How much money does it take to win the Premier League?
By Sihan Zheng
Vichai Srivaddhanaprabha, chairman of newly promoted Leicester City, recently claimed that he will invest £180 million over the next three years to make the top 5 in the Premier League. It was an offhanded comment that really didn’t outline anything, but it did get me thinking; just how much money and squad investment does it take to contend in the Premier League? How far will £180 million take you?
While the £180 million comment was grand in gesture, he didn’t really mention how the £180 million would be spent. It was an offhanded comment, but it did get me thinking, if you increase the wage budget and transfer expenditure of a team by a combined £180 million over three years, assuming that the money is spent efficiently, how much better would the team be? Using Leicester City as an example, lets look at the problem.
Premier League wages are probably the closest representation of a players anticipated contribution in any league in any sport. Why are Premier League salaries a very accurate representation of a player’s perceived skill? First of all, the average duration of a contract in the Premier League is short. A player on multiple short contracts would be effectively “re-evaluated” every year or so and paid accordingly. There are also no measures that artificially limit how much a player can earn, like the NBA’s maximum contract, nor is there a league wide salary cap like the MLS. Sometimes a player might be horribly overpaid, as a team would overestimate their level of skill, but very rarely do you see a player who is underpaid. After all, a player can simply demand a new contract or a transfer if he believes that he deserves more.
Now the owners of Leicester City (King Power International) said that they would invest an additional £180 million into the team. Let’s assume for a minute here that all £180 million will be invested into wages through 3 years, looking at it from a pure theoretical perspective, what would adding £180 million to the wage bill do? How far would it go? With an additional £60 million spent per year, how much better should we expect Leicester City FC to be?
First of all, it should be possible to look at historical numbers and plot them. Using a data set of 119 individual teams seasons from the 2008 – 2009 season all the way up to the 2013-2014 season, I have plotted it on a graph, and used Excel to find a curve that best fits to find a function of points relative to wage bill. I plotted the wage bill of every single club but Portsmouth, as the club entered administration before the season ended.
The curve can be described as y = 24.754ln(x) – 51.587, with an R2 value of 0.6435. Or in simpler terms, it is a logarithmic curve where the independent variable (x) is the wage bill, and the dependent variable (y) is points. This curve that there is a positive relationship between wages and points. The R2 value (which describes the accuracy) does show that there is a significant margin of error, probably due to luck, market inefficiency, or simply just genius management and coaching.
To understand this relationship, we first have to look at the structure of the Premier League. The maximum number of possible points is 114. The cost per point goes up the more points a team has. After all, top players are rare, and command disproportionately higher wages. Remember, wages are supposedly an estimation of player skill combined with certain market factors. There are too many factors such as health and teamwork that scouts and analysts cannot predict accurately, and these factors play a huge role in determining team performance.
Since we are overanalyzing offhanded comments here, I would say that hypothetically if Leicester City increase their wage bill by £60 million per season, they should have a realistic shot at making top 5. However, a bigger question is the availability of players. Simply paying a player more does not make him better, can Leicester City obtain enough players who are worth paying the extra £60 million to?
Further more, even though the money will be good, they have to contend with the likes of United, City, Chelsea, Arsenal and Liverpool when it comes to players good enough to push for a top-five place. Leicester City would also have to spend heavily in transfers to be able to buy the players worth paying the extra money to, but that will prove difficult given the amount of clubs with far higher prestige.
Overall, this is a very rough estimate, the formula derived here is a very, very rough prediction. Of course, there are too many factors other than wages that affect how well a team actually does. But overall, I would say that wages are a decent predictor of success, and that a £85 million wage bill can reasonably allow a team to make the top 5. There is a major factor that I did not consider however, and that is Premier League wage inflation, which if taken into account can make the formula significantly more accurate. If I can obtain the needed data, I will discuss the effects of wage inflation in a later post.