Salary determination in professional football: empirical evidence from goalkeepers

Figures & data

Table 1. Descriptive statistics for Wage and Ln(Wage).

Statistic	Wage (€m)	Ln(Wage)
Mean	2.08	7.24
Standard deviation	2.42	0.98
10th percentile	0.41	6.01
25th percentile	0.70	6.55
Median	1.42	7.29
75th percentile	2.50	7.87
90th percentile	4.50	8.43
Skewness	3.56	−0.10
Kurtosis	20.81	3.23
N observations	739	739
N players	260	260
p value for joint test of skewness & kurtosis		0.23

Table 2. Descriptive statistics for goalkeeper performance and continuous control variables.

Variable	Mean	St. Dev	Min	Max	Source
Age	28.7	4.51	17	42	Whoscored
Top 5 appearances	138	116	0	658	Whoscored
UEFA appearances	19.6	27.0	0	165	Whoscored
Other league appearances	91.1	73.4	0	520	Whoscored
National team appearances	14.9	28.1	0	175	Whoscored
Minutes	2372	947	450	3420	Whoscored
Goalkeeper rating	6.71	0.21	5.80	7.66	Whoscored
Shots faced	4.26	1.25	1.16	18.67	Whoscored
Saves per shot	0.69	0.11	0	0.89	Whoscored
Goals against	1.29	0.45	0	4.67	Whoscored
Pass success	58.4	11.2	30.6	91.1	Whoscored
Log attendance	3.33	0.58	1.34	4.40	Soccerbase
Saves minus post shot xG per shot	0.43	0.08	0.18	0.66	StatsBomb/DSG
Post shot expected goals per shot	0.29	0.03	0.20	0.36	StatsBomb/DSG
Pass 40 ratio	40.0	6.25	25.3	56.9	StatsBomb/DSG
% goalkick launches	73.1	17.1	19.4	100	StatsBomb/DSG
Launch pass rate	48.5	14.5	13.9	87.3	StatsBomb/DSG
Average pass length	40.9	6.95	24.3	59.6	StatsBomb/DSG
Stop ratio	8.05	2.66	0	14.8	StatsBomb/DSG
Actions outside penalty area	0.68	0.39	0.11	3.20	StatsBomb/DSG
Average sweep	14.6	1.57	11.3	19.0	StatsBomb/DSG
Throws per 90 mins	4.14	1.63	1.18	14.4	StatsBomb/DSG

Figure 1. Kernel density plot of Ln(Wage) for goalkeepers.

Table 3. Goalkeeper salary estimates, OLS with player fixed effects.

Variable	(1)	(2)	(3)	(4)
Age	0.382 (3.02)***	0.332 (2.69)***	0.334 (2.74)***	0.128 (2.04)**
Age^2	−0.009 (5.41)***	−0.009 (4.96)***	−0.008 (4.93)***	−0.003 (2.86)***
Top 5 app	−0.001 (0.75)	−0.001 (0.69)	−0.001 (0.79)	0.003 (6.03)***
UEFA app	0.001 (0.32)	0.002 (0.40)	0.001 (0.28)	0.005 (2.52)**
Other league app	−0.003 (0.53)	−0.004 (0.07)	−0.001 (0.19)	0.001 (2.44)**
National team app	0.011 (1.63)	0.011 (1.64)	0.011 (1.69)*	0.011 (0.91)
Minutes/1000	0.083 (3.52)***	0.088 (3.77)***	0.091 (3.89)***	0.157 (6.73)***
Goalkeeper rating	0.049 (0.61)
Shots faced		0.024 (0.47)
Saves per shot		−0.162 (0.22)
Goals against		−0.194 (1.04)	−0.104 (2.49)**	−0.311 (5.57)***
Pass success		0.669 (2.31)**	0.661 (2.33)**	0.847 (2.74)***
Transfer	0.125 (2.61)***	0.143 (2.96)***	0.146 (2.99)***	0.135 (2.03)**
Log attendance	0.374 (4.64)***	0.367 (4.69)***	0.344 (4.91)***	0.453 (6.74)***
R^2 Player fixed effects	0.42 Yes	0.44 Yes	0.44 Yes	0.60 No
N	739	727	739	739

Note: For Tables 3–5, ***, ** and * denote statistical significance at 1, 5 and 10 per cent respectively. t statistics in parentheses. Standard errors are clustered by player. Table 3 columns (1) to (3) report R²(within), column (4) reports R² (adjusted).

Table 4. Coefficients on StatsBomb performance measures, OLS estimates. Dependent variable is Ln(Wage).

Variable	(1)
Post shot expected goals per shot	−1.859 (1.95)*
Saves minus post shot expected goals per shot	1.211 (2.07)**
Pass 40 ratio	0.015 (2.10)**
% goalkick launches	−0.007 (2.10)**
Launch pass rate	−0.007 (1.84)*
Average pass length	−0.013 (1.54)
Stop ratio	0.022 (1.47)
Actions outside penalty area	−0.003 (0.53)
Average sweep	−0.006 (0.19)
Throws per 90 mins	−0.021 (0.59)

Note: Each variable is entered in separate regressions with control variables as for Tables 3 and 4.

Table 5. Coefficients on player performance measures, all positions, unconditional quantile regression estimated at median log wage.

Variable	(1)	(2)
Goalkeeper rating	−0.023 (0.54)
Defender rating	0.433 (8.77)***
Midfield rating	0.243 (8.93)***
Forward rating	0.123 (5.78)**
Goalkeeper*Goals against		−0.001 (0.71)
Saves per shot		0.080 (1.50)
Goalkeeper*Pass success		0.004 (2.84)***
Defender*Pass success		0.011 (10.06)***
Midfield*Pass success		0.006 (4.73)***
Forward*Shots on target		0.062 (2.98)***
N	7560	7560