A Comprehensive Model For Evaluating Total Team Valuation (TTV)

Chelsea 2006/07. The Premier League's all-time most expensive team at £657M in 2010 CTTV.

For nearly two years Paul Tomkins, Graeme Riley, Gary Fulcher, Dan Kennett, and I have been using the Transfer Price Index (TPI) to shed light on the financial commitments required to finish in the top echelons of the Premier League.  A number of findings were published in Pay As You Play, while Dan and I have followed up with a number of posts at the Transfer Price Index blog.

We’ve published detailed accountings of each club’s transfer dealings, translated all of the transfers into present costs, built sophisticated models that estimate how much a club must spend to finish in a top 4 position, and have even estimated what kind of advantage financial resources bring to individual matches.  Along the way we’ve profiled a number of managers and clubs, come up with a list of the best and worst performers versus our models, commented on how transfer spending may be ruining the competitive balance of the EPL, tried to predict the 2011/12 table, and re-imagined what past tables might look like if transfer spending were taken into account.

Out of all that material perhaps the most provocative analysis was one of the original ones to appear on the Transfer Price Index blog. Titled “Soccernomics Was Wrong: Why Transfer Expenditures Matter“, it was meant to make a clear statement on what our data told us: that in contrast to Chapter Three of the aforementioned book, the more clubs spend on transfers and the greater the sum of the ‘current transfer purchase price’ (CTPP) of players at the club the more likely the club was to finish at the top of the table.

(Note: CTPP is the price paid for the player, adjusted to modern prices using TPI’s unique football inflation calculator, given that the prices of players has risen far more sharply than standard inflation. In 1980, a loaf of bread in the UK cost 33 pence, which in 2009 the Telegraph listed as £1.10 in today’s money. And yet in 1980, the British record transfer fee was roughly £1m; so while the cost of a ’1980 loaf of bread’ would be three times higher in today’s money, a British transfer record player – Fernando Torres – is fifty times more expensive than Trevor Francis and the other £1m players of 32 years ago.)

This was a very deliberate difference in opinion with the otherwise great statistical insights contained in Simon Kuper’s and Stefan Szymanski’s book. Within several hours of the post going live I was contacted by Stefan Szymanski, and an exchange of emails on the topic ensued (a synopsis of which can be found here). Graeme provided Stefan with the TPI database, and discussions continued off-and-on for the next year and a half.  Szymanski and Kuper took enough notice of the TPI and our analysis that they’ve dedicated a good bit of the revision to (now) Chapter Two of the second edition of Soccernomics to address the points we brought up. I won’t ruin the story for prospective readers, but let’s just say both groups of writers would agree economics dominate the Premier League.  The relative effect transfer spending and wages have on such outcomes is where we continue to disagree a bit.

What the disagreement does point to is the weaknesses the two teams’ approaches to the question. Szymanski’s skepticism of media accuracy when it comes to reporting transfer fees has led him to be a bit shy in integrating such analysis into his studies.  Thus, his approach only tells the half of the story that focuses on wages. Meanwhile, Graeme Riley’s exhaustive work in compiling the TPI has meant we have not had a corresponding database for wages.  Not having both data sets meant neither one of use could tell the complete story of how financial resources play a reasonably deterministic role in the Premier League.

That issue is now resolved. Professor Szymanski has been gracious enough to share a subset of his nearly 40 years of financial data that he and his research team at the University of Michigan have compiled for the top four divisions of English football.  Szymanki’s database is part of expansive project that goes well beyond wages and will be used to describe the impact the economics of English football have had on the game since 1974. The data has been compiled from the financial accounts provided to the Companies House in the UK, and is publicly available through the UK government for a small fee. Readers of this post or others based upon Prof. Szymanski’s data set may notice small differences with accounts published via other sites like Deloitte’s Money League. This is to be expected as groups like Deloitte do make adjustments based upon their own internal accounting rules. In a desire to use a consistent source of data, Prof. Szymanski has stuck with the original filings made with the Companies House.

Professor Szymanski supplied the TPI team with wage data for the Premier League era only. That wage data has been integrated into the TPI, with the sum of player wages and the CTTP value of the club being combined into an overall metric called “Total Valuation” (ToVa).

The total valuation metric is the one player compensation measure needed to estimate what it would cost to assemble and pay a squad in a given season. Like the CTPP metric, ToVa can be expressed in current pounds cost, with everything expressed in 2010 money as that is the latest season for which Prof. Szymanski has data for all 20 Premier League clubs. What follows is a dissection of the ToVa metric and the data that goes into it. This will provide a comprehensive view of how much a club must pay to compete for the top positions in the Premier League. Hold on to your hats, these financial figures will be staggering.

The Growth In Premier League Wages

Anyone who’s been following the TPI posts over the last two years knows that transfer fees and squad transfer cost (Sq£) have been escalating at a dizzying rate. As Dan Kennett pointed out last autumn, the average transfer fee has skyrocketed nearly 730% since the founding of the Premier League, while the British economy has only since a 77.1% increase in the average costs of goods and services over the same time period.  Hence the need for a transfer-specific inflation rate when considering the current value of clubs built nearly 20 years ago.

What of wages? It’s been long suspected that a same growth exists, but there have been very few resources like Prof. Szymanki’s wage database that allow us to take a long-term view of league wage growth. Before diving in to any analysis of total player valuation it is worth examining the interplay between the two ways clubs spend money on players.

The graph below provides such a comparison. It utilizes the Sq£ numbers (total squad cost with inflation applied) from the TPI database (red line), albeit adjusted from their current day value back to the equivalent value of the corresponding season. The black line represents the wage data in Prof. Szymanski’s database. The trends are generally positive for both lines, indicating how the explosion in TV revenue and commercial operations impacted the English game over the last two decades. The Premier League broke away from the Football League twenty years ago based upon the premise that they could deliver a bigger windfall for their clubs and players, and it appears that they’ve succeeded in realizing that goal.

Note: Throughout this post the median, rather than the average, fee or wage is used.  This is due to the fact that most of the squad wage or Sq£ data distributions for each season are non-normal, which means that the average value should not be used (in most cases it’s because it is skewed higher than the actual center point of the data).  In such cases the median is used as it is a much better estimator of the central value of the data set – either the squad wages or Sq£ value that equates to the average between the 10th and 11th ranked club out of 20.

What’s simply amazing to newer fans who have only known the worldwide spectacle of the Premier League is how humble a beginning it had. The median club wage bill in the inaugural season was only £3.8M, and it didn’t cross the £10M barrier until 1998. Wage growth has only been negative over two seasons (2003 and 2004), and even then it was a mild average of –2.8% for each of those two years. Eight of the first nine seasons saw median club wage growth rates of greater than 20%, which suggests that the entire league was benefiting from all of the revenue growth. Only two seasons out of eight since then have seen double-digit growth in the median club wage bill, while overall spending on wages has been a much higher percentage each of those years. This indicates that lately a greater share of the wages have gone to fewer players at the top clubs, which might have contributed to the increase in competitive imbalance the last few years. Overall, the median Premier League wage bill is up 1357% since the first season was played in 1992/93. This suggests that the growth in player wages has outpaced the growth in transfer spending, which might be considered good if one is concerned about ensuring the players on the pitch garner the majority of the financial rewards for the league’s success.

The gap between the red and black lines demonstrates that the total outlay by a club on transfer fees over a number of seasons costs a good bit more than the wages they will pay that team in a single year. The relationship between the two is intuitive from an economics standpoint – there is a substantial capital investment outlay (transfer fees) and then ongoing operating costs (wages) to build a successful business enterprise. And let’s not kid ourselves – the clubs in the modern Premier League are business enterprises that happen to be engaged in the sports entertainment trade.

How the limited resources are spent on players will vary from club to club.  Some clubs, like Arsenal, may try to stay way from large transfer fees they feel are not worth the money, and instead try to lock up a good bit of emerging or young talent by paying them higher salaries than they might get elsewhere.  Some clubs, like Manchester City or Chelsea, may not have a care about overpaying on both fronts and splash cash for both transfers and their subsequent wages.  What of the middle teams in the Premier League?  How do they choose to spend the balance of their money?

The graph below provides a comparison of the median club-wages-to-Sq£ ratio from each season of the Premier League.  This gives us an indication of how the “average” club is choosing to spend their money when given a choice between transfers and wages.

The wage trends seen in the first graph show up in the graph above as well.  After an initial drop to the lowest ratio of 0.24 in 1996, the median wage-to-Sq£ ratio increased by an average of 5.6% per season to hit a high of 0.95 in 2007.  Two trends were at work during this time period.  First, the median Premier League club wage bill was certainly increasing.  Second, the median Sq£ was not increasing nearly as fast, and this was especially the case in the post-Abramovich era of 2004 and later.  The vast majority of clubs couldn’t spend the huge sums of money on transfers that the top clubs in the Premier League were spending.  A smaller share of those clubs budgets were going to the sticker shock of large transfer fees, with a greater share going to wages they felt they could better afford and sustain. Wages had to be paid first to field a competitive team with the required number of players, and whatever was leftover or could be borrowed was applied to the few transfers the middling clubs bought.  As the numbers of such clubs increased, their corresponding wage-to-Sq£ ratios went up and thus the median wage-to-Sq£ ratio also went up.  Fewer clubs were spending big money in the transfer market as overall wages increased, with only the economic challenges of 2008 and later leading to a readjustment to historical norms closer to a ratio of 0.5 to 0.6.

It is clear that wages and transfer fees are related.  If this is the case, how should the existing TPI models for MSq£, M£XI, and m£XIR be modified given the new data (see bottom of post for a reminder of the definitions of each model)?  What does the updated model say about the impact of economics on the English game?  These are questions best addressed via some light statistical analysis and the creation of an overall “total valuation” model.

Creating a Comprehensive Metric for Total Player Valuation

One way to understand how club wages and Sq£ values relate to each other is to run a correlation study.  If the study does show that the variables are correlated, simply adding a term for wages to the existing TPI models will violate one of the more basic assumptions of regression theory that variables be independent and not correlated.

It helps to use a common metric when trying to understand if club wages and Sq£ may be correlated.  As both Soccernomics and the TPI models both use a “multiple of an average squad wage or Sq£” independent variable, it is useful to translate the wage data for each club into a multiple of the median club wage bill (mTW) for the season.  A similar transformation was performed on the Sq£ values (mSq£).  The pairs of values for mTW and mSq£ are plotted in the graph below, with regression lines and equations shown as well.

The graph demonstrates the high degree of correlation between a club’s multiple of the median club total wage and its multiple of the medain Sq£.  In fact, nearly 80% of the variation in mTW can be explained by mSq£.  This greatly surpasses the minimum required score on a correlation test, and suggests that the two metrics are highly intertwined.  Thus, adding an mTW term to the existing regression models built upon the mSq£ is not appropriate.

An alternative metric focused on total team valuation (TTV) could be used.  Doing so would answer the question, “How much money must a club spend in transfer fees to assembly a team and subsequent wages to pay the squad capable of finishing in X position in the table?”  Such a metric would be defined as:

TTV = TW + Sq£

The TW and Sq£ terms are not inflated – they use the numbers for the wage and transfer valuations at the time the season is played.  Once all of the TTV values for each club and each season have been a compiled an inflation factor for TTV is calculated by taking the change in median TTV’s from season to season.  Values for the median TTV and per cent change in TTV by season are shown in the graph below.

If one looks at the graph above and the first graph in this article they will see that the solid black line above is simply the addition of the two solid lines in the first graph.  The dip in median TTV from 2002 to 2006 is due exclusively to the drop in median Sq£, and is almost exclusively due to the player transfer fee arms race initiated by Roman Abramovich and Chelsea.  Again, when an players arms race goes on and player valuation is concentrated at the top levels of the Premier League it depresses the Sq£ values of the middle clubs.  A second influx of cash that led to modest wage gains and huge transfer fee gains led to a spike in TTV by 2009.  The departure of several “expensive” clubs in the 2009/2010, including Newcastle United, depressed the TTV value for that season from it’s high in 2009 of nearly £140M.

Overall, a club must have spent 8.8 times more than they did in 1992/93 to sit middle of the table for total valuation in 2009/2010.  In pure cash terms, the median club spent £13.3M in 1992/93 to assemble and pay the wages of their players, while in 2009/10 it had exploded to more than £117M current total team valuation (CTTV).  Recalling the earlier wage data, the same median club would then pay at least £51M a year in wages to keep the club assembled, and millions more on the constant swapping of players to maintain a Sq£ value of £66M.  Such quantification gives new meaning to the term “a rich man’s game”!

One of the rich men who has pushed player compensation and transfer fees to such stratospheric levels also owns the record for the most expensive club ever assembled on a CTTV basis.  Chelsea’s  runner-up 2007 side was built upon a £265M Sq£ and £202M in wages.  When translated to a CTTV basis, that Chelsea squad cost more than £657M to assemble and pay.  Chelsea were above £625M CTTV’s each of the three seasons from 2004/2005 to 2006/2007, with an average CTTV of £646M.  There next closest competitors on a CTTV basis were Manchester United, with CTTV’s of £399M, £440M, and £440M, respectively.  Chelsea had to spend more than £200M more than their closest economic rival to ensure they won two Premier League trophies during that time.

How Total Valuation Impacts The League Table

As the 2006/07 season demonstrated, money could buy a lot but it couldn’t guarantee continual Premier League titles.  Jose Mourinho’s Chelsea side would finish second that season to Manchester United, the second biggest spender in terms of total valuation.  Mourinho would depart for Italy in the offseason, and Chelsea would continue on a carousel of managers in search of the elusive Champions League title.  While the team did fall short of it’s champsionship goal in 2007 it would finish 2-3-1-2 in the next four successive seasons, demonstrating that money could at least buy the club a shot at winning the championship each year.

Just how much must a club spend in total valuation to have certain odds of winning the Premier League?  How much must they spend to have good odds of making it into the lucrative Champions League?  The graph below can help answer these questions, and those familiar with the MSq£ and M£XI regressions will find it to be very familiar.  It is a regression of all of the Premier League clubs’ average multiple of the median TTV each season (mTTV) and their average finish position from each season.  The solid black line is the regression line, while the dashed lines represent various confidence intervals.  The regression line can be thought of the 50% line – for a given mTTV value, half the clubs will finish above the line (lower table position), and half will finish below it (higher table position).  The 50% confidence interval demonstrates where 50% of the teams would finish (y-axis position) given performance to expectations corresponding average mTTV value (x-axis position).  The band within the two black lines is considered normal variation – finish below it and a club is over performing (higher average table position) , while clubs finishing above the band are under performing (lower average table position).  The green band is the lower bound of the 95% confidence interval – only 5% of clubs are expected to finish below this line (gross over performance) for a given mTTV value.  Conversely, the red line is the upper bound of the 95% confidence interval, where finishing above the line is gross under performance.

The graph and the resultant regression equations have several key implications for spending and its impact on league table position:

  • The mTTV metric can explain 71% of the variation in average finish position in the Premier League.  The other 29% of the variation is due to factors not accounted for in the model or other random behavior.
  • For every multiple of the median TTV that a club spends, they’re expected to improve their table position by seven places.
  • Spending the median TTV means that a club has a 50% chance of finishing 12th or lower in the table.
  • Only one club has grossly over performed the model (Queens Park Rangers).
  • Of the top 10 clubs on an average mTTV basis, two have under performed (Chelsea, Manchester City) and one has over performed (Arsenal).
  • Of the seven clubs who have been in the Premier League since its inception, Aston Villa has the lowest average mTTV of 1.11.  Clearly their performances over the last two seasons have put that record in jeopardy, with Everton being the next closest with an average mTTV of 1.18.
  • Given the regression statistics, the following sums of money must be spent to ensure corresponding odds for each of the listed table positions:

On an individual season basis in the post-Abramovich era (2003/04 to present), the TTV database offers the following observations about how big spending has come to dominate the Premier League:

  •  Outside of Arsenal’s Invincibles of 2003/2004, no team in the post-Abramovich era has won a Premier League title with an mTTV less than 3.24 (£374M on a CTTV basis).
  • Liverpool owns the record for the least expensive 2nd place squad, with their 2009 team having an mTTV of 2.11 (CTTV of £247M).  Arsenal’s runner-up team in 2005 had the second lowest mTTV of a second place team at 2.50 (£293M CTTV), while the third lowest runner up was the 2010 Manchester United side with an mTTV of 3.52 (£412M CTTV).
  • In terms of Champions League qualification, Everton holds the record for least expensive club.  Their 2005 side qualified for play-in matches with a 4th place finish built upon a team with an mTTV of 1.12 (£131M CTTV).  They subsequently fell to Villareal during the second round of qualifying for the 2005/2006 Champions League tournament.
  • Arsenal’s 2008 4th place finish is the least expensive Champions League qualification that resulted in group play in the subsequent season’s tournament.  The Gunners finished fourth in the league with a squad made from an mTTV of 1.54 (£180M CTTV).  No too far behind them is Liverpool’s 2004 team that had an mTTV of 1.87 (£219M CTTV), and would go on to win the 2004/2005 Champions League in dramatic fashion.

Conclusions

The Premier League was created in 1992 as a way to funnel more money to the top clubs in the English game in the hopes of making them more competitive within the wider European soccer marketplace.  If wages and transfer fees are to be a measure of the league’s success, they have likely succeeded beyond the wildest dreams of the league’s initial participants.  Double digit wage growth for players during the first decade of the league’s existence.  Rapidly escalating TTV revenue, with the original Sky contract worth only £50M per season (2010 £’s) and the latest contract worth more than £440M per season.  Clubs like Manchester United, Chelsea, Liverpool, and Arsenal that are the envy of the world.  Performances in confederation competitions that assure the greatest number of Champions League teams of any nation in the tournament.  The EPL has come to be regarded as the most competitive and best league in the world.  Things certainly have changed a lot since the post-Heysel low point of English soccer that only ended with the continental competition ban being cancelled only a year before the formation of the Premier League.

There is a sense that things have begun to go a bit too far with the Premier League’s commercialism.  By the mid 2000′s, with Roman Abramovich’s money igniting a wage and transfer fee arms race, the Premier League had begun to become bifurcated between the haves and the have nots.  Chelsea’s ownership spent money without regard for ever running a break even business, a luxury no other team could afford until Sheikh Mansour bought Manchester City in 2008.  By 2006 the Premier League had met the basic definition of an oligopoly.  Clubs were required to spend hundreds of millions of pounds, often three to six times as much as the average club, to finish in the rarified air of Top 4 position.  Given the huge sums of money available in the Champions League, such high spending came with high risk if the club finished outside the Top 4 and missed out on Champions League glory (see Leeds United earlier in the decade).  What had started out as an experiment in raising the fortunes of all clubs in the Premier League had turned into the enrichment and increased competitiveness of a rare few clubs by the end of the league’s second decade.  While no where near as bifurcated as Spain’s La Liga duopoly, the English game has become far more predictable in the season’s outcome over the last twenty years.  Such predictability can almost solely be based on the economic fortunes of the clubs, which may or may not make for supporter excitement depending on how one views the game should be played and governed at the professional level.

Zach Slaton is the author of A Beautiful Numbers Game blog, and a contributor at The Tomkins Times and the Transfer Price Index. You can follow him on Twitter and Facebook.

Definitions of terms/models from prior posts:

  • CTPP = Current Transfer Purchase Price.  The player’s original transfer value adjusted for football inflation using the same method – but not the same figures – as the Retail Price Index. (Andriy Shevchenko holds the highest CTPP, his £30.8m transfer in July 2006 now worth £68.2m; the increase down to the difference in the average cost of a Premier League transfer that season – around £2m – and how the average in 2011 is c.£5m)
  • Sq£ = The cost of a club’s squad for a season
  • £XI = The average cost of the starting XIs in Premier League matches that season
  • MSq£ = Multiple of average Sq£. Not how much a squad costs, but how much more (or less) it costs versus the average squad that season.
  • M£XI = Multiple of average Sq£. Not how much a starting XI costs, but how much more (or less) it costs versus the average starting XI that season.
  • m£XIR = estimate of win, draw or loss (and thus expected resultant points) in relation to venue (home/away) and match starting XI cost ratios (the greater the advantage in the CTPP cost of the XI over an opponent the higher the chances of winning; but also taking the big advantage of being at home into account.)

3 Responses to “A Comprehensive Model For Evaluating Total Team Valuation (TTV)”

  1. Shashi Kiran May 2, 2012 at 5:36 pm #

    Amazing post Zach. Really appreciate the work you guys are doing. Any chance of seeing the TTV table of teams for individual seasons or maybe even the last. I am curious to see how Arsenal compare to their rivals.

    • Zach May 3, 2012 at 1:33 am #

      Shashi – Thank you for the feedback! It certainly was fun to write the post. I will be doing several follow up posts on key clubs either here or at The Tomkins Times. I am sure Arsenal will be on the list, being a Gooner myself. We typically don’t put up tables of our data set as it’s tantamount to giving away the crown jewels. The preference is to produce high value graphics, or perhaps a subset of the data in a tabular form that’s a bit more limited than the full data set. Thanks for commenting, and please do check back every so often for new posts.

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  1. A Beautiful Numbers Game: A Comprehensive Model For Evaluating Total Team Valuation (TTV) - May 2, 2012

    [...]  The Premier League's all-time most expensive team at £657M in 2010 CTTV. I just made my latest post over at the Transfer Price Index blog.  Our working group has been lucky enough to exchange data with Stefan Szymanski, which has [...]

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