and books with a few cultural ones along the way. Wading too deep into the numbers makes one forget the emotional aspect of what makes sport great. While not taking such a numerical tact, Gaming the World: How Sports Are Reshaping Global Politics and Culture does take an academic approach to describing the wider cultural impacts of sports and is a must read for anyone comfortable with a book that comes from an academic press (Princeton University, to be exact).

The premise of the book is simple - describe how global sports culture has become hegemonic and helps knock down barriers society would rather leave up - and complex at the same time - why did soccer succeed in Europe and not North America even though both continents had nascent soccer cultures in the 1800's? As with any academic book, the authors have a substantial number of citations for each chapter, providing a great historical walk through the issues they tackle - the rise of global sports culture, the clash and reconciliation of competing sports cultures, the feminization of sports culture, and a great study of the unique nature of US college athletics. This book is a product of two authors who represent its main themes - a German and an American attached to their own sport cultures who fell in love with University of Michigan athletics and quickly realized they had fertile ground to explore. Given the path they travelled to writing such a book, the material within it is easily understood by the casual fan who wants to understand how the major sports of our day - soccer, basketball, American football, baseball, and hockey - evolved and the challenges they face as they as they now intersect each other in a globalized world.
The first takeaway from the book could clearly be "let your talent travel overseas". In studying the success of North American sports that have grown overseas or overseas sports they have seen grow in the US, there is one common theme - to build interest in a newer sport a less experienced nation must allow their talent to compete in the top professional level in the more experienced nation. After recounting what the "Nowitzki effect" has done for basketball in Germany, the authors start Chapter 3 with this observation:
Just think of Lance Armstrong's immense influence on having spawned a coterie of superb American bicycle racers and on having raised his sport's profile in the United States. America professional soccer, thus, is in need of a Lance Armstrong equivalent to emerge as a superstar in one of Europe's premier soccer leagues to dramatically improve its cultural roll stateside.
I couldn't agree more, and that's why I feel that having Landon Donovan stay in MLS is a huge mistake for US soccer. Some might argue that he's not the caliber of player to be considered a "superstar", but we'll never know as he didn't take the chance when he was in the greatest demand. Imagine how much attention would be paid to him and US soccer if he had translated last year's World Cup run into a full time stint in the Premier League? Instead, he came back to an LA Galaxy side that had clearly peaked earlier in 2010 the season, saw them fail to make the MLS Cup, and then saw the leading goal scorer from his team depart for a second tier German squad. All the while, people are now calling for the US national team to be built around another American who is making waves in England rather than play in MLS.

Yet all hope for US soccer isn't lost. While MLS's product is still inconsistent and clearly second tier on the world scene, there is growth in US soccer. Recent immigrants "import soccer into the United States and instantly provide a strong base for MS games, which have an average attendance of circa 15,000." This type of attendance figure makes MLS one of the top ten in the world when it comes to game attendance (on the other hand, television viewership leaves much to be desired). Ultimately, the authors argue that soccer in America is still an "Olympicized sport", meaning that most US soccer fans show up for the big international competitions like the World Cup, but fade away when it comes to the annual MLS season.

The authors do a great job of also explaining the difference between US and European professional sports. Key differences include:
  • A greater amount of success achieved by minority athletes when compared to Europe, which serves as "an integrative substitute for other forms of social (welfare) mechanisms".
  • The geographically large area of the US contributing to long travel distances that inhibit travel by the away team's fans, making the in-stadium experience very different than Europe's soccer stadiums. This distance also leads to an unbalanced schedule that is a key difference with European soccer.
  • The presence of a single team in a city (except in New York and Los Angeles), which ensures larger stadiums and less intense rivalries
  • By effect of a lack of such local proximity, intense cross-town or cross-state rivalries are saved for the uniquely American college athletics landscape. The authors do a great job in taking a whole chapter to explain the rise of US college athletics, how they are most similar to European national soccer leagues, and how they serve to democratize the US sports scene.
In studying the cross-cultural sports landscape, it appears there are two areas where the authors see the United States as more advanced - inclusion of women and acceptance of minorities (except the GLBT community, which is still universally marginalized). While the authors do argue that sports in general do provide a good bit of cross cultural acceptance, they can also incite a nativist backlash that focuses on local identity. This "counter cosmopolitan" reaction is especially prevalent in the second tier of European soccer and Italy's Serie A, as is the continued second-tier treatment of women in sports. As a counter-example, the authors look to the United States as a shining example of racial and gender integration. Racist taunts and anti-Semitic salutes found in European stadiums would never be tolerated at the lowest level of American athletics, while US women's teams in soccer, softball, and other sports dominate the world stage due to their equal treatment in the college athletics that help feed the national teams. To be sure, female pro athletes still have a long way to go to match their male counterparts, but on a national level the success of the US Women's soccer team is certainly the envy of the US Men's team.

The authors' detailed history of such gender and racial developments is key to understanding their real point about sports' true capital: cultural, not economic Sports, especially in the US, become a prime mode of recreation for millions of participants and an even greater number of observers. It dominates talk radio, our weekends, and sometimes even our weeknights. Americans buy jerseys, scarves, high-definition televisions and cable services, and tickets to matches. Stadiums are routinely sold out, and the recreational calendar is dominated by which sport is in season at the time. The book compiles some interesting statistics:
  • College football generates $2 billion in revenue a year.
  • Men's basketball brought in $600 million during the 2007-2008 season.
  • College hockey and baseball brought in far less.
  • The professional leagues, while bringing in a far more respectable $15 billion per year, would only rank 170th on the Forbes 500.
Of an interesting personal note, that would put them between a company named Computer Sciences and my employer, PACCAR. Thus, it is the outsized cultural influence that makes someone like me don an Arsenal jersey every weekend even though I will be lucky to go to a single match at the Emirates in my lifetime. Certainly their financial position in the world of soccer helps provide access to their product, but it pales in comparison to other companies that could be demanding the time and effort many of us put into following, playing, and interacting via sports. It's the cultural interactions - in the stadiums, in the pubs, and online - that drive such a disproportionate amount of our time to an activity with such a minimal economic impact.

Ultimately, that's perhaps the most re-assuring aspect of the book. Sports predominantly grew out of working and lower-middle class communities looking for a way to compete, relax, and build community identity. It's how soccer began in working class English communities, and why college athletics took off in remote locations of the United State via land grants from the government. For all the money that gets wrapped up in sports, it is the kid who picks up the basketball in the inner city, or a suburban girl who picks up a soccer ball, that helps democratize the sport and the wider culture. We always need to be vigilant of someone trying to buy a championship or violate the rules of amateurship, but by and large sports are natural to humans and the biggest effect they have is to empower the players and they provide a wider acceptance of the minority the players represent.

Friday, February 25, 2011

Friday Night Links

Here's your Carling Cup edition of my favorite links from the past week:

With that, have a great soccer viewing weekend.  As a Gooner, all I care about is Sunday's Carling Cup final.  I've only been an Arsenal fan for two years now, but I know enough longtime fans to know how important this match is.  It may be the least prestigious of the four championships for which Arsenal is competing this year, but that doesn't matter.  A cup is a cup at this point, and there is a huge sense that getting this first one will make these players better prepared to win more of them.  It's not something that I can quantify with numbers, but rather an intangible gut feeling.

C'MON YOU GUNNERS!

See you all on the other side of the weekend.

Thursday, February 24, 2011

Comparing Econometric Models of the English Premier League: Reconciling the TPI and Soccernomics Data Sets

Note: This is a re-post from analysis I did back in January 2011 for the Transfer Price Index blog. I am posting it here to complete my series of posts on squad transfer costs, and to set up a forthcoming series of posts on the impact of starting XI transfer costs on table position

I’ve participated in many discussions since my original post on the relationship between a squad’s current transfer cost and their table position. Much of it has been centered on the debate over the predictive power of Soccernomics wage data versus my analysis using current transfer costs. Many readers on The Tomkins Times have come to the same general conclusions as me: each analysis has its valid points and different uses, and the two are not necessarily in conflict with each other.

I’ve also had the pleasure of discussing the two studies with none other than Stefan Szymanski. I plan on keeping much of our conversation private, but you can get a sense of his respect for the overall Transfer Price Index approach and the differences in the two data sets via his review of Pay As You Play. Stefan’s review is a positive one, summarized best in the following observation.

“[I]n a fascinating new book Paul Tomkins, Graeme Riley and Gary Fulcher have developed a method of converting transfer fee data into a squad valuation… With every squad member given a value, this can then be used to compare spending to performance in the league. It is a true labour of love, collecting all the transfer fee values for Premier League clubs going back to the beginning of the 1990s.”
Szymanski closes out his review with this glowing recommendation:

“The book is a treasure trove of interesting financial facts and would make a great gift for any football statto…”
What’s interesting is how much correlation there is between the Soccernomics wage data and the TPI’s cost of the starting XI. Stefan’s metrics in the column are both relative measures (RW for wages and R£XI for relative starting squad cost), and he observes they show 90% correlation to each other. Unfortunately, the Evening Standard did not include the very compelling graph Stefan generated as part of his review of Pay As You Play. Luckily, Stefan has supplied us with that graph and it is reproduced below.


The graph clearly demonstrates the correlation between the two metrics, the weakness of the models at either end of the table, and the strength of the model in the middle of the table. Stefan’s observation of over predicting the resources needed for top table positions has been invaluable in explaining the discrepancy between regression predictions and historical data related to Champions League qualification that will be discussed in an upcoming post.

Stefan’s review rightfully points out the reliability of the publicly audited wage data versus the TPI’s privately compiled transfer data. At the same time, I would stand by the TPI as the most comprehensive and meticulously compiled set of transfer data within the English Premier League era. It was indeed a “labour of love” for the authors, a labour that continues to pay dividends in our financial understanding of the league.

Beyond the quality of the data and its impact on any resultant statistical analysis, Stefan’s data set has a bit of an advantage over the TPI. The Soccernomics wage data looks at overall team wages, thus taking into account the total cost of operating the squad in current British pounds. Combine this with the fact that wages are a dynamic measure adjusted over time by team and player, while the TPI is a static inflation of a one-time transfer fee, and we see why wages may be a better predictor of actual team success. It’s also no surprise that the £XI metric correlates very well with that wage data, as it takes into account all the players who have made it on the pitch and how much time they spent on it. There’s no dead weight contributing nothing to the team’s performance on the pitch, good or bad.

Indeed, analysis by Graeme Riley and me has proven this point statistically. Graeme looked at the squad and XI transfer cost order versus table position, while I looked at the multiple of the average squad and XI transfer costs. Both Graeme and I calculated these for each team, and then quantified the correlation of each metric to finish position for each individual season via the square of the Pearson product moment correlation coefficient (the commonly seen R² value in a regression plot). In Graeme’s analysis, the order of £XI had a higher R² value than the order of Sq£ in 16 out of the 18 seasons. In my analysis, M£XI had a higher R² value than MSq£ in 14 out of the 18 seasons. In the final comparison, I looked at the average and standard deviation of the R² values for each metric – order of £XI, order of Sq£, M£XI, and MSq£ – to determine which provides the best, most consistent prediction of table position over the 18 seasons. The M£XI had the lowest overall standard deviation (14.7%) and highest overall average (45.4%), indicating it provided the best fit versus table position (although it is far lower than the R² values in the long-term analysis in my original post and Soccernomics). Ultimately, this confirms my preference for relative measures, especially multiples of averages, and why I prefer to look at long term averages rather than individual seasons.

On the other hand, the TPI data I used in my original analysis only considered the impact of the total cost of transfers on team performance, and neglected those of the free variety as well as trainees. It also doesn’t look to utilization rate. It essentially looks at a reduced data set from the full squad or starting XI, and the graph below quantifies how much of a reduced data set non-free transfers represent over the history of the Premier League.


The graph above shows the cumulative percentage of three types of players within the league each year as categorized within the TPI – trainees, free transfers, and the rest of the players. The vast majority of this final category consists of transfers with confirmed fees, while the rest of it consists of a small number of players whose transfer fees couldn’t be confirmed. The graph is cumulative, so to understand the percentage of free transfers for any single year one must identify the free transfer value on the graph and then subtract the corresponding trainee value from it. As an example, the cumulative percentage (represented by the upper value of the red zone) in 2001-02 is approximately 30% while the league share of trainees is about 20%. This means that free transfers made up about 10% of the league in 2001-02.

What is clearly seen via the graph is that transfers have consistently accounted for nearly 70% of the Premier League’s players since its inception. That’s not to say 70% of the players transfer teams each year, but rather that at some point in their past they were purchased by the team they played for that season. What has changed over the league’s eighteen years is the number of trainees within it. This number has plummeted from nearly 30% of league player classifications in 1992/93 to below 20% by last season. Much of this change has happened due to an increasing number of free transfers, which were given official UEFA sanction with 1995's Bosman ruling. Free transfers have gone from only 2% of league player classification in 1995 to nearly 10% last season. Overall, transfers of any variety came to represent 80% of league players by the 2009/2010 season. In many regards, the Premier League is a microcosm of the increasingly globalized world it operates within: greater international ownership and investment, greater employee mobility, fewer employees staying with a single firm from “graduation” to retirement, and increased dominance by a few brands within the marketplace.

What this all means is that any analysis of league performance on a squad basis that uses the TPI is going to miss nearly 30% of the players in the league. Given that fact and the reasonably good R-squared value my regression analysis achieved, I would consider the relationship to be a reasonably strong one. Ultimately a study by Stefan Szymanski, similar to this one where he statistically examined the causality of the wage/performance correlation, would be fascinating. We might then determine whether it was transfer fees, wages, or table position that drove the relationship with the other two. That is a very advanced analysis best left to a statistician of Stefan’s caliber.

At the end of the day, what Stefan’s analysis, my analysis, and the overall TPI database prove is that one must pay, and pay big, to compete for the top few spots in the Premier League. One must pay dearly for the right to even negotiate wages with 70% of their players that end up on their squad, and then they must be willing to pay dearly again to keep the talent to challenge for a top spot. Each metric, whether it’s based upon £XI or MSq£, has its use in quantifying the roll of ever increasing transfer budgets in a club’s success. Generally, I concur with Paul Tomkins’ assessment that “Sq£ is the only predictive tool, but £XI is surely the better retrospective analyzer.”

To a certain degree this all makes sense, as we want a somewhat meritocratic system where excellence is financially rewarded. It all gives us pause, however, when the same teams can dominate everyone else each year by outspending their rivals, sometimes even with money that had no origination in the soccer world in which each team operates.

Wednesday, February 23, 2011

A Few Quick Reactions to the 2011 MLS Playoff Format

MLS has finally released their 2011 playoff format, and I certainly have a few ideas based upon my series I did on their past playoff formats and outcomes.  I dealt with my recommendations for the 2011 format in this post.

  1. The format largely follows what I outlined in my "Recommendations for 2011" in this post.  The top six get a bye, the Supporter's Shield winner gets the lowest seeded team out of the wild card round, and we generally eliminate all the crossing over from conferences found in the last few seasons.
  2. What I don't understand is why the wild card round is one match, then the conference semifinals are two legged, and then the conference finals and MLS Cup are back to single matches.  This makes no sense, and it just seems like MLS is trying to follow previous playoff formats in some desperate attempt the provide continuity.  A much better, and natural, approach would have made the wild card round a two legged series of matches.  This would not only provide a natural progression via a reduced number of matches each round, but it would also add two critical matches to the lower seeds and close the likely gap in matches played between them and their second round competition.
  3. Yet again, the Supporter's Shield winner gets minimal benefit.  If the two-legged series was played in in the wild card round, the Supporter's Shield winner would be guaranteed to play all their playoff games at home and benefit from MLS's outstanding home field advantage.
  4. MLS didn't announce the location for the MLS Cup yet, so we'll reserve judgement on my recommendation to allow the highest seeded team of the final two to host it.
  5. MLS needs to stop making excuses for this awful playoff format.  The story on their website is chock full of excuses from the league.  Here are a few samples:
"It will mean that the battle and the race for the playoffs will have added intensity and last longer through the regular season. And that, on balance, should be a good thing for the play on the field, and for the fans in the stands and at home."
This statement defies logic.  Letting in the highest proportion of teams to the playoffs in over five years won't enhance competition, it will dilute it.  You can't have the lowest standard of admission, with the greatest number of teams admitted in the history of the league, and think that it won't bring more parity and a lower standard of playoff team as a result.
“There are so many variables that any system is imperfect in that regard,” Rodriguez said. “You could be facing the lowest-remaining seed who’s on a 10-game winning streak to close the season and they’re the hottest team in the league. … Any playoff system has, within it, some fault or a flaw that could easily be pointed to.”
Not if you followed my recommendations and kept the two-legged series in the Wild Card round!  MLS is seriously trying to blame "the random nature of the playoffs" to excuse their failure to properly design a playoff system over which they have total control.
“At the end of the day, you try to create a playoff system that is fair and relatable to the regular season,
This is only the case if MLS's goal is the complete random nature of a league that exhibits the most parity of any US pro league (too much parity, in my opinion).  Perhaps it's that parity and the random results it produced that led to the awful MLS Cup ratings last year?

I can only hope MLS is serious in their desire to "spend the next bit of time trying to finalize a long-term playoff situation that can take us into the future."  We deserve a better system for determining the MLS champion.

Soccernomics Was Wrong: Why Transfer Expenditures Matter, and How They Can Predict Table Position

Note: This is a re-post from analysis I did back in December 2010 for The Tomkins Times.  I am posting it here to complete my series of posts on squad transfer costs, and to set up a forthcoming series of posts on the impact of starting XI transfer costs on table position.

“In fact, the amount that almost any club spends on transfer fees bears little relation to where it finishes in the league. We studied the spending of forty English clubs between 1978 and 1997, and found that their outlay on transfers explained only 16 percent of their total variation in league position. By contrast, their spending on salaries explained a massive 92 percent of that variation. In the 1998-2007 period, spending on salaries by clubs in the Premier League and the Championship… still explained 89 percent of the variation in league position. It seems that high wages help a club much more than do spectacular transfers.”
So begins Chapter 3 of the wonderful book Soccernomics, where authors Simon Kuper and Stefan Szymanski use the above analysis to launch into an explanation of:
  • Why the transfer market is inefficient.
  • The unique approach Brian Clough took to building his Nottingham Forest teams through good bargains in the transfer market.
  • How most clubs spend little money helping such prized individuals adapt to their new team and culture.How Olympique Lyon make money buying low and selling high.
Each of these examples of individual success and failure in the transfer market makes for a compelling case. However, suppose that’s what they were – good examples of individual successes and failures. What if the authors were wrong in their initial analysis, and that on average spending more in the transfer market is a key enabler of league success?

I loved Soccernomics, and thought it was full of many thought-provoking analyses. I loved it so much that it has spurred my exploration of soccer statistics and fueled the material on my own blog. But no matter how much I liked the book the authors’ claim at the outset of Chapter 3 never sat right with me. It didn’t make sense to me after seeing the performance of Chelsea and Manchester United over the last half decade, but I never had the data to prove it. Luckily, the Transfer Price Index provides such data, and my analysis of the data suggests that large expenditures in the transfer market are a pre-requisite to building a team that can consistently compete for the Premier League title.

Do Wages or Transfer Expenditures Help Predict Table Position?

One of the reasons that the Soccernomics analysis never sounded exactly correct was the qualifier they gave to their transfer expenditure analysis:
“In short, the more you pay your players in wages, the higher you will finish; but what you pay for them in transfer fees doesn’t seem to make much difference.”
Combined with the opening quote, I suspect the authors looked at what each team spent on transfers in a year, attempted to correlate the expenditures to the next season’s performance, and found little correlation. That would make sense, as the few players a team brings in over a single year may not be able to have that big of an impact on a squad of eleven. That’s even assuming each transfer moves immediately into the match day squad, which isn’t often the case.

That exact thought – who plays on the pitch most of the time: transfers or home grown players? – was answered via the data assembled for Pay As You Play. The authors assembled data on the average number of homegrown players in each game for each team over each season, and I have plotted that relationship below for each of the eighteen Premier League seasons. For comparison I have also plotted the same data for the Big Four clubs on a second axis on the right side of the graph (click on graph to enlarge).



The data shows that the Premier League averaged only 2.6 homegrown players per match (24% of the players on the pitch) in its inaugural season. Since then, it has been on a steady erosion of about a tenth of a player per game per season to the point of being under a player per game (8% of players on the pitch) by the 2009-2010 season. By comparison, the average percentage of a squad composition of youth players bounced between 15% and 20% the last ten seasons, meaning that homegrown players are getting very few shots at playing time. In fact, the difference is considered “extremely statistically significant” when the proper statistical tests are performed, which is a rarity in the sports statistics world.

The Big Four have been on similar declines since the beginning of the Premier League, although they seemed to have essentially bottomed out since season nine (Manchester’s inevitable decline after unusual homegrown success is the one exception). Transfers must play a key roll in the team’s success if anywhere from 8.5 to 10 players on any side of a match are not homegrown.

Pay As You Play also provides the other key data set in helping determine if wages or transfer expenditures help predict league success. Its current transfer purchase price (CTPP©) database provides a way to compare the cost to assemble the squad versus the Soccernomics wage data, and the conclusions are interesting. For this analysis, I will be using the CTTP’s Sq£, which denotes the total costs of transfers within the squad, inflated to current values using TPI.

Some might question why a squad metric is used instead of a utilization metric, like £XI (the average cost of the XI over the course of a season, with inflation taken into account). The reason is twofold. The first is that the data must be viewed in the order of events as they actually occur, and not how one might view it in hindsight. A transfer must take place before a player and team can negotiate wages and before they can play a game for the new team. Thus, if a relationship does exist between squad transfer cost and performance, it would be the more important predictor of future success than a later event that is dependent upon the transfer occurring in the first place. The second reason is that because a measurement like £XI is dependent upon a player’s utilization, it is not effective at predicting pre-season performance and setting realistic expectations. The £XI may be very good at understanding why a team is under- or over performing once a reasonable amount of play has transpired, but not necessarily in judging how team’s transfer expenditures will contribute to future success.

There’s also a reason to look at a model based on transfer fees rather than wages – transparency. The world of soccer finance is murky any way you cut it, but it gets murkier once the financial transactions are contained within a single team. In conversations related to this post Graeme Riley explained his philosophy regarding transfers and wages, which is a common one:
“[W]ages show how a one-sided relationship values a player and so is less representative than transfers. Firstly the details are likely to be confidential and therefore less easily identified. Secondly the wages can be varied almost by the day (e.g. play bonus, win bonus, …there even used to be share of attendance bonus!), whereas the transfer price is “relatively” fixed (even allowing for appearance add-ons etc).”
If the quality of the data is variable, the outcome of the model is less trustworthy. We have no idea the quality of the data used for the Soccernomics model, but in general wages are a murky matter. The CTPP database is clearly constructed, attributed, and transparent and the quality of the data is superb.*

A little background must be provided before diving into the analysis. In their study, the authors of Soccernomics compared average league finishing position to the average of each club’s wage expenditure relative to the league average wage expenditure. To complete a comparison to the CTPP data, a similar metric was created that looked at the Sq£ data for each club versus that season’s average Sq£ value. This figure is denoted by MSq£ for “multiple of average Sq£”. Thus, the metric is not measuring how much a squad costs, but how much more (or less) it costs versus the average squad that season. This corresponds with the finish position against which variable wages and costs were compared. Finish position is only measuring how well one team performed against their competition, and is not an absolute measure like points.

In addition to creating the wage and table position data, the authors of Soccernomics had to transform the data sets using a natural logarithm to satisfy the pre-requisites for regression analysis. I won’t bore the casual reader with any more details on this process, but more statistically inclined readers can see this blog post for more detail. I provide this bit of background only to speak to the power of the CTPP data later in this post.

Finally, the CTPP had to be isolated to the years 1997-2008 given that the Soccernomics data was only plotted over a similar time period. Given that the Soccernomics data contains Championship and Premier League data while the CTPP only contains Premier League data, the CTPP was further trimmed to clubs that had missed only two seasons or less of Premier League play during that time period. This ensured the effects of budget cuts due to relegation or large transfer outlays due to recent promotion would be minimized yet keep the sample size large enough. Ultimately, that left thirteen clubs for the wage data vs. CTPP analysis – Arsenal, Aston Villa, Blackburn, Charlton, Chelsea, Everton, Liverpool, Manchester United, Middlesbrough, Newcastle, Southampton, Tottenham Hotspur, and West Ham United. A plot of the data is shown below (click on graph to enlarge).


Clearly there is a strong relationship between the current wages of a squad and the current cost in transfer fees paid to assemble it – 94% of the relationship is explained by the regression model. This is intuitive, but until the CTPP database we didn’t have the data to prove it. Perhaps the authors of Soccernomics weren’t demonstrating a relationship between wages and finish position, but rather confounding it with the actual relationship between the MSq£ and finish position. Combined with the youth player data, it would appear there is enough evidence to indicate transfers costs are key to assembling a team. Now the relationship between MSq£ and finishing position can be explored.

The Effect of MSq£ on Finishing Position

Given that it seems wages and MSq£ are highly correlated, a study of MSq£ vs. table position was undertaken. Data from all eighteen seasons of the Premier League was used for the analysis. Interestingly, unlike the Soccernomics data sets, both the table position data and the MSq£ data satisfied the requirements for regression analysis without the need for transformations. Standard statistical tests indicate the data is undoubtedly correlated, and the need to not transform the data provides a much more direct equation for explaining the relationship between the two. A plot of the regression study’s analysis is shown below (click on graph to enlarge).


The regression plot demonstrates that nearly 70% of the variability (quite a good value given the sample size) between finish position and squad cost is explained by the relationship:

Average Finish Position = -7.2221*(MSq£) + 18.32

Points that fall below the line show that, on average, a team has outperformed the model and finishes better than their average MSq£ would indicate. Teams above the line fair worse than projected. The implications of the equation are:
  • Teams that are built with a league average Sq£ (MSq£ = 1.0) have typically finished in 11th place.
  • If a club wants a good chance staying away from relegation, they typically need to have a Sq£ of at least 20% of the average Sq£ for that season.
  • If a club wants a good chance at a Champions League spot, they typically need to have a Sq£ of at least 1.98 times the average Sq£ for that season.
  • To finish fifth and qualify automatically for the Europa League, a club typically need to have a Sq£ of at least 1.85 times the average Sq£ for that season.
Spending money certainly doesn’t mean success, and single seasons may present under- or over-performance versus the historical average. Part of that may have to do with how much of the squad’s cost makes it onto the field of play, but one must undoubtedly spend the money in the first place to have a shot at getting them on the field. The regression analysis above should leave no doubt that not only does it pay to spend, it pays to spend big relative to your competition.

Looking at teams that spent the league average or more over time leads to some interesting observations. The image below focuses on those clubs.


The following observations can be made:
  • Only twelve teams out of forty-four in the history of the Premier League have averaged an MSq£ greater than 1.0.
  • All seven of the teams that have never been relegated from the Premier League – Everton, Aston Villa, Tottenham Hotspur, Liverpool, Arsenal, Chelsea, and Manchester United – have an average MSq£ of 1.0 or better. Five of the seven have an average MSq£ of 1.3 or better.
  • Aston Villa and Arsenal are the biggest overachievers, as represented by each of them having the biggest gap to the lower side of the regression line. Each has performed about six places better than their MSq£ would suggest.
  • Chelsea and Newcastle are the biggest underachievers. Chelsea suffers from a lower average finish due their performance in the league’s first decade and their consequent spend explosion in spending the second half.
There is also one common denominator of the top five spenders: DEBT. Much has been made of the Big Four’s debt woes via UEFA’s own reports and resultant fair play rules. I’ve done my own analysis using the annual Forbes rankings, using their 2006 through 2010 data to look at revenue-to-debt and profit margins before taxes for the Big Four (Newcastle have their own debt problems) to understand their ability to manage such debt. Each of them has different challenges before them:
  • While Arsenal has a healthy profit margin that has grown over each of the last four years, they carry the heaviest revenue-to-debt burden due to the recent construction of Emirates Stadium. Good debt indeed, but debt that must be serviced nonetheless.
  • Chelsea, through a forgiveness of debt by Roman Abramovich, has the best revenue-to-debt ratio of the four. However, they have yet to show a profit since 2006 and will be challenged by the fair play rules.
  • Liverpool may be the most challenged of the four. Their revenue-to-debt ratio and profit margins have been heading in the wrong direction since 2006. NESV’s purchase and effective dismissal of debt will undoubtedly help, but the ownership group’s cautious approach and the continued need for a new stadium will weigh heavily on the team’s ability to increase their MSq£.
  • Manchester United is a mixed bag like Arsenal, although likely not in as good a position. The Glazer debt is suffocating, providing them with the lowest revenue-to-debt ratio of the four even though they outstrip the next closest club’s revenue (Arsenal) by nearly 25%. However, they are the most profitable club at a 30% margin (before taxes).
All of this suggests that the Big Four, in attempting to maintain their dominance, have embarked on an unsustainable path. Each has taken different paths towards large debt loads – whether it is in players, stadiums, or overseas marketing. Whatever they have spent their (or others’) money on, it appears that such spending and the associated annual placement in the top four table positions is unsustainable given the debt load they carry today. Perhaps what we have witnessed over the last decade will be viewed years hence as not the natural order of things, but an aberration where funny money ruled the decade and led to the long term fiscal sickness of several clubs.

Indeed, the financial dominance of the Big Four has waned since its peak mid-decade. The plot below shows the MSq£ in the post-Abramovich era for the Big Four plus Tottenham and Manchester City (click on graph to enlarge).


By 2006 Tottenham had passed their rivals Arsenal in MSq£, while that year also represented the peak of Chelsea’s MSq£ advantage. Since then, Tottenham has steadied themselves around an MSq£ of 1.7 while Manchester City has increased their squad cost to the second highest MSq£ in the 2010-2011 season. Aston Villa’s sixth place finish last season notwithstanding, these are the six teams that battled over the four Champions League spots. What was a domination of four teams in 2003-2004 (no one was closer to them than Tottenham’s 57% of Liverpool’s MSq£) is now a six team race with two of the former Big Four relegated to the 5th and 6th positions. This is just further evidence that perhaps a decade or so of dominance by four teams is likely at an end, and also means risky bets of debt-loaded operations that count on continual Champions League income are not such a safe bet anymore.

The Usefulness of the MSq£ Regression Equation: A Case Study of Liverpool FC

In Pay as You Play, the authors pay close attention to each team’s rank in £XI and their associated finish, using the metric to understand the variability in pay-for-performance from season to season. With the creation of the MSq£ regression equation there is now an explicit numeric relationship between the relative cost to assemble a squad and their likely performance. Combining the two approaches allows us to understand whether a team or a manager under- or over performed versus the cost of their squad.

There are two ways to determine if a team has over- or underperformed versus expectations:
  • How they have finished versus their MSq£ rank. If the MSq£ rank is numerically higher than the table finish, they have overperformed. If the MSq£ rank is numerically lower than table finish, they have underperformed. The MSq£ rank will be the same as Pay as You Play’s Sq£ rank.
  • Translating their MSq£ value to a predicted finish, and comparing that predicted finish to the actual table finish. If the predicted finish is less than the actual table finish, the team has over performed. If the predicted finish is greater than the actual table finish, the team has underperformed.
The added benefit of using the regression equation is that it shows what teams with similar expenditures have achieved in the past. If several teams end up spending a similar MSq£, a close cluster of predicted finishes will be predicted and we will get a much clearer perspective of which teams have over- and underperformed than a traditional ranking of expenditures. Applying both metrics also gives us the ability to make a better determination of the team’s performance versus its expenditures. If both the rank and predicted place metrics break the same way, a more definite declaration that the team has exceeded or failed to meet expectations can be made. If a discrepancy exists between the two methods, a push is declared (also known as a tie to the non-gambling reader).

The first table below shows how Liverpool’s Premier League managers have fared against the rank and regression metrics. The “Total” column contains the average MSq£ of each manager, followed by the average number of teams that had a squad more costly then them. The fourth column of data shows how the manager’s average finish compared to the regression prediction from their average MSq£ – a negative score indicates better-than-predicted placement (over-performance), while a positive score indicates less-than-predicted placement (under-performance). The fifth column is self explanatory, while the final column combines the regression and rank performance to an overall judgment on the manager’s performance.

The second table displays the total count of season-by-season manager performance versus both metrics (click on tables to enlarge).



As was pointed out in Pay as You Play, Graeme Souness’ record at Liverpool was one of underachievement versus the financial resources expended. He had a MSq£ well into the twos for the one full season he was in the Premier League, while only being able to pull a sixth place finish in the table. His replacement, Roy Evans, had mixed results. He did well versus the regression predictions, but on average only a single team had a higher Sq£ only one team on average throughout his career at Liverpool. The strain of underachievement of the squad led him to quit the partnership with Gerard Houllier during the 1998-1999 season.

What becomes clear is that Gerard Houllier’s years seem to be the only managerial term where the team consistently outperformed expenditures. Houllier’s term also coincides with Liverpool’s Premier League era peak for youth players – see years six (’98-99) through eight (’00-’01) in the youth player chart earlier in this post. At that point Liverpool were running nearly double the league average with almost four homegrown players per match. Houllier leveraged players like Jamie Carragher, Steven Gerrard, Robbie Fowler, Michael Owen, David Thompson, Dominic Matteo and Steve McManaman to outperform the MSq£ regression model (although some would point out Houllier inherited all of the homegrown talent). The later years of Houlier’s term represented a movement in the wrong direction both in terms of youth players and MSq£ – while still over performing versus expenditures, the club’s backwards slide in the table was not satisfying ownership or supporters’ expectations. Enter Rafael Benítez.

Rafa Benítez’s record is mixed. Overall, it’s a push with three seasons of over-performance, two as pushes, and one under-performance. The under-performance came in the first season, but the two pushes came in Rafa’s final three seasons with the club. Benítez didn’t inherit as many quality homegrown players and continued the steady downward trend in this metric, relying mainly on Carragher and Gerrard. This meant more of his team would be built on transfers, making success more challenging given Liverpool’s modest resources versus the competition (especially after a leveraged buyout).

His best over-performance was clearly the 2008-2009 campaign where Liverpool finished with 86 points. That year’s MSq£ was fourth highest, while the regression equation would have predicted a finish position of 6.62. Sadly, poor performance and low team morale resulted in the predicted seventh place finish in 2010. Rafa, who averaged 7 points a season more than Houllier (and who did far better in Europe) left soon afterward. [The analysis in Pay As You Play clearly shows how much better Benítez's spending was in comparison with Houllier, particularly in terms of how their respective signings increased in value.]

Overall, Liverpool’s years in the Premier League have been a push. They have underperformed versus the MSq£ rank, but outperformed the regression equation. Until the ’06-’07 season they were also had the second highest utilization of youth players within the Big Four, nearly double Chelsea and Arsenal. These points are key, as history establishes realistic expectations going forward. While Liverpool has ranked high in MSq£ rank, they have consistently been number four within the Big Four.

They also seem to have occupied an interesting position in the Big Four. Chelsea has spent absurd amounts of money to compensate for the manager carousel they’ve experienced. Manchester United has been able to combine both high expenditures and management stability to set the standard for championships in the Premier League. Arsenal has relied on the genius of Arsene Wenger to keep them competitive with a modest MSq£. Liverpool seems to have had the worst of both worlds – a high turnover in managers and a very modest MSq£ compared to the big spenders they were chasing.

Liverpool’s MSq£ has steadily fallen by about 0.1 each season since 2003-2004, and is now the second lowest of the top six in the league (Arsenal is the only team with a lower MSq£). Liverpool has regressed to an MSq£ of 1.3 for the 2010-2011 season, leading to a predicted finish of 8.64. In the near term, Liverpool looks to be an upper mid-table club if they can get the right management and spend modest money. Longer term, they face a rebuilding task that needs a vision, a budget, and a manager to execute it.

The 2010-2011 Season So Far

So what does this all mean for this season?

The chart below summarizes each team’s performance to date versus their rank of MSq£ and the regression equation’s predicted finish. Chelsea’s, Manchester United’s, and Manchester City’s predicted finish from the regression equation had to be clipped to 1.0 as their MSq£ for 2010-2011 was so high that it lead to projected finishes of less than zero. Negative values versus the regression indicate over-performance, while positive values indicate under-performance (click on table to enlarge).





Clearly, the two biggest over performers are Bolton and West Bromwich Albion – both of which are placing nearly nine spots higher than the regression would predict and 10 spots higher than their place in the MSq£ rankings. Arsenal, Blackburn, and Blackpool also deserve special mention – each is at least five places higher than both the regression analysis and MSq£ rankings would indicate.

Chelsea and Manchester City are penalized due to their large spend (ranking 1-2 in MSq£), while dropping points and expected table position. Nothing short of a top finish for either will match the expectations set by their expenditures. Spurs and Manchester United are right where they should be. All of this makes for a congested top six in the table, where at least two of the current Champions League participants have a real chance of not being able to find a seat when the music stops playing at the end of the season.

At the bottom end of the table, perennial Premier League members Aston Villa are disappointing their management given the cash they’ve outlayed for them. They are 10 spots below their MSq£ rank and more than four positions below their regression equation prediction. The biggest underperformer of all is West Ham United, whose mid-table MSq£ outlay has resulted in a disappointing run at the bottom and six places lower than the regression equation predicts. Fulham and Wigan are punching five spots below their MSq£ rank, but only two to three spots below what the regression equation predicts.

It’s a long season, and a lot can change between now and May 2011. As Graeme Riley has pointed out, this season has been far less predictable than those past. Perhaps we’re witnessing the beginning of a new age when money matters less, or maybe it’s just one where the disparity in squad cost, and resultant performance, is far less. Either way, it may leave some big spenders disappointed, some frugal clubs pleasantly surprised, and others just happy to not be relegated.

Conclusions

The quote at the outset of this post noted that the Soccernomics wage model accounted for 89% of the variation between wages and finish position, while the MSq£ model accounts for nearly 70% of the variation between MSq£ and finish position. A stronger relationship to wages makes sense. Players’ contracts can be renegotiated or extended to account for improvement or degradation in play since they initially arrived, while the CTPP data used to generate the MSq£ data is a static value that only changes based on overall transfer market conditions and not an individual player’s performance after the transfer. Nonetheless, a transfer must take place before anyone can negotiate wages or play a game for the new team and begin to generate data for “relative contribution” metrics. Paying for transfers is a pre-requisite for getting the talent a team hopes contributes to superior finishes on match day. Combine this with the uncertainty in obtaining reliable wage data versus more public transactions in the transfer market, and a compelling case can be made to look at transfers first and conclude they are the price-of-entry to having a shot at Premier League success. Once a player has been purchased, wages or utilization metrics are better suited to diagnosing actual performance versus expectations.

Understanding who’s spending money on transfers and how much more they are spending than the other teams in the league is critical to understanding their ability to compete for top finishing positions. At any moment in the 2010-2011 season, the average Premier League team is fielding a squad of ten transfers and one home grown player. The quality of those transfers as indicated by their current transfer purchase price and the team’s likely finish position seem to be highly correlated.

To understand a team’s relative expenditures is to begin to understand their potential table position. Doing so helps set realistic expectations for the squad, the team’s management, and its supporters. Ignoring this reality can lead to unrealistic expectations which in the end create a desire for quick solutions that can cause more organization and financial turmoil, setting the team further back from its goals for table finish.

*[Since the original publication of this blog entry I have been contacted by Soccernomics author Stefan Szymanski and this is what he had to say about the wage data used within Soccernomics:
“You question the quality of the wage data but I’m not sure that’s right- this is audited data from the company accounts published annually - not a guess like you see in Forbes. Its one weakness is that it is total payroll data, not just players- but players account for 90% plus of payroll normally. It must be much better quality than transfer fee data which is not audited and represents figures mentioned in the newspapers- the clubs never reveal the actual transaction value, and I’m told there are a lot of inaccuracies. Without getting confirmation directly from the clubs, there is no way to check this.”
Indeed, it appears the wage data used in Soccernomics is of the highest quality. I retract my earlier comment questioning its quality. At the same time, I would stand by the CTPP database being the most accurate of its kind for transfers. Stefan was quite complimentary of the overall post and its predecessor deconstructing his work at my blog, for which I am very grateful. Ultimately, he and I would agree on the wage data being a better predictor given its higher R-squared value for the same reasons I gave at the conclusion of my post. I hope that Paul and I can engage Stefan in future analysis of the CTPP database and continue to shed light on the impact of finances on the result on the pitch.]

Tuesday, February 22, 2011

Quantifying the Bias of Arsenal's Referees


A few posts ago, I attempted to quantify the bias of Phil Dowd’s record over the last two years of officiating versus the bias of all other referees who have officiated at least three Arsenal matches over the same time period. Since then, I have received a good bit of constructive feedback, especially when it came to the sample sizes used in the study. None of the feedback indicated any major errors, but more regarding the subtleties associated with varying statistical theories that could be used as a substitute for my Mann-Whitney approach.

Nonetheless, the feedback indicated there was a good bit of demand for a more extensive analysis. Thus, I contacted Tim at 7AM Kickoff and made a deal – he would compiled the earlier seasons of data , and I would analyze the data using common statistical methods. This post is the output of that study.

Developing the Model and Collecting The Data

The approach I wished to pursue in this study was a general liner model (GLM) as it allows for the study of the impact of multiple factors (and their interactions) on various outcomes. In this case, Tim and I were interested in studying the effects of Premier League season, referee, and match venue on fouls, cards, and shots. This study grew out of two mutual interests: Tim’s desire to quantify perceived overall referee bias during this Premier League season when compared to previous ones, and our joint desire to understand the most- and least-favorable referees when it comes to our beloved Gunners. I decided to throw in the match venue impacts at the suggestion of a dedicated reader of my blog.

A GLM has one unique requirement that presents challenges when applying it to officiating data: it requires at least one sample of each unique combination of attributes. This means that to build an overall GLM, we would need a data point from each season where each referee officiated at least one home and one away game in each season analyzed. This immediately presents a challenge, because leagues purposefully randomize assignments to minimize the effects of officiating on match outcome, and thus have unbalanced officiating from year-to-year. Increasing the number of seasons in a desire to increase sample size ends up limiting the types of GLMs that can be created. Tim and I settled on pulling data from the 2006-2007 seasons through the current season – it provided enough balance in sample size and attribute combinations to allow a two-phase study of officiating of Arsenal’s matches.

A table displaying the count of each referee’s matches officiated over the last 4+ seasons is shown below – 178 matches in all (current through the Wolves game on February 12th). The columns across the top indicate the season, where the second half of each season is used to denote the full season (thus, the 2006-2007 data is found in the column labeled “2007"). Each referee has three rows associated with their name – a row indicating their count of home matches (1), away matches (-1) and total number of matches. The column on the far right, labeled “Grand Total”, shows the total number of home and away matches officiated by each referee. Click on table to enlarge it.


What becomes immediately clear is that a GLM of seasons 2007 through 2010 by official and by match venue would have an extremely limited data set – only Atkinson, Bennett, Webb, and Wiley have officiated at least one home and one away match during that time period. Most importantly, a study of Dowd’s officiating would be left out of such a model. Such a GLM can be useful in studying a few of the large effects and their interactions, but not in directly evaluating a wider set of referees.

What’s also interesting is that the some of the numbers in the “Grand Total” column are greatly skewed. Over time, Bennett, Dowd, Foy, and Riley seem to have officiated more Arsenal home matches than away matches, while Clattenberg, Dean, Marinner, Riley, and Webb have experienced the inverse in their assignments. If Scorecasting’s study on home pitch officiating bias holds true in the Premier League, we might have some confounding of individual referee performance with general bias against a visiting team.

Two GLM’s were constructed given the match count shown in the table above:
  1. A wider GLM that looked at the effects of the 2007-2011 seasons and match venue. This will help confirm or deny Scorecasting’s general conclusion regarding referee bias against visiting teams as they apply to the Premier League.
  2. A GLM of the 2007-2010 seasons using the data from Atkinson, Bennett, Dean, Dowd, Foy, Halsey, Webb, and Wiley while ignoring the aspect of match venue. This will help answer the question as to which referees are the most biased for and against Arsenal.
Each GLM will look at four main attributes that officiating can impact: shots taken, the ratio of shots-on-goal to shots taken, fouls, and Premier League points for yellow and red cards (see my last post on this topic for an explanation).  Each of these attributes is expressed as a differential. To be consistent with the direction of the differential in the first post, a negative differential in any attribute indicates Arsenal had the advantage (took more shots, had a higher ratio of shots-on-goal, fewer cards etc.), while the opposite indicates the opponent had the advantage in the match.

In the end, the two GLM’s should help us understand where the bias lies, and a few of its potential causes.

Addressing the Home Pitch Bias of Referees

The first GLMScorecasting, exists the Premier League.

The GLM used all data from the 2007 through 2011 seasons for all referees, categorizing it as home and away while ignoring the contributions of individual referees. It turned out that none of the interaction effects were statistically significant, so the analysis focused on the main effects.  Main effects plots for each of the four attributes are shown below, with commentary below each plot.

Note: The key to reading main effects plots is to look for the center line traveling across the middle of the graph. This indicates the overall average value for that metric, with the average values associated with the individual levels of the factors (x-axis) are indicated by the discrete points on the graph.


It is clear that while match venue has little impact on the foul differential, Arsenal’s beneficial foul differential has shrunk to nothing over the last 4+ seasons. In fact, this shrinkage is one of the rare statistically significant factors not aligned with match venue in any GLM in this study. Perhaps it’s Arsenal’s increasingly tough response to “kick them off the pitch” tactics that has generated this shift? Whatever the case, Arsenal has gone from being on of the cleanest teams to middle of the pack when it comes to fair play.


When it comes to throwing cards, 2011 does represent a new high point for Arsenal but the trend is not statistically significant. Clearly, though, match venue has a huge impact (statistically significant, in fact!). The average home match (value of 1) sees Arsenal acquiring one less Premier League fantasy soccer penalty point (essentially one less yellow card) than the opposition, while away from home (value of -1) they acquire a similar amount of penalty points as their opponents. Scorecasting’s biased referee observations are alive and well!


The behavior witnessed in the shots metric is similar to that seen in the cards category. Arsenal holds a pretty steady seven shots per game advantage over the competition over the last three years, but a statistically significant gap exists between home and away matches.


Finally, it seems Arsenal are improving their effectiveness at putting shots on target versus the competition. The last two seasons have seen the Gunners turn around what was a deficiency into a benefit – not only do they take more shots on average, but they also put a greater percentage of them on target. The fact that the difference between home and away performance is not statistically significant ensures that they are using their reduced shot advantage when away from the Emirates in a manner consistent with home performance.

Ultimately, Arsenal seems to be doing pretty well in the shots department, getting worse when it comes to fouls, and consequently suffering from expected referee bias against away teams when it comes to cards. This final conclusion is especially important given the skewed home/away officiating opportunities afforded several of the referees highlighted in the next section.

Identifying Referees Who Are Biased For and Against Arsenal

The second GLM involved using 2007 through 2010 data to observe any possible bias in the following referees: Atkinson, Bennett, Dean, Dowd, Foy, Halsey, Webb, and Wiley. These referees have officiated 56% of Arsenal’s matches over the last four seasons. Main effects plots for each of the four attributes are shown below, with commentary below each plot. In general, none of the factors studied is statistically significant per the standard GLM tests. What is interesting is that the average value for every metric shrinks compared to the full 2007 through 2011 study performed above. Perhaps the big name matches that guys like Webb officiate provide a better balance between the teams, or maybe it's an effect of the "better" referees getting more matches. Either way, the average gap between Arsenal and their opponents closes when these eight referees are involved.


In general, the average foul differential is tilted slightly in Arsenal’s favor when these eight referees officiate a match compared to the overall average seen in the previous section. This may be due to the exclusion of 2011 to achieve a balanced GLM in the first example, where we observed that overall they've seen their foul differential disappear. It also seems as if Dowd is one of the more generous referees when his 2011 performance is dropped and his 2007 through 2009 performance is added. This may indicate a shift in his average officiating in 2011, a subject I will explore later in this post. Conversely, Dean, Webb, and Wiley have their bias against Arsenal confirmed in the foul department. They also are the top three referees when it comes to the number of Arsenal matches officiated, with Wiley and Webb having a pretty even home/away split while Dean has a 2/13 home/away split that may be unduly influencing the results of his officiating in Arsenal matches.


While Wiley has the highest foul differentials against Arsenal, he has one of the lowest card differentials. On the other hand, Webb and Dean follow through on the fouls with the two highest card differentials. With an average card differential of nearly -0.50 with these eight referees, Dean’s and Webb’s nearly 0.5 card differential against Arsenal represents nearly 1 extra yellow card per match for the Gunners. Again, Dean’s results may be biased based upon his high ratio of away matches, but Webb’s officiating is nearly evenly split between home and away matches.


As with the other responses, average shot differential goes down compared to the total sample of 2007 through 2011 matches. Dean and Webb again lead the pack in terms of officials showing an anti-Arsenal bias. Bennett and Foy appear to be the most pro-Arsenal referees, with Atkinson and Dowd not far behind.


The shots-on-goal ratio shows perhaps the biggest average shift when compared to the full 2007 through 2011 GLM. Webb and Dean rank close to the average, with Dean even showing slight favor to Arsenal. Matches where Foy officiates show the biggest disadvantage for Arsenal, with nearly a 10% gap between their ratio of shots-on-goal versus the opponent’s.

The Increasing Bias of Phil Dowd

So where does this leave Phil Dowd in relation to the Gunners, especially given my last post?  It would appear from the data above that he's actually biased for, and not against, Arsenal!  A closer examination of the data suggests otherwise.

It seems as if there is a shift afoot in Mr. Dowd’s officiating when it comes to the Gunners.  We can see this shift when looking at the interaction plot of year vs. referee from the second GLM that was created.  The interaction plot shows the average value of each combination of factors - year and official.  The key element for which to look is non-parallel lines, which indicate bias by one of the officials.  The interaction plot is shown below (click it to enlarge).


Looking at the lower left graph shows how nearly every referee's average points based upon yellow and red cards went down from 2009 to 2010.  The only referee's score to go up was Dowd's.  Things have gotten worse in 2011 as well, with Dowd's average over the three games he's officiated coming in at a whopping 2.33.  Dowd is the most biased against Arsenal in the 2011 season and has seen his card point total increase by nearly three points (a full red card!) from last season.  In four seasons Dowd has gone from a -2.0 card point total in 2008 to a 2.33 total in 2011 (a full read and yellow card swing).  No other referee exhibits this kind of shift. Over that time period Dowd has officiated seven home matches and four away matches, clearly bucking the trend of biased officiating coming against away teams.

Conclusions

Clearly Webb and Dean are the referees that generally make more calls against Arsenal, with Webb the only one of the two with a reasonably balanced home/away officiating record that would eliminate away team bias from consideration.  Phil Dowd is rapidly approaching Webb's level of bias, with a massive shift in the way he's called matches since 2008, and a higher proportion of home matches officiated that eliminates away team bias as an excuse.

Foy and Atkinson may provide the most reliably pro-Arsenal calls.  Both provide the best combination of foul and red/yellow card advantages to Arsenal after Dowd is eliminated for his time-based shift in officiating results.

While Arsenal have consistently had a penalty and card advantage in years past, such an advantage is almost non-existent this season and last.  However, they have maintained their advantage in number of shots and percentage of shots on goal.

As a Gooner, I hope that we draw guys like Atkinson and Foy the last quarter of the season.  This gives the Gunners the best chance to close the gap to Manchester United.  I'll come back to this topic once the season is complete and we hopefully have a higher number of referees with home and away match officiating opportunities.  That would allow a more complete GLM of officials vs. venue and year.

Of immediate concern to Gooners is the fact that Dean will be officiating this Sunday's Carling Cup final.  Here's hoping he shows far less bias on the neutral pitch of Wembley than he has in Arsenal's away matches.

Friday, February 18, 2011

Friday Night Links

I'm sorry - I can't get enough of this scene!

I am back in the Pacific Northwest, happy as hell about being home and being a Gooner after Arsenal out-Barca'd Barca.  Time for my favorite reads from the week of travel.

Alright, it's time to head off to work. It's a long weekend here in the states, where we recognize the birthdays of Abraham Lincoln and George Washington on Monday - one of the rare occurrences where my European friends are at work and we Yanks are on a Bank Holiday.  Posting will likely be non-existent, as I am spending the weekend in Portland, Oregon doing various things (even catching up with a Swedish Gooner!).

Enjoy the FA Cup weekend. For us Gunners it is a match against Leyton Orient, where we attempt to keep the dream (fantasy?) of a quadruple alive.

Thursday, February 17, 2011

Nick Hornby as my Psychoanalyst the Morning After the Barcelona Match

Animated GIF courtesy of 7AM Kickoff's Twitter account

Yesterday I came home from eight days of business travel in Mississippi.  It was a rewarding trip, but I was ready to get home.  I don't begrudge people's lifestyle choices, but I do know Mississippi is not for me.  So yesterday's chain of events couldn't be better: I got to come home to the Pacific Northwest, got to enjoy the company of my wife for the first time in over a week, and then I got to see my Gunners exorcise a bit of a demon in classic fashion.  They still have lot of soccer left to play, but last night was a big step forward for a much maligned set of young Gunners.  They've stood strong against Manchester United, with a return match yet to play. They've beaten Chelsea.  Now they've beaten Barcelona.

Watching last night's game, I couldn't help but recall Nick Hornby's keys to an exciting match in Fever Pitch.  First up on his list is what happened last night:
Goals: As many as possible.  There is an argument which says that goals begin to lose their value in particularly easy victories, but I have never found this a problem... If the goals are to be shared, then it is best if the other team get their first..."
Knocking on the door for so long only to be rewarded with a Barca goal was tough, but it made the van Persie and Arshavin goals all the more satisfying.  The crowd seemed to feel the same way, as their volume only intensified to levels I had not heard in my several years of watching matches from the Emirates.  That leads us to Hornby's third ingredient to a great match.
A noisy crowd: In my experience, crowds are at their best when their team is losing but playing well, which is one of the reasons why coming back for a 3-2 win is my favorite kind of score.
It may not have been a 3-2 win, but a 2-1 win against Barcelona sure feels like a 3-2 win with the way they can score goals at an instant.  The defense last night was stout.  The offense threatened many times, and it seems the substitution strategy by both managers proved the difference.  It was simply brilliant soccer to watch, a match well worth the hype.

So much of my blog is about the numbers, almost as a way to cope with the flowing emotion that is the beautiful game. Last night I was exhausted, eight days on the road that had culminated in 10 hours of travel and two hours of time zone changes.  I was beat, and the first half of the match was a bit tough for me. No matter the numbers - the shots on goal, the time of possession, etc. - I had faith things would turn around in the second half.  And no matter how calm and collected the numbers may make me, there was no sense in holding back my emotion after Arsenal's goals.  The first goal by van Persie led to a "Are you kidding me?!?!?!" yell with a couple of expletives I won't repeat here.  Several minutes later, Arshavin's goal led me to jump off the coach and run down the hallway yelling.  No matter how many matches I watch, I think Hornby was right:
Absurdly, I haven't yet got around to saying that football is a wonderful sport, but of course it is. Goals have a rarity value that points and runs and sets do not, and so there will always be that thrill, the thrill of seeing someone do something that can only be done three or four times in a whole game if you are lucky... It allows players to look beautiful and balletic in a way that some sports do not: a perfectly-timed diving header, or a perfectly-struck volley, allow the body to achieve a poise and grace that some sportsmen can never exhibit.
I can't wait for the return match three weeks from now.