The Rising Cost of the Starting XI in the English Premier League

Somewhere in there is the most expensive starting XI, in terms of M£XI, in the history of the Premier League - Chelsea's 2006-2007 squad.  Too bad they finished second to Manchester United who were a full 1.5x lower than them on the M£XI metric.

In my recent series of posts on the correlation between squad transfer costs and table position in the English Premier League, it was shown that:

1. Transfers are an ever increasing source of a team's players, with trainees constituting less than 20% of a team's squad
2. Such squad transfer costs continue to escalate, with the average increase at £1.55M per year (or ~1.4% per year at the current average squade cost).  The actual average transfer cost inflation rate via the TPI database is often in the double digits percentage-wise. The average squad cost has now eclipsed more than £110M. 
3. Squad transfer costs are highly correlated to squad wage costs, begging the question whether its really wages or transfers that is driving the high correlation between financially rich clubs and finishing in the top quarter of the table.
4. A model was created to identify over and under performers, and was applied to teams and managers.

It's clear that if English soccer were an arms race, the result has been that those with the biggest budgets have won the war of championships and berths into UEFA competitions.

However, this explains the average behavior over the long term.  In the short term, players and managers have off years, players get injured, and in general things don't go according to plan.  Ultimately, this impacts who the manager can put on the pitch, which is quantified in Pay As You Play with the £XI metric.  This metric measures the cost of the starting XI on the pitch at a match.  If squad cost (Sq£) is a measure of cost of the weapons in a manager's arsenal (pun totally intended...), then the related £XI can be thought of the cost of the weapons he was able to bring to the battle.  Concurently, if MSq£ measures the relative cost of a manager's weapons against the league average's, a similar metric in M£XI can be used to measure the relative costs of a manager's talent on the pitch to the league average.

It's this metric - M£XI - that is best correlated to table position in the short term, and it will be the subject of several forthcoming posts.  Combined with the MSq£ this will provide a powerful forward- and backward-looking model at the impacts of squad transfer costs in the English Premier League.  After all, one must first have the tools at their disposal, and then deploy as many of them as possible on the pitch, to have a chance at success.

Note: In the interest of keeping this series of posts a bit shorter than the MSq£ posts, I will not be repeating my detailed explanation of the statistical theory that is being reused.  Newer readers, or those wishing a deeper discussion on the statistical theory, can see this post for a discussion of regression theory, this post for a discussion of prediction intervals, and this post for a discussion of ranking methdology based upon identifying over and under performance and then "shrinking variation before shifting the mean."

The Escalating Cost of Talent on English Premier League Pitches

While the average squad cost in terms of transfer expenditures has been going up over time, so too has the cost of the average starting XI that make it on to the pitch.  The table below shows how this cost has escalated over time.  Readers familiar with a similar graph in one of the MSq£ posts will notice a slight difference, as the graph below does not include the first three years of Premier League data.  This was done to eliminate the bias introduced in the data from those three seasons when the average squad and starting XI costs were diluted by the presence of two additional teams (click image to enlarge).

The elimination of the first three years actually worsens the fit of the regression lines compared to those for MSq£, but the coefficient in front of the x-term that indicates the typical annual rise in starting XI cost is far more accurate than the similar term found in the MSq£ graph.  Ultimately, the coefficient in the graph above is compared to the rise in MSq£ recounted at the outset of this post - £1.55M per year or 1.4% compared to 2010-11 squad costs.  In the case of M£XI, it is rising at a rate of £585.5k (or £0.5855M) per year, which in 2009-2010 £XI costs equates to a 1.1% increase.  While not statistically significant, this is lower than the rate of increase on the squad cost front.

Part of the explanation comes in the lower half of the graph, which re-plots the average utilization rate discussed in earlier posts.  With the removal of the first three seasons of data, the rate of decline in utilization is 0.33% per year, or approximately 1% every three seasons.  This declining utilization means a lower percentage of the average Premier League's cost, in terms of the Sq£ measure, is making it on to the pitch each passing year.  Thus while an increasing amount of money is spent on squad costs every year, a lower percentage of that squad cost shows up on the pitch and thus the growth in squad costs is higher than the starting XI cost.

Note: To the statistically inclined, the relationship between the average utilization rate and season is indeed statistically significant.  For the fourteen samples shown in the graph, an R-squared value of 0.4575 or higher would indicate statistical significance.

The Impact on Utilization on Starting XI Cost for the Big Six

While the first graph in this post explains what the league average has done over time, of greatest importance is to observe what the most successful clubs have done over the last several years.  Just like the MSq£ series, I have focused on the Big Six clubs in the post-Abramovich era - Arsenal, Chelsea, Liverpool, Manchester City, Manchester United, and Tottenham Hotspur.  The graph below shows their utilization rate by season (click on graph to enlarge)

Closely related to this graph is one that plots the difference between each squad's utilization rate and the season's average utilization rate.  This gives us an idea of how effectively the team used their purchased talent versus the average club.  Click on the graph below to enlarge.

There are a few things to take away from trends shown in the graphs above:

• Manchester United is the only club that has a statistically significant higher utilization rate than the average team each season.  They finished with an average of 6.25% greater utilization than the league average each season, and only had two season out of seven that were below the average - the first (-0.5%) and last (-0.7%) in the series.  The first year of there latest championship three-peat saw them reach a peak of +15.8% vs. the league average.  During the seven season run, Manchester United has not finished lower than second amongst the big six in utilization, and hold the top three spots in the Big Six for utilization versus the league average over all seven seasons.  Say what you like about Alex Ferguson, but he not only knows how to buy talent he also knows how to get more of it on the pitch.
• At the other end of the spectrum is Tottenham Hotspur.  They have finished to the positive side of the league average utilization only once - +5.9% in 2006-2007.  All other seasons they have been on the negative side, and while just barely not statistically significant they have averaged -3.2% over the seven seasons.
• Arsenal, Chelsea, and Manchester City all have been on a general downward trend in terms of utilization since the 2005-2006 season.
• Liverpool has generally bounced around the league average for utilization rate, but have been on a general upward trend since their nadir in the 2004-2005 season. Ironically, they reached their peak over the seven seasons in Rafael Benitez's final season as manager.

The graphs above confirm the general trend that teams who spend a good bit on transfer budgets for their squad get the talent on the pitch.  Besides being concerned about purchased championships, another side effect of huge spending is a "hoarding effect" - one where teams buy up players but where they don't see significant playing time due to limited space on the pitch.  While not the most economically efficient manner to win, it could nonetheless be a useful strategy to keep good players from signing with competitors.  This concern arises out of the general trend in the first graph, where over time transfer budgets have gone up by less of the costly talent shows up on the pitch.

Luckily, the statistics don't bear such a strategy out.  If one tests each season's utilization rates vs. MSq£'s, one will find that only four out of the seventeen seasons in the Premier League have had Pearson correlation coefficients that are significant - 94/95, 96/97, 99/00, and 05/06.  Each time, the coefficient was positive and the slope of the linear relationship was at least 3.5%, which means rather than horde talent the teams with higher squad transfer costs were putting more of it on the pitch.  The other 13 seasons showed no relationship between the two variables.  For the time being the main concern should remain focused on the ability of teams to buy better talent at higher costs and thus put more expensive talent on the pitch.

So what does all of this translate to in terms of an advantage in starting XI cost for the Big Six?  In general, their advantage versus the rest of the league has grown when compared to the similar advantages they enjoyed in MSq£.  See the graph below for a plot of the Big Six's M£XI for the last seven seasons (click on graph to enlarge).

Recall this graph that was part of my original post in the MSq£ series.  While most of the shapes of the lines are the same between the two graphs, the magnitude of the absolute values is certainly greater on the graph above.  Notice that Chelsea's M£XI reached a peak of 4.77 in the 2006/2007 season - this is a full 0.25 multiple above their similar peak in the MSq£ metric.  A similar shift is seen in Manchester United's M£XI data, but notice they actually close the gap to less than 0.25 with Chelsea's drop in utilization rate in the last few seasons.  Overall the order of the bottom four teams does not change much from their MSq£ order, although Tottenham's anemic utilization rate leads them to switch positions with Liverpool.  Thus, increasing one's squad costs relative to the competition seems to pay even greater dividends when it comes to starting XI transfer cost advantages.

Conclusions

The cost of talent on the pitch is certainly going up each year, although at a slower rate than the overall cost of the squad.  This is due to the steadily decreasing utilization rate, which is dropping by about 1% every three years.  While many of the same trends observed in the Big Six's MSq£ were maintained when looking at M£XI, the disparity was a bit larger and utilization rates provided a few subtle differences.

In the end, how does M£XI impact team performance in the table?  And if a relationship does exist, how can it be used to evaluate how well managers and teams have done given the cost of the players they could get on to the pitch?  These topics will be discussed in the second and third posts in this series.