Is Football players’ performance influenced by the quality of opposition? Application of the Golden Index formula in Club Atlético de Madrid 2016/2017

Pereira, Tiago; Ribeiro, João; Grilo, Filipe; Barreira, Daniel

doi:10.1590/S1980-6574201900010022

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Motriz: Revista de Educação Física

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Original Article (short paper) • Motriz: rev. educ. fis. 25 (1) • 2019 • https://doi.org/10.1590/S1980-6574201900010022 copy

Is Football players’ performance influenced by the quality of opposition? Application of the Golden Index formula in Club Atlético de Madrid 2016/2017

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Aim:

In this study, we sought to analyze the influence of the quality of opposition on players’ performance of Club Atlético de Madrid (ATM) 2016/2017. For that, the Golden Index (GI) formula was applied to identify and rank the Golden Players of ATM when playing against opponents of different quality levels.

Methods:

GI formula variables were collected through notational analysis and three global adjacency matrices were constructed to record all successful ball-passing actions performed. Next, the matrices were imported to SocNetV to collect the network centrality metrics. To uniformize each variable, the statistical standardization technique was applied to all variables. ATM opponents were classified into three groups: high-level (n=4), medium-level (n=2) and low-level (n=2), according to their classification in La Liga and participation in the final stage of UEFA Champions League 2016/2017.

Results:

Koke was considered the Golden Player playing against high-level teams, while opposing low-level opponents he was ranked as second. Against medium- and low-level teams, Antoine Griezmann was considered the Golden Player, but was not classified in the three first positions against high-level opponents. Yannick Carrasco and Filipe Luís were ranked in the second and third positions, respectively, when playing against high- and medium-level opponents. Also, Saúl Ñíguez obtained the third higher index against low-level teams.

Conclusions:

This study evidenced that players’ individual performance is influenced by the quality of the opposition. Additionally, the GI formula proved to be a potent tool in analyzing player’s performance in attacking plays in Football.

Keywords:
golden index formula; golden player; individual performance; quality of opposition

Match	Competition	Result	Opponent level
Leicester City Football Club vs ATM	Champions League	1-1	High
ATM vs Real Madrid Club de Fútbol	Champions League	2-1	High
Real Madrid Cub de Fútbol vs ATM	La Liga	1-1	High
ATM vs Futbol Club Barcelona	La Liga	1-2	High
ATM vs Sevilla Fútbol Club	La Liga	3-1	Medium
Reial Club Deportiu Espanyol de Barcelona vs ATM	La Liga	0-1	Medium
Real Sporting de Gijón vs ATM	La Liga	1-4	Low
ATM vs Unión Deportiva Las Palmas	La Liga	1-0	Low

Player	SP	SCP	Tp vs H-L	Tp vs M-L	Tp vs L-L
Ángel Correa	W	OM	90	-	64
Antoine Griezmann	SS	-	371	186	184
Diego Godín	CB	-	371	186	94
Fernando Torres	S	-	188	76	81
Filipe Luís	FB	-	355	186	94
Gabi	CM	-	371	186	188
José Giménez	FB	CM	155	92	-
Juanfran	FB	-	149	92	-
Kevin Gameiro	S	-	108	91	116
Koke	WM	CM	356	186	188
Lucas Hernández	CB	FB	39	-	188
Nicolás Gaitán	W	-	-	10	8
Saúl Ñíguez	CM	WM	339	186	126
Šime Vrsaljko	FB	-	94	2	188
Stefan Savić	CB	-	371	186	188
Thomas Partey	CM	WM	51	46	30
Yannick Carrasco	W	-	318	149	147

Steps	Name	Description	Formula
1	Mean of each variable on the team (X1)	Values of each individual player, after being added up, and divided by the number of players.	$X 1 = \frac{\sum x}{n}$
			∑x: sum of the values of each player
			n: number of players
2	Difference between the player's ratio and the mean of the team in each variable (X2)	The player's individual value is measured by subtracting his ratio value for the mean of the team in the variable (1), obtaining negative or positive values, being below or above the mean of the team in the variable	$X 2 = Xo - M$
			Xo: player's ratio in the variable
			M: mean of the variable
3	Standard deviation of the values of all team players for each variable (S)	The determination of the standard deviation (S) of the variable allows verifying to verify the measure of dispersion relatedive to the means. This can only assume non-negative values, and the greater its value, the greater is the dispersion of the sample.	$S = \sqrt{\frac{\sum {(xi - x)}^{2}}{n - 1}}$
			Xi: value at position i in the data
			X: mean of the data
			n-1: amount of data minus 1
4	Standardization of each variable (Z)	The value of the player (2) is subtracted by the mean value of all players for each variable (1), divided by the standard deviation of all players for each variable (3).	$Z = \frac{x - μ}{σ}$
			x: value of the player (2)
			μ: mean of all players in the variable (3)
			σ: standard deviation of the players in the variable (4)

R	Player	SP	GI	PRec	PPer	PR	BC	IRCC	PCr	RB	*BL	DB	A	Shots	Goal
1	Koke	WM	39.846	0.404	0.430	0.086	341.9	30.3	0.006	0.008	0.169	0.003	0.022	0.003	0
2	Yannick Carrasco	W	35.863	0.299	0.208	0.069	0	24.6	0.003	0.041	0.145	0.016	0.016	0.016	0
3	Filipe Luís	FB	27.565	0.279	0.287	0.069	487.5	27.6	0.008	0.017	0.124	0.003	0.003	0.003	0
4	Gabi	CM	20.467	0.358	0.420	0.114	188.3	30.7	0	0.005	0.178	0.003	0.011	0.003	0
5	Antoine Griezmann	SS	16.425	0.253	0.218	0.085	1.5	26.2	0	0.022	0.146	0	0.003	0.016	0.005
6	Saúl Ñíguez	CM	13.634	0.206	0.183	0.080	0	24.4	0	0.006	0.094	0.003	0	0.018	0.006
7	Kevin Gameiro	S	3.950	0.148	0.083	0.040	0	14.7	0	0.019	0.037	0.009	0.009	0.019	0
8	Ángel Correa	W	-4.564	0.211	0.156	0.045	0	12.1	0	0.022	0.078	0	0.011	0.011	0
9	Diego Godín	CB	-10.367	0.124	0.124	0.047	0	22.4	0	0	0.040	0	0	0.008	0.003
10	Fernando Torres	S	-11.849	0.128	0.043	0.067	0	9.4	0	0.011	0.074	0.005	0	0.016	0
11	Juanfran	FB	-15.783	0.235	0.262	0.054	0	20.8	0	0.007	0.141	0	0	0	0
12	Stefan Savić	CB	-17.126	0.065	0.116	0.056	0	23.1	0	0	0.022	0	0	0.005	0
13	José Giménez	FB	-19.845	0.135	0.200	0.062	0	19.8	0	0	0.194	0.006	0	0	0
14	Thomas Partey	CM	-20.546	0.157	0.196	0.034	0	9.2	0	0.020	0.059	0	0	0	0
15	Šime Vrsaljko	FB	-26.460	0	0.117	0.029	12.560	0	0	0.053	0	0.011	0	0	0
16	Lucas Hernández	CB	-31.210	0.128	0.051	0.034	0	10.0	0	0	0.051	0	0	0	0
17	Nicolás Gaitán	W	-	-	-	-	-	-	-	-	-	-	-	-	-

R	Player	SP	GI	PRec	PPer	PR	BC	IRCC	PCr	RB	*BL	DB	A	Shots	Goal
1	Antoine Griezmann	SS	32.560	0.395	0.333	0.108	10.0	17.5	0	0.075	0.075	0	0.011	0.022	0.011
2	Yannick Carrasco	W	25.287	0.369	0.268	0.116	4.250	16.7	0	0.040	0.121	0.020	0.013	0.027	0
3	Filipe Luis	FB	17.861	0.333	0.387	0.079	369.0	18.5	0.005	0.022	0.070	0.005	0.005	0.011	0
4	Koke	WM	16.437	0.435	0.398	0.092	131.5	18.2	0	0.016	0.081	0.005	0.011	0.005	0.005
5	Nicolás Gaitán	W	8.530	0.400	0.400	0.021	0	19.3	0	0	0	0	0.100	0	0
6	Diego Godín	CB	6.127	0.194	0.247	0.060	891.8	17.1	0	0.005	0.054	0	0	0.005	0.005
7	Gabi	CM	3.826	0.333	0.435	0.072	56.0	19.5	0	0.016	0.043	0.005	0	0	0
8	Saúl Ñíguez	CM	-2.169	0.280	0.296	0.075	33.5	17.1	0	0.011	0.032	0	0.005	0.016	0
9	Fernando Torres	S	-3.956	0.211	0.132	0.055	0	14.0	0.013	0.013	0.053	0	0	0.013	0
10	Šime Vrsaljko	FB	-9.562	1	0.5	0.025	0	19.2	0	0	0.5	0	0	0	0
11	Juanfran	FB	-9.837	0.185	0.228	0.044	0	15.9	0	0	0.043	0.011	0	0.011	0
12	Thomas Partey	CM	-12.542	0.239	0.283	0.053	0	17.3	0	0.022	0.043	0	0	0	0
13	Kevin Gameiro	S	-17.418	0.231	0.077	0.067	0	12.4	0	0.011	0.099	0	0.011	0.022	0
14	José Giménez	FB	-27.214	0.174	0.174	0.051	0	14.3	0	0	0.098	0	0	0	0
15	Stefan Savić	CB	-27.931	0.124	0.145	0.052	0	13.6	0	0	0.032	0	0	0	0
16	Ángel Correa	W	-	-	-	-	-	-	-	-	-	-	-	-	-
17	Lucas Hernández	CB	-	-	-	-	-	-	-	-	-	-	-	-	-

R	Player	SP	GI	PRec	PPer	PR	BC	IRCC	PCr	RB	*BL	DB	A	Shots	Goal
1	Antoine Griezmann	SS	30.016	0.245	0.174	0.086	46.5	14.8	0	0.027	0.076	0.011	0.016	0.022	0
2	Koke	WM	29.754	0.431	0.394	0.079	253.6	19.0	0	0.005	0.069	0	0.011	0.011	0
3	Saúl Ñíguez	CM	19.601	0.310	0.294	0.081	30.5	16.8	0	0.024	0.063	0	0	0.024	0.008
4	Yannick Carrasco	W	17.601	0.224	0.150	0.069	15.0	12.4	0.007	0.027	0.061	0	0.007	0.014	0.007
5	Šime Vrsaljko	FB	15.055	0.191	0.250	0.073	0	16.3	0.005	0.021	0.069	0.005	0.005	0.005	0
6	Gabi	CM	10.143	0.303	0.356	0.078	67.9	17.7	0	0.005	0.059	0	0.011	0.005	0
7	Kevin Gameiro	S	7.926	0.198	0.121	0.065	0	13.0	0	0.017	0.069	0	0	0.017	0.026
8	Thomas Partey	CM	6.824	0.267	0.333	0.037	0	18.9	0	0	0.033	0	0.033	0	0
9	Filipe Luis	FB	0.038	0.351	0.394	0.051	16.0	19.6	0	0.011	0.074	0	0	0	0
10	Lucas Hernández	CB	-7.929	0.186	0.250	0.055	7.3	17.3	0	0.011	0.016	0	0	0	0
11	Fernando Torres	S	-10.824	0.259	0.111	0.067	0	11.3	0	0.012	0.136	0	0.012	0.012	0
12	Stefan Savić	CB	-16.228	0.144	0.202	0.067	23.7	13.8	0	0	0.037	0	0	0	0
13	Diego Godín	CB	-22.809	0.106	0.117	0.035	0	11.4	0	0	0.021	0	0	0.011	0
14	Ángel Correa	W	-27.662	0.188	0.125	0.038	0	13.6	0	0.016	0.141	0	0	0	0
15	Nicolás Gaitán	W	-51.884	0.125	0	0.014	0	0	0	0	0.125	0	0	0	0
16	José Giménez	FB	-	-	-	-	-	-	-	-	-	-	-	-	-
17	Juanfran	FB	-	-	-	-	-	-	-	-	-	-	-	-	-

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[1] Corresponding author Daniel Barreira Faculty of Sport, University of Porto, Porto, Portugal Centre of Research, Training, Innovation and Intervention in Sport (CIFI2D), University of Porto, Portugal Rua Dr. Plácido Costa, 91, 4200-450, Porto, Portugal Email: dbarreira@fade.up.pt