How much success can money buy in football?

Massive inflow of investment into English football prompts us to consider question "Does money buy glory?" more often. Most of supporters would love "No" to be the answer - in fact, as a hope, we get some fairy-tail results from cup competitions, like Wigan beating Manchester City in the FA Cup in two consecutive years. Yet, quite sadly, it seems that the examples of money-not-buying-glory are mostly limited to cups and are a natural result of big number of one-game encounters, where a 1-in-10 chance of underdog beating favorite will provide a couple of very unexpected results every season.

This article presents relationship between wage bill and performance of Premier League teams in 21st century - starting with the season 2000/01 and until 2012/13 (the latest data available). Just in case you don't want to go through the whole article (full of numbers, I must warn), the bottom-line is the following: money may not guarantee the success, but it buys most of it - just above two-thirds, to be precise.

And here comes the proof. On the graph below I plotted relative payroll (horizontal axis) and points gained (vertical axis) by every team in every season between 2000/01 and 2012/13. Relative payroll is measured by percentage of total league payroll for given year - after all, it only matters how much teams spend comparing to the rest of the league. Points are simply points, since the structure of the league remained constant for this period. No more boring details, here you go:

There are 251 dots on the graph - 20 teams times 13 seasons minus 9 occasions when no wage bill data was available. The black dotted line is a trend line - basically, one can use it to predict with decent accuracy how many points a team will collect given its relative payroll. 

Perhaps even more importantly, this line allows us to assess performance of the team given its resources. Being above the line means "beating the market", while being below it means that perhaps the team should have done better with its resources.

The R²  number is a very important piece of the picture, as it shows the fraction of variability in performance that occurs due to variability of wage bills. To say that over two-thirds of performance is explained by wage bill might be an overstatement, but it's not far from truth either.

While drawing conclusions from this graph might not be an easy task, here are some other statistics that demonstrate how payroll may predict performance. Let us start with those privileged ones who lift the trophy - how do their payroll compare to that of others?

The chart above shows how high Premier League champions were ranked by wage bill. It is true that the highest spending on salaries does not guarantee the title (only 5 times out of 13 the winners were the biggest spenders); but it is also true that, as data shows, you can only win the title with a top-3 payroll: it has never occurred in past 13 years that a team with a non-top-3 payroll won the Premier League. Liverpool almost broke this tradition in 2013/14. Just in case you struggle to find the key word in the last sentence, it's almost.

How about getting to top-4? What kind of payroll do you need to find yourself a place in the European elite? Here's your data:

84% of all top-4 positions have been occupied by the teams with top-4 wage bills. You can literally count on fingers the cases in past 13 seasons when a team with non-top-4 payroll actually finished in the top 4:

Arsenal 2000/01 (5th payroll; 2nd place)

Newcastle 2001/02 (8th payroll; 4th place)

Newcastle 2002/03 (6th payroll; 3rd place)

Everton 2004/05 (11th payroll; 4th place)

Arsenal 2009/10 (5th payroll; 3rd place)

Tottenham 2009/10 (7th payroll; 4th place)

Arsenal 2010/11 (5th payroll; 4th place)

Tottenham 2011/12 (6th payroll; 4th place)

Eight fingers is enough, and you'd spend the entire palm on North London teams. Notably, there were four consecutive seasons (2005/06-2008/09) where top-4 payrolls occupied top-4 places. 

On the other hand, here are the teams that failed to finish in the top 4 despite a top-4 wage bill:

Chelsea 2000/01 (1st payroll; 6th place)

Chelsea 2001/02 (4th payroll; 6th place)

Leeds United 2002/03 (3rd payroll; 15th place) 

Liverpool 2004/05 (4th payroll; 5th place)

Manchester City 2009/10 (2nd payroll; 5th place)

Liverpool 2009/10 (4th payroll; 7th place)

Liverpool 2010/11 (4th payroll; 6th place)

Chelsea 2011/12 (2nd payroll; 6th place)

Good that we have Arsenal, Tottenham, Chelsea and Liverpool who provide at least some unpredictability for top-4 finishes.

Surviving in the Premier League is an immensely important task for smaller-budget teams. Let's now look what it takes to make sure you stay in the top tier:

First of all, it needs to be mentioned that the picture may be distorted by 9 teams for which there was no data, meaning that for those years there were only 19 teams ranked by wage bill.

Even so, it happened only three times in 13 years that a team with a top-10 payroll goes down. You are safe if you pay your players earn above median unless you are Leeds United 03/04 (7th payroll; 19th place), Newcastle 08/09 (6th payroll; 18th place) or QPR 12/13 (7th payroll; 20th place). More than 75% of relegated teams had 15th-and-below payroll. Comparing to championship and top-4 finish, it might not be as predictable, but at the bottom of the payroll rankings the differences are smaller, which results in more deviation of payroll ranking from football ranking.

Finally, imagine that at the start of the season all you know about a team is how it is ranked by its wage bill. Will you be able to predict where it will finish? Below you can see the differences between payroll ranking and place in the final table for past 13 seasons:

33 (12,7%) times the teams finished in exact accordance with their wage bill. If someone generous allows you to choose the interval of three position where the team will end up, your chances go up to 36,1% - not bad given that you don't even know what team you are talking about. If you are allowed to choose interval of 5 positions, your chances are now slightly better than a coin flip at 50,9%.

Good news is that Premier League is still able to surprise with 47 teams having moved further than 5 positions up or down comparing to what their budget predicted. Unfortunately, the closer to bottom of the table, the more likely such surprises are to happen - the top of the table is an exclusive club and very, very reluctantly accepts strangers.

Now, it should be understood that performance is not expected to improve by 20% if you simply start paying your players 20% more. The idea is that football labour market appears to be pretty efficient - the players contribute proportionally to what they are paid much more often than they do not. Moreover, since it is uncommon for contracts to be signed for longer than 4 years, underperforming and overachieving players relatively quickly reestablish their market value in terms of salary. It is particularly true for overachievers, as they rarely enter free agency, but rather are being sold or prolonged by current teams on better personal terms.

I will return to the first graph to discuss performance of particular teams and their managers, but as of now, it is clear that if you have no information about the team other than how its wage bill compares to opposition, you are still able to draw a respectable prediction on where the team will end up at the end of the season.