From Sessegnon to Sanchez: How to calculate the correct market salary for EPL players.

In the 2018 January transfer window, Manchester United signed Alexis Sanchez on a four-and-a-half year contract. He had just turned 29, which is towards the end of the peak years for an elite forward. Yet Ed Woodward made him the highest paid player in the country, offering him a reported £350,000 per week, which equates to £18.2 million per year, or £82 million over the duration of the contract (before bonuses and signing-on fee).

United have undoubtedly received a spectacularly poor return on their acquisition. Granted, Sanchez has had his fair share of injuries, but it is clear that United chose to massively overpay a player whose abilities were likely to decline. Putting their recruitment issues aside (for now), what would have been a more reasonable salary for an EPL player of Sanchez's age and calibre? What should Woodward have offered him?

Market value salaries

We can attempt to answer this question by combining two very useful datasets: the Transfermarkt.com estimate of the market value of EPL players, and the Capology.com database of their current weekly salary (see this thread for a nice comparison of the average player salary across Europe's top leagues).

Transfermarkt uses an innovative crowd-sourcing technique to generate estimates of the perceived market (i.e. transfer) value of any professional player in Europe. Registered users on the site can submit their own estimate of a player's value; Transfermarkt then aggregates these estimates to produce the latest valuation of each player, which are updated every 6-12 months. Their player valuations are thought to be some of the best available, are regularly quoted by major media outlets around the world and have been the subject of numerous academic studies (e.g. here). Transfermarkt's player valuations are also a key input into FiveThirtyEight's match prediction model. For reference, Messi's current value is estimated to be £140m, Pogba is valued at £80m and Trent Alexander-Arnold at £44m.

Figure 1 plots the current Transfermarkt  market values of each player in the English Premier League last season (x-axis) against their gross weekly salary, as reported by Capology (y-axis). Valuations and salaries encompass several orders of magnitude, so the results are plotted on a logarithmic scale.

There is clearly a very strong relationship between player value and the salary they are paid. The black-dashed line shows the results of a regression of salary on value (assuming a power-law relationship), indicating the typical salary for a player of a given value. In the current EPL market, the average weekly salary for a player valued at £10m is about £50k per week. For a player valued at £50m it is about £100k per week, and for a player valued at £100m it is about £136k. Roughly speaking, salary increases with the square-root of market value (scroll to the end for the complete formula).

Figure 1 - Weekly salary plotted against market value (as estimated by Transfermarkt) for current EPL players. Players labelled in red earn more than double their market value-implied salary; players in green earn less than half their market average salary.

The red shaded region indicates players that are paid more than double their market value-implied salary. Alexis Sanchez is only the third most over-paid player in the English Premier League: Mesut Ozil takes top spot, his reported salary of £350k per week is over four times higher than the market salary of £83k/week that is implied by his current Transfermarkt valuation of £35m. Second is another Arsenal player, Petr Cech, who - despite being valued at only £2.5m (he is 37, after all) currently earns £110k per week, just over four times above the £26k weekly salary implied by his current market value. Alexis Sanchez is paid 3.8 times the market-implied salary of £92k/week for his £45m valuation.

The players highlighted in green earn less than half their market-implied salary.  The common characteristic of these players is that they are young: their average age is less than 22. Zinchenko, Foden and Wan-Bissaka have only recently broken into the first team at their respective clubs, while others are purely valued based on their potential; in both cases, their values have risen quickly and salaries haven't caught up yet. There are some older players in this group - Denis Odoi and Floyd Ayite (both at Fulham) - but they are very close to the low (£1m) end of the valuation scale.

The ratio of a player's salary to his market-implied salary has a very clear trend with age. Players aged 24 and below tend to be paid at less than two-thirds of their market rate, while players over the age of 30 are paid 33% above than their market value rate. While younger players are valued based on their potential, it appears that salaries of older players are determined by their past achievements.  The data indicates that clubs systematically over-pay older players, implying a need for more careful contract design.

Who are the main culprits?

Which clubs have a tendency to pay their players significantly more than the market rate? Figure 2 shows the median ratio of player salary to their market value-implied salary for each premier league squad. Values above 1 indicate that a club tends to pay above market-rate salaries; values below 1 suggest that they pay below the market rate. Scatter plots for each club (similar to Figure 1) can be found here.

Figure 2: Median ratio of player salary to market value-implied salary for each EPL squad last season. Values above 1 indicate that a club tends to pay above market-rate salaries; values below 1 suggest that they pay below the market rate.

Manchester United and Arsenal are the biggest culprits when it comes to overpaying their players: the average player in their squads earns 40% more than their market value says they should. There are six players in United's squad that earn more than double their market-implied salary -- Pogba, Sanchez, Mata, Young, Valencia and Shaw -- and five  in Arsenal's squad (Ozil, Mkhitaryan, Wellbeck, Cech, and Lichsteiner). Outside the top 6, West Ham are the biggest payers of inflated salaries. Notable high-earners include Javier Hernandez, who earns more than 2.5 times more than his market-implied salary, Andy Carrol and Pablo Zabaleta.  

Most EPL clubs managed their salary roll well last season, with 11 of the 20 clubs paying their players at or below the market salary, on average. Spurs are the most financially savvy of the top 6, typically paying their players 84% of the market-implied salary; only Fernando Llorente earns significantly more than his value suggests he should. Wolves deserve a special mention: on average they paid only 66% of the market-implied salary, and only three players -- Moutinho, Patricio and Ruddy -- earned more than their market value indicates they should.

Flash the cash and fail

Premier League salaries are a frequently and hotly discussed topic. As the excellent Swiss Rambler shows, from 2008 to 2018, Manchester United's wage bill almost tripled, Liverpool's did triple and Manchester City's wage bill increased by a factor of 5. In the 2017/18 season, the top 6 spent more on players wages than the rest of the league combined. Of course, we all know that UEFA Champions League participation and commercial partnerships have enabled the revenues of the rich to grow quickly, and it is no surprise that the top 6 are shelling out huge sums of money to ensure they remain there. 

However, there are large discrepancies in the how effectively the money is being spent. In particular, Arsenal and United - whose levels of squad talent have fallen behind the other top-6 clubs - are throwing money at players in the hope that something clicks. The results shown above demonstrate that they are paying many of their players more than their abilities deserve (relative to the rest of the Premier League).  This strategy - if you can call it that - is failing. Both teams have bloated wage bills that dwarf the quality of their squads. Furthermore, they have destroyed whatever kind of wage structures that they may previously have had in place. Ed Woodward and Sir Chips Keswick would both seem to have cases of financial mismanagement to answer. 

On the other hand, it is reassuring that many of the clubs with vastly fewer resources than the Big 6 are shrewdly effective in extracting value for money from their wage bill. Cardiff, Huddersfield and Fulham may have been relegated, but at least the data indicates that they didn't fall into the trap of over-paying aging stars in a short-sighted attempt to retain their Premier League status. This is where the benefits of a Moneyball-type strategy should be most effectively realised: smaller clubs aiming to outperform their resources by optimizing the ratio of their squad value to total wage bill.

To calculate the current fair market salary (FMS, £k/week) for any EPL player, plug their Transfermarkt value, V (in £m),  into this formula: FMS = 19.4 V^0.42 ).