---

Title: Introduction to Soccer Pass Network Analysis with Python

Author: Indranil Ghosh

Institute: School of Fundamental Sciences, Massey University

Twitter: @indraghosh314

Website: https://indrag49.github.io/

Date: 31-07-2021

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Abstract

This talk teaches four simple concepts to those who want to start working on football data analysis:

• How to get open access event data from statsbomb using statsbombpy,

• How to draw a soccer pitch using mplsoccer,

• How to visualize a pass network for a particular team in a particular match, and

• How to use NetworkX module to analyze the pass network.

Start with statsbombpy

• Use pip to install statsbombpy by using the following command:

pip install statsbombpy

The open data from Statsbomb can be accessed without any need of authentication from the user but it is always advised to go through the Terms & Conditions section stated at their documentation page.

• Now we will go step by step to understand how to extract the relevant data. Before that, we need to import the statsbombpy package.

from statsbombpy import sb

• We then import the numpy and the pandas packages that help us manipulate our datasets and perform analyses like data cleaning and data extraction.

import numpy as np
import pandas as pd

• To get access to the Competitions dataset type the following:

comp = sb.competitions()

credentials were not supplied. open data access only

• The dataset comp look like this:

comp.head(15)

	competition_id	season_id	country_name	competition_name	competition_gender	season_name	match_updated	match_available
0	16	4	Europe	Champions League	male	2018/2019	2021-04-19T17:36:05.724116	2021-04-19T17:36:05.724116
1	16	1	Europe	Champions League	male	2017/2018	2021-01-23T21:55:30.425330	2021-01-23T21:55:30.425330
2	16	2	Europe	Champions League	male	2016/2017	2020-08-26T12:33:15.869622	2020-07-29T05:00
3	16	27	Europe	Champions League	male	2015/2016	2020-08-26T12:33:15.869622	2020-07-29T05:00
4	16	26	Europe	Champions League	male	2014/2015	2020-08-26T12:33:15.869622	2020-07-29T05:00
5	16	25	Europe	Champions League	male	2013/2014	2020-08-26T12:33:15.869622	2020-07-29T05:00
6	16	24	Europe	Champions League	male	2012/2013	2020-08-26T12:33:15.869622	2020-07-29T05:00
7	16	23	Europe	Champions League	male	2011/2012	2020-08-26T12:33:15.869622	2020-07-29T05:00
8	16	22	Europe	Champions League	male	2010/2011	2020-07-29T05:00	2020-07-29T05:00
9	16	21	Europe	Champions League	male	2009/2010	2020-07-29T05:00	2020-07-29T05:00
10	16	41	Europe	Champions League	male	2008/2009	2020-08-30T10:18:39.435424	2020-08-30T10:18:39.435424
11	16	39	Europe	Champions League	male	2006/2007	2021-03-31T04:18:30.437060	2021-03-31T04:18:30.437060
12	16	37	Europe	Champions League	male	2004/2005	2021-04-01T06:18:57.459032	2021-04-01T06:18:57.459032
13	16	44	Europe	Champions League	male	2003/2004	2021-04-01T00:34:59.472485	2021-04-01T00:34:59.472485
14	16	76	Europe	Champions League	male	1999/2000	2020-07-29T05:00	2020-07-29T05:00

• We can extract the column names of comp to understand the dataset better and draw out relevant information from the same. Type the following:

print(comp.columns)

Index(['competition_id', 'season_id', 'country_name', 'competition_name',
       'competition_gender', 'season_name', 'match_updated',
       'match_available'],
      dtype='object')

• Let us make sense of a particular row from the comp dataset. For example, if we look into the row where the competition_id is 16and the season_id is 1, we notice that the country_name is Europe, the competition_name is Champions League, the season_name is 2017/2018, and so on. Suppose we are satisfied with the above information, and we want to analyze a game from 1017/18's Champions League season. We keep note of the competition_id and season_id at that row, which are 16 and 1 respectively. Now we extract out the matches dataset by typing the following:

mat = sb.matches(competition_id = 16, season_id = 1)

credentials were not supplied. open data access only

• The dataset mat looks like this:

mat

	match_id	match_date	kick_off	competition	season	home_team	away_team	home_score	away_score	match_status	match_status_360	last_updated	last_updated_360	match_week	competition_stage	stadium	referee	data_version	shot_fidelity_version	xy_fidelity_version
0	18245	2018-05-26	20:45:00.000	Europe - Champions League	2017/2018	Real Madrid	Liverpool	3	1	available	unscheduled	2021-01-23T21:55:30.425330	None	7	Final	NSK Olimpijs'kyj	M. Mažić	1.1.0	2	2

• Evidently, the mat dataset gives us the match ids, the match dates, the kick off times, the home and away teams, the scores in a particular match, the name of the referee who officiated the match and so on. Here match_id is the unique id that will help us draw out event data for a particular match from 2017/18's Champion's League season. Let us get the event data from a match. We see there is only one match available, with match_id = 18245, which was the Champions League final match between Real Madrid and Liverpool ⚽ that took place at the Olimpiyskiy National Sports Complex, Moscow stadium and it ended up 3-1 in Real Madrid's favor 👀 👀 👀 👀. A great feat to be honest! Let us obtain the event data for this match.

events = sb.events(match_id = 18245)

credentials were not supplied. open data access only

• The dataset events fetching us the event data for the particular match looks like this:

events

	50_50	ball_receipt_outcome	ball_recovery_recovery_failure	block_offensive	carry_end_location	clearance_aerial_won	clearance_body_part	clearance_head	clearance_left_foot	clearance_right_foot	...	shot_statsbomb_xg	shot_technique	shot_type	substitution_outcome	substitution_replacement	tactics	team	timestamp	type	under_pressure
0	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	{'formation': 41212, 'lineup': [{'player': {'i...	Real Madrid	00:00:00.000	Starting XI	NaN
1	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	{'formation': 433, 'lineup': [{'player': {'id'...	Liverpool	00:00:00.000	Starting XI	NaN
2	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	Real Madrid	00:00:00.000	Half Start	NaN
3	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	Liverpool	00:00:00.000	Half Start	NaN
4	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	Liverpool	00:00:00.000	Half Start	NaN
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
3492	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	Real Madrid	00:42:21.211	Offside	NaN
3493	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	Real Madrid	00:48:31.725	Half End	NaN
3494	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	Liverpool	00:48:31.725	Half End	NaN
3495	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	Liverpool	00:48:02.893	Half End	NaN
3496	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	...	NaN	NaN	NaN	NaN	NaN	NaN	Real Madrid	00:48:02.893	Half End	NaN

3497 rows × 86 columns

• We see that we were able to get access to all the events from the Real Madrid vs. Liverpool match. We can jot down the column names to get a clearer overview of what kinds of events to expect from the match.

print(events.columns)

Index(['50_50', 'ball_receipt_outcome', 'ball_recovery_recovery_failure',
       'block_offensive', 'carry_end_location', 'clearance_aerial_won',
       'clearance_body_part', 'clearance_head', 'clearance_left_foot',
       'clearance_right_foot', 'counterpress', 'dribble_nutmeg',
       'dribble_outcome', 'dribble_overrun', 'duel_outcome', 'duel_type',
       'duration', 'foul_committed_advantage', 'foul_committed_card',
       'foul_committed_type', 'foul_won_advantage', 'foul_won_defensive',
       'goalkeeper_body_part', 'goalkeeper_end_location', 'goalkeeper_outcome',
       'goalkeeper_position', 'goalkeeper_punched_out', 'goalkeeper_technique',
       'goalkeeper_type', 'id', 'index', 'injury_stoppage_in_chain',
       'interception_outcome', 'location', 'match_id', 'minute', 'off_camera',
       'out', 'pass_aerial_won', 'pass_angle', 'pass_assisted_shot_id',
       'pass_body_part', 'pass_cross', 'pass_cut_back', 'pass_end_location',
       'pass_goal_assist', 'pass_height', 'pass_inswinging', 'pass_length',
       'pass_miscommunication', 'pass_outcome', 'pass_outswinging',
       'pass_recipient', 'pass_shot_assist', 'pass_straight', 'pass_switch',
       'pass_technique', 'pass_through_ball', 'pass_type', 'period',
       'play_pattern', 'player', 'position', 'possession', 'possession_team',
       'related_events', 'second', 'shot_aerial_won', 'shot_body_part',
       'shot_end_location', 'shot_first_time', 'shot_freeze_frame',
       'shot_key_pass_id', 'shot_one_on_one', 'shot_outcome', 'shot_redirect',
       'shot_statsbomb_xg', 'shot_technique', 'shot_type',
       'substitution_outcome', 'substitution_replacement', 'tactics', 'team',
       'timestamp', 'type', 'under_pressure'],
      dtype='object')

• This completes our section on how to get access to open event data for a particular football match. We need to filter out only those events on which we want to perform advanced mathematical analyses and build conclusions. Next, we will learn how to visualize a football pitch using mplsoccer.

Draw a Football Pitch

• If you do not want to recreate a football pitch manually using Python (which would be rather tedious) you can simply use the mplsoccer module without any concern. To my knowledge it provides with the best functionalities to draw a football pitch. This package is maintained by Anmol Durgapal and Andrew Rowlinson.

• Keep in mind you can do a lot more advanced visualization stuffs using mplsoccer besides drawing a football pitch. We will encounter them as we move forward with other posts later. For now let us focus on visualizing a pitch in the simplest way possible. We need to pip install the package first:

pip install mplsoccer

• Note that mplsoccer uses Python 3.6+. Next we need to import matplotlib and the Pitch classes.

import matplotlib.pyplot as plt
from mplsoccer.pitch import Pitch

• Let us try to draw the simplest football pitch that satisfies our visualization needs.

pitch = Pitch(pitch_color = 'grass', line_color = 'white', stripe = True, constrained_layout = True,
        tight_layout = False, goal_type = 'box', label = True,  axis = True, tick = True)
fig, ax = pitch.draw()
plt.show()

• Let us try to understand what is happening here. Personally, I like setting the pitch_color argument to 'grass' giving an impression of a real life football pitch. Note that any other color can be set, for example, 'black' or any color represented by its hex code. Discarding the stripe argument removes the darker stripes that appear on the pitch. The line_color is self-explanatory and the user can change its color too according to their need. By default, the axis, labels and the ticks representing the scales are switched off. The user can turn it on by setting label, axis and tick arguments to be True, as evident in the above pitch. Let us draw a different pitch with its color changed and stripes removed.

pitch = Pitch(pitch_color='black', line_color = 'white', constrained_layout = True,
        tight_layout = False, goal_type = 'box', label = True,  axis = True, tick = True)
fig, ax = pitch.draw()
plt.show()

• Now let us focus on the axis range for a moment. By default the Pitch() function sets the pitch type to be statsbomb where the y-axis is inverted and ranges from 80 to 0. The x-axis ranges from 0 to 120. We will be mostly working with statsbomb data, so, these orientations of the axes won't be of much concern. Nevertheless this information is way too useful and we must keep this in mind, in case we deal with football data from other sources.

• To be precise, there are eight different pitch types that mplsoccer provides us with. They are 'statsbomb', 'opta', 'tracab', 'skillcorner', 'wyscout','metricasports', 'uefa', and 'custom'. This can be set using the pitch_type argument inside the Pitch() function. Let us check the orientation of the uefa pitch type:

pitch = Pitch(pitch_color='grass', stripe = True, pitch_type = 'uefa', line_color = 'white', constrained_layout = True,
        tight_layout = False, goal_type = 'box', label = True,  axis = True, tick = True)
fig, ax = pitch.draw()
plt.show()

• The reader might have noticed that by default, the pitch has a horizontal appearance. If the user wants it to be vertical, they should pass an additional argument orientation and set it to 'vertical'.

pitch = Pitch(orientation = 'vertical', pitch_color = 'grass', line_color = 'white', stripe = True, constrained_layout = True,
        tight_layout = False, goal_type = 'box')
fig, ax = pitch.draw()
plt.show()

• The user can also make the pitch appear half by setting the view argument to be 'half'.

pitch = Pitch(view = 'half', pitch_color = 'grass', line_color = 'white', stripe = True, constrained_layout = True,
        tight_layout = False, goal_type = 'box')
fig, ax = pitch.draw()
plt.show()

• These are the most basic concepts covering the topic of drawing and visualizing a football pitch using mplsoccer. The pitches can be further customized to meet the users' visualization needs. Keep an eye on the mplsoccer documentation to learn more about the same. In the next section, we will learn how to visualize a pass network for a particular team from a match and analyze the network with the help of NetworkX Python package. This package will help us use basic concepts from complex network analysis literature to analyze the network and deduce some interesting properties from the same.

Visualize a Pass Network

• We will employ the NetworkX Python package for the analysis purpose. Let us pip install the package:

pip install networkx

• After installing the package we will import networkx:

import networkx as nx

• We will also pip install the seaborn package which is a Python package built on matplotlib and is used for generating informative and appealing statistical graphs for analysis purposes.

pip install seaborn

• Let's import seaborn too

import seaborn as sns

• If we look into the events dataset, we notice that there is a column named tactics that provides us with team lineups, formations, player ids and their jersey number from both the teams. The corresponding row values for column type gives us an idea about whether it was the starting 11 formation or was a tactical shift or any other developments in the teams. Let us generate a completely new dataset only focusing on the tactics and the type columns. We will filter the data in such a way that the tactics column has no rows set to nan.

tact = events[events['tactics'].isnull() == False]
tact = tact[['tactics', 'team', 'type']]

• The tact dataset looks like:

tact

	tactics	team	type
0	{'formation': 41212, 'lineup': [{'player': {'i...	Real Madrid	Starting XI
1	{'formation': 433, 'lineup': [{'player': {'id'...	Liverpool	Starting XI
3489	{'formation': 433, 'lineup': [{'player': {'id'...	Liverpool	Tactical Shift
3490	{'formation': 433, 'lineup': [{'player': {'id'...	Real Madrid	Tactical Shift
3491	{'formation': 433, 'lineup': [{'player': {'id'...	Real Madrid	Tactical Shift

• Let us focus only on the tactics for the starting 11 set up from both the teams. We will build and analyze the pass network generated from among the starting 11 players from either of the teams. If we look into the first two rows of the type column in tact, we see that they are set as 'Starting XI', one for each team. Let us separately fetch the data for the teams, filtering by type

tact = tact[tact['type'] == 'Starting XI']
tact_Real = tact[tact['team'] == 'Real Madrid']
tact_Liv = tact[tact['team'] == 'Liverpool']
tact_Real = tact_Real['tactics']
tact_Liv = tact_Liv['tactics']

• So both tact_Real and tact_Liv are dataframes made of single rows with their indices (Which we will use to extract the data), and the tactics column is made up of a Python dict object. For now we are only interested in the key 'lineup' to get all the information about the players from the teams.

dict_Real = tact_Real[0]['lineup']
dict_Liv = tact_Liv[1]['lineup']

• We will use the from_dict() function provided by pandas to convert the dictionary into a dataframe.

lineup_Real = pd.DataFrame.from_dict(dict_Real)
lineup_Real

	player	position	jersey_number
0	{'id': 5597, 'name': 'Keylor Navas Gamboa'}	{'id': 1, 'name': 'Goalkeeper'}	1
1	{'id': 5721, 'name': 'Daniel Carvajal Ramos'}	{'id': 2, 'name': 'Right Back'}	2
2	{'id': 5485, 'name': 'Raphaël Varane'}	{'id': 3, 'name': 'Right Center Back'}	5
3	{'id': 5201, 'name': 'Sergio Ramos García'}	{'id': 5, 'name': 'Left Center Back'}	4
4	{'id': 5552, 'name': 'Marcelo Vieira da Silva ...	{'id': 6, 'name': 'Left Back'}	12
5	{'id': 5539, 'name': 'Carlos Henrique Casimiro'}	{'id': 10, 'name': 'Center Defensive Midfield'}	14
6	{'id': 5463, 'name': 'Luka Modrić'}	{'id': 13, 'name': 'Right Center Midfield'}	10
7	{'id': 5574, 'name': 'Toni Kroos'}	{'id': 15, 'name': 'Left Center Midfield'}	8
8	{'id': 4926, 'name': 'Francisco Román Alarcón ...	{'id': 19, 'name': 'Center Attacking Midfield'}	22
9	{'id': 19677, 'name': 'Karim Benzema'}	{'id': 22, 'name': 'Right Center Forward'}	9
10	{'id': 5207, 'name': 'Cristiano Ronaldo dos Sa...	{'id': 24, 'name': 'Left Center Forward'}	7

lineup_Liv = pd.DataFrame.from_dict(dict_Liv)
lineup_Liv

	player	position	jersey_number
0	{'id': 3630, 'name': 'Loris Karius'}	{'id': 1, 'name': 'Goalkeeper'}	1
1	{'id': 3664, 'name': 'Trent Alexander-Arnold'}	{'id': 2, 'name': 'Right Back'}	66
2	{'id': 3471, 'name': 'Dejan Lovren'}	{'id': 3, 'name': 'Right Center Back'}	6
3	{'id': 3669, 'name': 'Virgil van Dijk'}	{'id': 5, 'name': 'Left Center Back'}	4
4	{'id': 3655, 'name': 'Andrew Robertson'}	{'id': 6, 'name': 'Left Back'}	26
5	{'id': 3532, 'name': 'Jordan Brian Henderson'}	{'id': 10, 'name': 'Center Defensive Midfield'}	14
6	{'id': 3567, 'name': 'Georginio Wijnaldum'}	{'id': 13, 'name': 'Right Center Midfield'}	5
7	{'id': 3473, 'name': 'James Philip Milner'}	{'id': 15, 'name': 'Left Center Midfield'}	7
8	{'id': 3531, 'name': 'Mohamed Salah'}	{'id': 17, 'name': 'Right Wing'}	11
9	{'id': 3629, 'name': 'Sadio Mané'}	{'id': 21, 'name': 'Left Wing'}	19
10	{'id': 3535, 'name': 'Roberto Firmino Barbosa ...	{'id': 23, 'name': 'Center Forward'}	9

• We are basically interested in the players name and their corresponding jersey numbers. We will use a simple for loop and store the information in seperate dictionaries for both the teams.

players_Real = {}
for i in range(len(lineup_Real)):
    key = lineup_Real.player[i]['name']
    val = lineup_Real.jersey_number[i]
    players_Real[key] = str(val)
print(players_Real)

{'Keylor Navas Gamboa': '1', 'Daniel Carvajal Ramos': '2', 'Raphaël Varane': '5', 'Sergio Ramos García': '4', 'Marcelo Vieira da Silva Júnior': '12', 'Carlos Henrique Casimiro': '14', 'Luka Modrić': '10', 'Toni Kroos': '8', 'Francisco Román Alarcón Suárez': '22', 'Karim Benzema': '9', 'Cristiano Ronaldo dos Santos Aveiro': '7'}

players_Liv = {}
for i in range(len(lineup_Liv)):
    key = lineup_Liv.player[i]['name']
    val = lineup_Liv.jersey_number[i]
    players_Liv[key] = str(val)
print(players_Liv)

{'Loris Karius': '1', 'Trent Alexander-Arnold': '66', 'Dejan Lovren': '6', 'Virgil van Dijk': '4', 'Andrew Robertson': '26', 'Jordan Brian Henderson': '14', 'Georginio Wijnaldum': '5', 'James Philip Milner': '7', 'Mohamed Salah': '11', 'Sadio Mané': '19', 'Roberto Firmino Barbosa de Oliveira': '9'}

• So, we have collected the names and the jersey number of the players (starting 11) from both the teams in separate dictionaries named players_Real and players_Liv. These will come handy later!

• Now from the events dataset we will extract out the relevant columns for our pass network analysis purposes.

events_pn = events[['minute', 'second', 'team', 'type', 'location', 'pass_end_location', 'pass_outcome', 'player']]

• The first 10 rows of the events_pn dataframe:

events_pn.head(10)

	minute	second	team	type	location	pass_end_location	pass_outcome	player
0	0	0	Real Madrid	Starting XI	NaN	NaN	NaN	NaN
1	0	0	Liverpool	Starting XI	NaN	NaN	NaN	NaN
2	0	0	Real Madrid	Half Start	NaN	NaN	NaN	NaN
3	0	0	Liverpool	Half Start	NaN	NaN	NaN	NaN
4	45	0	Liverpool	Half Start	NaN	NaN	NaN	NaN
5	45	0	Real Madrid	Half Start	NaN	NaN	NaN	NaN
6	0	0	Liverpool	Pass	[60.0, 40.0]	[32.1, 41.2]	NaN	James Philip Milner
7	0	3	Liverpool	Pass	[35.0, 40.8]	[92.7, 22.7]	Incomplete	Dejan Lovren
8	0	8	Real Madrid	Pass	[27.4, 60.2]	[36.1, 71.6]	NaN	Raphaël Varane
9	0	10	Real Madrid	Pass	[35.3, 75.4]	[22.4, 76.6]	NaN	Luka Modrić

• The last 10 rows of the events_pn dataframe:

events_pn.tail(10)

	minute	second	team	type	location	pass_end_location	pass_outcome	player
3487	82	27	Liverpool	Substitution	NaN	NaN	NaN	James Philip Milner
3488	88	21	Real Madrid	Substitution	NaN	NaN	NaN	Karim Benzema
3489	31	41	Liverpool	Tactical Shift	NaN	NaN	NaN	NaN
3490	61	1	Real Madrid	Tactical Shift	NaN	NaN	NaN	NaN
3491	88	34	Real Madrid	Tactical Shift	NaN	NaN	NaN	NaN
3492	42	21	Real Madrid	Offside	[114.8, 41.4]	NaN	NaN	Karim Benzema
3493	48	31	Real Madrid	Half End	NaN	NaN	NaN	NaN
3494	48	31	Liverpool	Half End	NaN	NaN	NaN	NaN
3495	93	2	Liverpool	Half End	NaN	NaN	NaN	NaN
3496	93	2	Real Madrid	Half End	NaN	NaN	NaN	NaN

• The next step is to filter the datset by teams and store them as new datasets:

events_Real = events_pn[events_pn['team'] == 'Real Madrid']
events_Liv = events_pn[events_pn['team'] == 'Liverpool']

View the first 10 rows from both the datasets:

events_Real.head(10)

	minute	second	team	type	location	pass_end_location	pass_outcome	player
0	0	0	Real Madrid	Starting XI	NaN	NaN	NaN	NaN
2	0	0	Real Madrid	Half Start	NaN	NaN	NaN	NaN
5	45	0	Real Madrid	Half Start	NaN	NaN	NaN	NaN
8	0	8	Real Madrid	Pass	[27.4, 60.2]	[36.1, 71.6]	NaN	Raphaël Varane
9	0	10	Real Madrid	Pass	[35.3, 75.4]	[22.4, 76.6]	NaN	Luka Modrić
10	0	11	Real Madrid	Pass	[22.3, 76.6]	[33.4, 68.0]	NaN	Daniel Carvajal Ramos
11	0	15	Real Madrid	Pass	[36.2, 75.3]	[43.6, 62.0]	Incomplete	Carlos Henrique Casimiro
16	0	25	Real Madrid	Pass	[14.7, 23.2]	[56.7, 6.2]	Incomplete	Sergio Ramos García
17	0	40	Real Madrid	Pass	[57.5, 4.6]	[49.2, 15.6]	NaN	Marcelo Vieira da Silva Júnior
18	0	43	Real Madrid	Pass	[48.8, 18.4]	[49.8, 12.5]	NaN	Carlos Henrique Casimiro

events_Liv.head(10)

	minute	second	team	type	location	pass_end_location	pass_outcome	player
1	0	0	Liverpool	Starting XI	NaN	NaN	NaN	NaN
3	0	0	Liverpool	Half Start	NaN	NaN	NaN	NaN
4	45	0	Liverpool	Half Start	NaN	NaN	NaN	NaN
6	0	0	Liverpool	Pass	[60.0, 40.0]	[32.1, 41.2]	NaN	James Philip Milner
7	0	3	Liverpool	Pass	[35.0, 40.8]	[92.7, 22.7]	Incomplete	Dejan Lovren
12	0	16	Liverpool	Pass	[76.5, 18.1]	[84.8, 9.5]	NaN	Jordan Brian Henderson
13	0	18	Liverpool	Pass	[84.4, 10.0]	[92.5, 19.1]	NaN	Sadio Mané
14	0	19	Liverpool	Pass	[91.6, 21.3]	[90.6, 50.7]	NaN	Roberto Firmino Barbosa de Oliveira
15	0	22	Liverpool	Pass	[92.2, 50.9]	[109.7, 46.4]	Incomplete	Mohamed Salah
25	1	7	Liverpool	Pass	[42.0, 75.9]	[115.6, 59.3]	Incomplete	Trent Alexander-Arnold

• As we are only interested in the pass network generation, we will filter the datasets by keeping those rows where type is set to Pass.

events_pn_Real = events_Real[events_Real['type'] == 'Pass']
events_pn_Liv = events_Liv[events_Liv['type'] == 'Pass']

• Again view the first 10 rows of the filtered datasets:

events_pn_Real.head(10)

	minute	second	team	type	location	pass_end_location	pass_outcome	player
8	0	8	Real Madrid	Pass	[27.4, 60.2]	[36.1, 71.6]	NaN	Raphaël Varane
9	0	10	Real Madrid	Pass	[35.3, 75.4]	[22.4, 76.6]	NaN	Luka Modrić
10	0	11	Real Madrid	Pass	[22.3, 76.6]	[33.4, 68.0]	NaN	Daniel Carvajal Ramos
11	0	15	Real Madrid	Pass	[36.2, 75.3]	[43.6, 62.0]	Incomplete	Carlos Henrique Casimiro
16	0	25	Real Madrid	Pass	[14.7, 23.2]	[56.7, 6.2]	Incomplete	Sergio Ramos García
17	0	40	Real Madrid	Pass	[57.5, 4.6]	[49.2, 15.6]	NaN	Marcelo Vieira da Silva Júnior
18	0	43	Real Madrid	Pass	[48.8, 18.4]	[49.8, 12.5]	NaN	Carlos Henrique Casimiro
19	0	46	Real Madrid	Pass	[48.8, 13.9]	[36.1, 56.3]	NaN	Toni Kroos
20	0	52	Real Madrid	Pass	[41.3, 54.8]	[34.4, 40.2]	NaN	Raphaël Varane
21	0	55	Real Madrid	Pass	[39.1, 36.5]	[65.4, 13.1]	NaN	Sergio Ramos García

events_pn_Liv.head(10)

	minute	second	team	type	location	pass_end_location	pass_outcome	player
6	0	0	Liverpool	Pass	[60.0, 40.0]	[32.1, 41.2]	NaN	James Philip Milner
7	0	3	Liverpool	Pass	[35.0, 40.8]	[92.7, 22.7]	Incomplete	Dejan Lovren
12	0	16	Liverpool	Pass	[76.5, 18.1]	[84.8, 9.5]	NaN	Jordan Brian Henderson
13	0	18	Liverpool	Pass	[84.4, 10.0]	[92.5, 19.1]	NaN	Sadio Mané
14	0	19	Liverpool	Pass	[91.6, 21.3]	[90.6, 50.7]	NaN	Roberto Firmino Barbosa de Oliveira
15	0	22	Liverpool	Pass	[92.2, 50.9]	[109.7, 46.4]	Incomplete	Mohamed Salah
25	1	7	Liverpool	Pass	[42.0, 75.9]	[115.6, 59.3]	Incomplete	Trent Alexander-Arnold
37	2	0	Liverpool	Pass	[9.9, 39.1]	[28.1, 4.2]	NaN	Virgil van Dijk
38	2	3	Liverpool	Pass	[43.2, 2.8]	[50.1, 4.8]	Incomplete	Andrew Robertson
39	2	7	Liverpool	Pass	[53.2, 0.1]	[50.0, 4.0]	NaN	Andrew Robertson

• Let us now very carefully observe the datasets. Suppose from the events_pn_Real dataset, we are focusing on the second and the third row (index 1 and 2). Luka Modrić makes the pass at around 0th minute and 10th second (Second row) and Daniel Carvajal Ramos receives the pass at around 0th minute and 11th second (third row). So in both the datasets we need to add two extra columns named as pass_maker and pass_receiver, where pass_maker column would be similar to player column and the pass_receiver column would be the player column whose index would be shifted by one place in the negative direction. This can be achieved by the shift() function provided by pandas. We will perform this operation on both events_pn_Real and events_pn_Liv.

events_pn_Real['pass_maker'] = events_pn_Real['player']
events_pn_Real['pass_receiver'] = events_pn_Real['player'].shift(-1)

events_pn_Liv['pass_maker'] = events_pn_Liv['player']
events_pn_Liv['pass_receiver'] = events_pn_Liv['player'].shift(-1)

• Let us check now how the modified datasets look:

events_pn_Real.head(10)

	minute	second	team	type	location	pass_end_location	pass_outcome	player	pass_maker	pass_receiver
8	0	8	Real Madrid	Pass	[27.4, 60.2]	[36.1, 71.6]	NaN	Raphaël Varane	Raphaël Varane	Luka Modrić
9	0	10	Real Madrid	Pass	[35.3, 75.4]	[22.4, 76.6]	NaN	Luka Modrić	Luka Modrić	Daniel Carvajal Ramos
10	0	11	Real Madrid	Pass	[22.3, 76.6]	[33.4, 68.0]	NaN	Daniel Carvajal Ramos	Daniel Carvajal Ramos	Carlos Henrique Casimiro
11	0	15	Real Madrid	Pass	[36.2, 75.3]	[43.6, 62.0]	Incomplete	Carlos Henrique Casimiro	Carlos Henrique Casimiro	Sergio Ramos García
16	0	25	Real Madrid	Pass	[14.7, 23.2]	[56.7, 6.2]	Incomplete	Sergio Ramos García	Sergio Ramos García	Marcelo Vieira da Silva Júnior
17	0	40	Real Madrid	Pass	[57.5, 4.6]	[49.2, 15.6]	NaN	Marcelo Vieira da Silva Júnior	Marcelo Vieira da Silva Júnior	Carlos Henrique Casimiro
18	0	43	Real Madrid	Pass	[48.8, 18.4]	[49.8, 12.5]	NaN	Carlos Henrique Casimiro	Carlos Henrique Casimiro	Toni Kroos
19	0	46	Real Madrid	Pass	[48.8, 13.9]	[36.1, 56.3]	NaN	Toni Kroos	Toni Kroos	Raphaël Varane
20	0	52	Real Madrid	Pass	[41.3, 54.8]	[34.4, 40.2]	NaN	Raphaël Varane	Raphaël Varane	Sergio Ramos García
21	0	55	Real Madrid	Pass	[39.1, 36.5]	[65.4, 13.1]	NaN	Sergio Ramos García	Sergio Ramos García	Cristiano Ronaldo dos Santos Aveiro

events_pn_Liv.head(10)

	minute	second	team	type	location	pass_end_location	pass_outcome	player	pass_maker	pass_receiver
6	0	0	Liverpool	Pass	[60.0, 40.0]	[32.1, 41.2]	NaN	James Philip Milner	James Philip Milner	Dejan Lovren
7	0	3	Liverpool	Pass	[35.0, 40.8]	[92.7, 22.7]	Incomplete	Dejan Lovren	Dejan Lovren	Jordan Brian Henderson
12	0	16	Liverpool	Pass	[76.5, 18.1]	[84.8, 9.5]	NaN	Jordan Brian Henderson	Jordan Brian Henderson	Sadio Mané
13	0	18	Liverpool	Pass	[84.4, 10.0]	[92.5, 19.1]	NaN	Sadio Mané	Sadio Mané	Roberto Firmino Barbosa de Oliveira
14	0	19	Liverpool	Pass	[91.6, 21.3]	[90.6, 50.7]	NaN	Roberto Firmino Barbosa de Oliveira	Roberto Firmino Barbosa de Oliveira	Mohamed Salah
15	0	22	Liverpool	Pass	[92.2, 50.9]	[109.7, 46.4]	Incomplete	Mohamed Salah	Mohamed Salah	Trent Alexander-Arnold
25	1	7	Liverpool	Pass	[42.0, 75.9]	[115.6, 59.3]	Incomplete	Trent Alexander-Arnold	Trent Alexander-Arnold	Virgil van Dijk
37	2	0	Liverpool	Pass	[9.9, 39.1]	[28.1, 4.2]	NaN	Virgil van Dijk	Virgil van Dijk	Andrew Robertson
38	2	3	Liverpool	Pass	[43.2, 2.8]	[50.1, 4.8]	Incomplete	Andrew Robertson	Andrew Robertson	Andrew Robertson
39	2	7	Liverpool	Pass	[53.2, 0.1]	[50.0, 4.0]	NaN	Andrew Robertson	Andrew Robertson	James Philip Milner

• Now, there might be passes which were not successful. Note that in the statsbomb data passes whose pass_outcome are set as nan are actually the successful passes. We will again filter the datasets by successful passes:

events_pn_Real = events_pn_Real[events_pn_Real['pass_outcome'].isnull() == True].reset_index()
events_pn_Liv = events_pn_Liv[events_pn_Liv['pass_outcome'].isnull() == True].reset_index()

• The first 10 rows of the filtered datasets:

events_pn_Real.head(10)

	index	minute	second	team	type	location	pass_end_location	pass_outcome	player	pass_maker	pass_receiver
0	8	0	8	Real Madrid	Pass	[27.4, 60.2]	[36.1, 71.6]	NaN	Raphaël Varane	Raphaël Varane	Luka Modrić
1	9	0	10	Real Madrid	Pass	[35.3, 75.4]	[22.4, 76.6]	NaN	Luka Modrić	Luka Modrić	Daniel Carvajal Ramos
2	10	0	11	Real Madrid	Pass	[22.3, 76.6]	[33.4, 68.0]	NaN	Daniel Carvajal Ramos	Daniel Carvajal Ramos	Carlos Henrique Casimiro
3	17	0	40	Real Madrid	Pass	[57.5, 4.6]	[49.2, 15.6]	NaN	Marcelo Vieira da Silva Júnior	Marcelo Vieira da Silva Júnior	Carlos Henrique Casimiro
4	18	0	43	Real Madrid	Pass	[48.8, 18.4]	[49.8, 12.5]	NaN	Carlos Henrique Casimiro	Carlos Henrique Casimiro	Toni Kroos
5	19	0	46	Real Madrid	Pass	[48.8, 13.9]	[36.1, 56.3]	NaN	Toni Kroos	Toni Kroos	Raphaël Varane
6	20	0	52	Real Madrid	Pass	[41.3, 54.8]	[34.4, 40.2]	NaN	Raphaël Varane	Raphaël Varane	Sergio Ramos García
7	21	0	55	Real Madrid	Pass	[39.1, 36.5]	[65.4, 13.1]	NaN	Sergio Ramos García	Sergio Ramos García	Cristiano Ronaldo dos Santos Aveiro
8	22	0	58	Real Madrid	Pass	[64.5, 11.1]	[54.2, 5.6]	NaN	Cristiano Ronaldo dos Santos Aveiro	Cristiano Ronaldo dos Santos Aveiro	Marcelo Vieira da Silva Júnior
9	23	0	59	Real Madrid	Pass	[55.3, 5.5]	[83.9, 4.3]	NaN	Marcelo Vieira da Silva Júnior	Marcelo Vieira da Silva Júnior	Karim Benzema

events_pn_Liv.head(10)

	index	minute	second	team	type	location	pass_end_location	pass_outcome	player	pass_maker	pass_receiver
0	6	0	0	Liverpool	Pass	[60.0, 40.0]	[32.1, 41.2]	NaN	James Philip Milner	James Philip Milner	Dejan Lovren
1	12	0	16	Liverpool	Pass	[76.5, 18.1]	[84.8, 9.5]	NaN	Jordan Brian Henderson	Jordan Brian Henderson	Sadio Mané
2	13	0	18	Liverpool	Pass	[84.4, 10.0]	[92.5, 19.1]	NaN	Sadio Mané	Sadio Mané	Roberto Firmino Barbosa de Oliveira
3	14	0	19	Liverpool	Pass	[91.6, 21.3]	[90.6, 50.7]	NaN	Roberto Firmino Barbosa de Oliveira	Roberto Firmino Barbosa de Oliveira	Mohamed Salah
4	37	2	0	Liverpool	Pass	[9.9, 39.1]	[28.1, 4.2]	NaN	Virgil van Dijk	Virgil van Dijk	Andrew Robertson
5	39	2	7	Liverpool	Pass	[53.2, 0.1]	[50.0, 4.0]	NaN	Andrew Robertson	Andrew Robertson	James Philip Milner
6	40	2	10	Liverpool	Pass	[45.5, 4.0]	[27.4, 16.8]	NaN	James Philip Milner	James Philip Milner	Virgil van Dijk
7	41	2	13	Liverpool	Pass	[26.7, 19.6]	[27.8, 47.3]	NaN	Virgil van Dijk	Virgil van Dijk	Dejan Lovren
8	42	2	16	Liverpool	Pass	[28.0, 45.4]	[28.4, 21.4]	NaN	Dejan Lovren	Dejan Lovren	Virgil van Dijk
9	43	2	19	Liverpool	Pass	[30.4, 25.7]	[30.7, 52.9]	NaN	Virgil van Dijk	Virgil van Dijk	Dejan Lovren

• So it seems we have been able to logically clean and modify the datasets. Now we are only focused on building the pass network among the players who were in the starting 11 from both the teams. So we will discard out the rows which consist of pass events that took place after the first substitution for either of the teams. Let us find the minute and second of the first substitution for both Real Madrid and Liverpool.

• Now, let us filter the datasets events_Real and events_Liv by setting the type to be Substitution. This will give us the information of when the first substitution had taken place for the teams.

substitution_Real = events_Real[events_Real['type'] == 'Substitution']
substitution_Liv = events_Liv[events_Liv['type'] == 'Substitution']

• And let us view the datasets:

substitution_Real

	minute	second	team	type	location	pass_end_location	pass_outcome	player
3485	36	17	Real Madrid	Substitution	NaN	NaN	NaN	Daniel Carvajal Ramos
3486	60	56	Real Madrid	Substitution	NaN	NaN	NaN	Francisco Román Alarcón Suárez
3488	88	21	Real Madrid	Substitution	NaN	NaN	NaN	Karim Benzema

substitution_Liv

	minute	second	team	type	location	pass_end_location	pass_outcome	player
3484	29	39	Liverpool	Substitution	NaN	NaN	NaN	Mohamed Salah
3487	82	27	Liverpool	Substitution	NaN	NaN	NaN	James Philip Milner

• We see that the first substitution takes place for Real Madrid at the 36th minute and 17th second, whereas for Liverpool it takes place around 29th minute and 39th second. Let us find these out by writing a small Python code:

substitution_Real_minute = np.min(substitution_Real['minute'])
substitution_Real_minute_data = substitution_Real[substitution_Real['minute'] == substitution_Real_minute]
substitution_Real_second = np.min(substitution_Real_minute_data['second'])
print("minute =", substitution_Real_minute, "second =",  substitution_Real_second)

minute = 36 second = 17

substitution_Liv_minute = np.min(substitution_Liv['minute'])
substitution_Liv_minute_data = substitution_Liv[substitution_Liv['minute'] == substitution_Liv_minute]
substitution_Liv_second = np.min(substitution_Liv_minute_data['second'])
print("minute = ", substitution_Liv_minute, "second = ", substitution_Liv_second)

minute =  29 second =  39

• We see that we have gotten the correct timings of when the first substitutions had taken place. Now we filter our datasets by taking tose pass events that took place before the first substitutions

events_pn_Real = events_pn_Real[(events_pn_Real['minute'] <= substitution_Real_minute)]

events_pn_Liv = events_pn_Liv[(events_pn_Liv['minute'] <= substitution_Liv_minute)]

• Let us again print the first 10 rows of the renewed datasets:

events_pn_Real.head(10)

	index	minute	second	team	type	location	pass_end_location	pass_outcome	player	pass_maker	pass_receiver
0	8	0	8	Real Madrid	Pass	[27.4, 60.2]	[36.1, 71.6]	NaN	Raphaël Varane	Raphaël Varane	Luka Modrić
1	9	0	10	Real Madrid	Pass	[35.3, 75.4]	[22.4, 76.6]	NaN	Luka Modrić	Luka Modrić	Daniel Carvajal Ramos
2	10	0	11	Real Madrid	Pass	[22.3, 76.6]	[33.4, 68.0]	NaN	Daniel Carvajal Ramos	Daniel Carvajal Ramos	Carlos Henrique Casimiro
3	17	0	40	Real Madrid	Pass	[57.5, 4.6]	[49.2, 15.6]	NaN	Marcelo Vieira da Silva Júnior	Marcelo Vieira da Silva Júnior	Carlos Henrique Casimiro
4	18	0	43	Real Madrid	Pass	[48.8, 18.4]	[49.8, 12.5]	NaN	Carlos Henrique Casimiro	Carlos Henrique Casimiro	Toni Kroos
5	19	0	46	Real Madrid	Pass	[48.8, 13.9]	[36.1, 56.3]	NaN	Toni Kroos	Toni Kroos	Raphaël Varane
6	20	0	52	Real Madrid	Pass	[41.3, 54.8]	[34.4, 40.2]	NaN	Raphaël Varane	Raphaël Varane	Sergio Ramos García
7	21	0	55	Real Madrid	Pass	[39.1, 36.5]	[65.4, 13.1]	NaN	Sergio Ramos García	Sergio Ramos García	Cristiano Ronaldo dos Santos Aveiro
8	22	0	58	Real Madrid	Pass	[64.5, 11.1]	[54.2, 5.6]	NaN	Cristiano Ronaldo dos Santos Aveiro	Cristiano Ronaldo dos Santos Aveiro	Marcelo Vieira da Silva Júnior
9	23	0	59	Real Madrid	Pass	[55.3, 5.5]	[83.9, 4.3]	NaN	Marcelo Vieira da Silva Júnior	Marcelo Vieira da Silva Júnior	Karim Benzema

events_pn_Liv.head(10)

	index	minute	second	team	type	location	pass_end_location	pass_outcome	player	pass_maker	pass_receiver
0	6	0	0	Liverpool	Pass	[60.0, 40.0]	[32.1, 41.2]	NaN	James Philip Milner	James Philip Milner	Dejan Lovren
1	12	0	16	Liverpool	Pass	[76.5, 18.1]	[84.8, 9.5]	NaN	Jordan Brian Henderson	Jordan Brian Henderson	Sadio Mané
2	13	0	18	Liverpool	Pass	[84.4, 10.0]	[92.5, 19.1]	NaN	Sadio Mané	Sadio Mané	Roberto Firmino Barbosa de Oliveira
3	14	0	19	Liverpool	Pass	[91.6, 21.3]	[90.6, 50.7]	NaN	Roberto Firmino Barbosa de Oliveira	Roberto Firmino Barbosa de Oliveira	Mohamed Salah
4	37	2	0	Liverpool	Pass	[9.9, 39.1]	[28.1, 4.2]	NaN	Virgil van Dijk	Virgil van Dijk	Andrew Robertson
5	39	2	7	Liverpool	Pass	[53.2, 0.1]	[50.0, 4.0]	NaN	Andrew Robertson	Andrew Robertson	James Philip Milner
6	40	2	10	Liverpool	Pass	[45.5, 4.0]	[27.4, 16.8]	NaN	James Philip Milner	James Philip Milner	Virgil van Dijk
7	41	2	13	Liverpool	Pass	[26.7, 19.6]	[27.8, 47.3]	NaN	Virgil van Dijk	Virgil van Dijk	Dejan Lovren
8	42	2	16	Liverpool	Pass	[28.0, 45.4]	[28.4, 21.4]	NaN	Dejan Lovren	Dejan Lovren	Virgil van Dijk
9	43	2	19	Liverpool	Pass	[30.4, 25.7]	[30.7, 52.9]	NaN	Virgil van Dijk	Virgil van Dijk	Dejan Lovren

• Now from the datasets, we will split the location and the pass_end_location columns into two columns each representing the coordinates and name them as pass_maker_x, pass_maker_y, pass_receiver_x and pass_receiver_y.

• Let us manipulate the dataset for Real Madrid first:

Loc = events_pn_Real['location']
Loc = pd.DataFrame(Loc.to_list(), columns=['pass_maker_x', 'pass_maker_y'])

Loc_end = events_pn_Real['pass_end_location']
Loc_end = pd.DataFrame(Loc_end.to_list(), columns=['pass_receiver_x', 'pass_receiver_y'])

events_pn_Real['pass_maker_x'] = Loc['pass_maker_x']
events_pn_Real['pass_maker_y'] = Loc['pass_maker_y']
events_pn_Real['pass_receiver_x'] = Loc_end['pass_receiver_x']
events_pn_Real['pass_receiver_y'] = Loc_end['pass_receiver_y']

events_pn_Real = events_pn_Real[['index', 'minute', 'second', 'team', 'type', 'pass_outcome', 
                                 'player', 'pass_maker', 'pass_receiver', 'pass_maker_x', 
                                 'pass_maker_y', 'pass_receiver_x', 'pass_receiver_y']]

events_pn_Real.head(10)

	index	minute	second	team	type	pass_outcome	player	pass_maker	pass_receiver	pass_maker_x	pass_maker_y	pass_receiver_x	pass_receiver_y
0	8	0	8	Real Madrid	Pass	NaN	Raphaël Varane	Raphaël Varane	Luka Modrić	27.4	60.2	36.1	71.6
1	9	0	10	Real Madrid	Pass	NaN	Luka Modrić	Luka Modrić	Daniel Carvajal Ramos	35.3	75.4	22.4	76.6
2	10	0	11	Real Madrid	Pass	NaN	Daniel Carvajal Ramos	Daniel Carvajal Ramos	Carlos Henrique Casimiro	22.3	76.6	33.4	68.0
3	17	0	40	Real Madrid	Pass	NaN	Marcelo Vieira da Silva Júnior	Marcelo Vieira da Silva Júnior	Carlos Henrique Casimiro	57.5	4.6	49.2	15.6
4	18	0	43	Real Madrid	Pass	NaN	Carlos Henrique Casimiro	Carlos Henrique Casimiro	Toni Kroos	48.8	18.4	49.8	12.5
5	19	0	46	Real Madrid	Pass	NaN	Toni Kroos	Toni Kroos	Raphaël Varane	48.8	13.9	36.1	56.3
6	20	0	52	Real Madrid	Pass	NaN	Raphaël Varane	Raphaël Varane	Sergio Ramos García	41.3	54.8	34.4	40.2
7	21	0	55	Real Madrid	Pass	NaN	Sergio Ramos García	Sergio Ramos García	Cristiano Ronaldo dos Santos Aveiro	39.1	36.5	65.4	13.1
8	22	0	58	Real Madrid	Pass	NaN	Cristiano Ronaldo dos Santos Aveiro	Cristiano Ronaldo dos Santos Aveiro	Marcelo Vieira da Silva Júnior	64.5	11.1	54.2	5.6
9	23	0	59	Real Madrid	Pass	NaN	Marcelo Vieira da Silva Júnior	Marcelo Vieira da Silva Júnior	Karim Benzema	55.3	5.5	83.9	4.3

• Same data manipulation for Liverpool:

Loc = events_pn_Liv['location']
Loc = pd.DataFrame(Loc.to_list(), columns=['pass_maker_x', 'pass_maker_y'])

Loc_end = events_pn_Liv['pass_end_location']
Loc_end = pd.DataFrame(Loc_end.to_list(), columns=['pass_receiver_x', 'pass_receiver_y'])

events_pn_Liv['pass_maker_x'] = Loc['pass_maker_x']
events_pn_Liv['pass_maker_y'] = Loc['pass_maker_y']
events_pn_Liv['pass_receiver_x'] = Loc_end['pass_receiver_x']
events_pn_Liv['pass_receiver_y'] = Loc_end['pass_receiver_y']

events_pn_Liv = events_pn_Liv[['index', 'minute', 'second', 'team', 'type', 'pass_outcome', 
                               'player', 'pass_maker', 'pass_receiver', 'pass_maker_x', 
                               'pass_maker_y', 'pass_receiver_x', 'pass_receiver_y']]

events_pn_Liv.head(10)

	index	minute	second	team	type	pass_outcome	player	pass_maker	pass_receiver	pass_maker_x	pass_maker_y	pass_receiver_x	pass_receiver_y
0	6	0	0	Liverpool	Pass	NaN	James Philip Milner	James Philip Milner	Dejan Lovren	60.0	40.0	32.1	41.2
1	12	0	16	Liverpool	Pass	NaN	Jordan Brian Henderson	Jordan Brian Henderson	Sadio Mané	76.5	18.1	84.8	9.5
2	13	0	18	Liverpool	Pass	NaN	Sadio Mané	Sadio Mané	Roberto Firmino Barbosa de Oliveira	84.4	10.0	92.5	19.1
3	14	0	19	Liverpool	Pass	NaN	Roberto Firmino Barbosa de Oliveira	Roberto Firmino Barbosa de Oliveira	Mohamed Salah	91.6	21.3	90.6	50.7
4	37	2	0	Liverpool	Pass	NaN	Virgil van Dijk	Virgil van Dijk	Andrew Robertson	9.9	39.1	28.1	4.2
5	39	2	7	Liverpool	Pass	NaN	Andrew Robertson	Andrew Robertson	James Philip Milner	53.2	0.1	50.0	4.0
6	40	2	10	Liverpool	Pass	NaN	James Philip Milner	James Philip Milner	Virgil van Dijk	45.5	4.0	27.4	16.8
7	41	2	13	Liverpool	Pass	NaN	Virgil van Dijk	Virgil van Dijk	Dejan Lovren	26.7	19.6	27.8	47.3
8	42	2	16	Liverpool	Pass	NaN	Dejan Lovren	Dejan Lovren	Virgil van Dijk	28.0	45.4	28.4	21.4
9	43	2	19	Liverpool	Pass	NaN	Virgil van Dijk	Virgil van Dijk	Dejan Lovren	30.4	25.7	30.7	52.9

• Inspired by the way given here, we will take the average locations of the starting 11 players on the field for a unified construction of the pass network, and also will count the number of passes created by these player:

av_loc_Real = events_pn_Real.groupby('pass_maker').agg({'pass_maker_x':['mean'], 
                                                        'pass_maker_y':['mean', 'count']})

av_loc_Real

	pass_maker_x	pass_maker_y
	mean	mean	count
pass_maker
Carlos Henrique Casimiro	60.845455	31.836364	11
Cristiano Ronaldo dos Santos Aveiro	81.580000	29.160000	10
Daniel Carvajal Ramos	64.341667	73.875000	24
Francisco Román Alarcón Suárez	62.323529	27.082353	17
Karim Benzema	65.081818	27.936364	11
Keylor Navas Gamboa	10.870000	41.810000	10
Luka Modrić	60.604762	55.028571	21
Marcelo Vieira da Silva Júnior	59.865217	11.130435	23
Raphaël Varane	37.436364	58.354545	22
Sergio Ramos García	41.282353	24.514706	34
Toni Kroos	51.190000	24.275000	40

• As we see the groupby() function from pandas splits events_pn_Real into groups indexed by the player names. Whereas, the agg() function aggregates the data into the averages of the pass makers' locations and also counts the number of passes made by these players. Now refine the column names of av_loc_Real:

av_loc_Real.columns = ['pass_maker_x', 'pass_maker_y', 'count']

av_loc_Real

	pass_maker_x	pass_maker_y	count
pass_maker
Carlos Henrique Casimiro	60.845455	31.836364	11
Cristiano Ronaldo dos Santos Aveiro	81.580000	29.160000	10
Daniel Carvajal Ramos	64.341667	73.875000	24
Francisco Román Alarcón Suárez	62.323529	27.082353	17
Karim Benzema	65.081818	27.936364	11
Keylor Navas Gamboa	10.870000	41.810000	10
Luka Modrić	60.604762	55.028571	21
Marcelo Vieira da Silva Júnior	59.865217	11.130435	23
Raphaël Varane	37.436364	58.354545	22
Sergio Ramos García	41.282353	24.514706	34
Toni Kroos	51.190000	24.275000	40

• Now perform the same operations for Liverpool:

av_loc_Liv = events_pn_Liv.groupby('pass_maker').agg({'pass_maker_x':['mean'], 
                                                      'pass_maker_y':['mean', 'count']})
av_loc_Liv.columns = ['pass_maker_x', 'pass_maker_y', 'count']

av_loc_Liv

	pass_maker_x	pass_maker_y	count
pass_maker
Andrew Robertson	59.815385	6.830769	13
Dejan Lovren	41.690909	60.172727	11
Georginio Wijnaldum	76.390909	28.518182	11
James Philip Milner	72.353333	36.153333	15
Jordan Brian Henderson	61.035294	37.152941	17
Loris Karius	12.914286	40.385714	7
Mohamed Salah	77.550000	64.710000	10
Roberto Firmino Barbosa de Oliveira	78.250000	43.570000	10
Sadio Mané	86.275000	22.075000	4
Trent Alexander-Arnold	64.666667	72.550000	12
Virgil van Dijk	43.366667	25.433333	9

• Once we sort out the starting 11 pass makers' average locations in a game, we will try to figure out the number of times a particular pass maker passed the ball to a particular pass receiver (be cautious to keep the direction of pass in mind, i.e, a pass from a player A to a player B is not identical to a pass from player B to player A). We will use the groupby() and the count() function to count the number of rows where a unique player A passed the ball to another unique player B.

pass_Real = events_pn_Real.groupby(['pass_maker', 'pass_receiver']).index.count().reset_index()

pass_Real.head(10)

	pass_maker	pass_receiver	index
0	Carlos Henrique Casimiro	Daniel Carvajal Ramos	1
1	Carlos Henrique Casimiro	Luka Modrić	1
2	Carlos Henrique Casimiro	Marcelo Vieira da Silva Júnior	1
3	Carlos Henrique Casimiro	Raphaël Varane	1
4	Carlos Henrique Casimiro	Sergio Ramos García	1
5	Carlos Henrique Casimiro	Toni Kroos	6
6	Cristiano Ronaldo dos Santos Aveiro	Daniel Carvajal Ramos	3
7	Cristiano Ronaldo dos Santos Aveiro	Karim Benzema	1
8	Cristiano Ronaldo dos Santos Aveiro	Luka Modrić	1
9	Cristiano Ronaldo dos Santos Aveiro	Marcelo Vieira da Silva Júnior	4

pass_Liv = events_pn_Liv.groupby(['pass_maker', 'pass_receiver']).index.count().reset_index()

pass_Liv.head(10)

	pass_maker	pass_receiver	index
0	Andrew Robertson	Andrew Robertson	1
1	Andrew Robertson	Georginio Wijnaldum	3
2	Andrew Robertson	James Philip Milner	3
3	Andrew Robertson	Jordan Brian Henderson	2
4	Andrew Robertson	Roberto Firmino Barbosa de Oliveira	2
5	Andrew Robertson	Virgil van Dijk	2
6	Dejan Lovren	James Philip Milner	1
7	Dejan Lovren	Jordan Brian Henderson	1
8	Dejan Lovren	Loris Karius	2
9	Dejan Lovren	Mohamed Salah	1

• Let's rename the index column to number_of_passes:

pass_Real.rename(columns = {'index':'number_of_passes'}, inplace = True)

pass_Real.head(10)

	pass_maker	pass_receiver	number_of_passes
0	Carlos Henrique Casimiro	Daniel Carvajal Ramos	1
1	Carlos Henrique Casimiro	Luka Modrić	1
2	Carlos Henrique Casimiro	Marcelo Vieira da Silva Júnior	1
3	Carlos Henrique Casimiro	Raphaël Varane	1
4	Carlos Henrique Casimiro	Sergio Ramos García	1
5	Carlos Henrique Casimiro	Toni Kroos	6
6	Cristiano Ronaldo dos Santos Aveiro	Daniel Carvajal Ramos	3
7	Cristiano Ronaldo dos Santos Aveiro	Karim Benzema	1
8	Cristiano Ronaldo dos Santos Aveiro	Luka Modrić	1
9	Cristiano Ronaldo dos Santos Aveiro	Marcelo Vieira da Silva Júnior	4

pass_Liv.rename(columns = {'index':'number_of_passes'}, inplace = True)

pass_Liv.head(10)

	pass_maker	pass_receiver	number_of_passes
0	Andrew Robertson	Andrew Robertson	1
1	Andrew Robertson	Georginio Wijnaldum	3
2	Andrew Robertson	James Philip Milner	3
3	Andrew Robertson	Jordan Brian Henderson	2
4	Andrew Robertson	Roberto Firmino Barbosa de Oliveira	2
5	Andrew Robertson	Virgil van Dijk	2
6	Dejan Lovren	James Philip Milner	1
7	Dejan Lovren	Jordan Brian Henderson	1
8	Dejan Lovren	Loris Karius	2
9	Dejan Lovren	Mohamed Salah	1

• Now, we will merge the datasets av_loc_Real and pass_Real, Let us identify the left and the right dataframes for performing the merge. Here, av_loc_Real is the left dataframe and pass_Real is the right. We will use the merge() function from pandas to carry out the merging operation.

pass_Real = pass_Real.merge(av_loc_Real, left_on = 'pass_maker', right_index = True)

pass_Real.head(10)

	pass_maker	pass_receiver	number_of_passes	pass_maker_x	pass_maker_y	count
0	Carlos Henrique Casimiro	Daniel Carvajal Ramos	1	60.845455	31.836364	11
1	Carlos Henrique Casimiro	Luka Modrić	1	60.845455	31.836364	11
2	Carlos Henrique Casimiro	Marcelo Vieira da Silva Júnior	1	60.845455	31.836364	11
3	Carlos Henrique Casimiro	Raphaël Varane	1	60.845455	31.836364	11
4	Carlos Henrique Casimiro	Sergio Ramos García	1	60.845455	31.836364	11
5	Carlos Henrique Casimiro	Toni Kroos	6	60.845455	31.836364	11
6	Cristiano Ronaldo dos Santos Aveiro	Daniel Carvajal Ramos	3	81.580000	29.160000	10
7	Cristiano Ronaldo dos Santos Aveiro	Karim Benzema	1	81.580000	29.160000	10
8	Cristiano Ronaldo dos Santos Aveiro	Luka Modrić	1	81.580000	29.160000	10
9	Cristiano Ronaldo dos Santos Aveiro	Marcelo Vieira da Silva Júnior	4	81.580000	29.160000	10

The left_on argument specifies the column names to join our right dataframe on, and the right_index argument decides whether to use the index from the right dataframe as the key for joining. Let us do the same operation for the other team:

pass_Liv = pass_Liv.merge(av_loc_Liv, left_on = 'pass_maker', right_index = True)

pass_Liv.head(10)

	pass_maker	pass_receiver	number_of_passes	pass_maker_x	pass_maker_y	count
0	Andrew Robertson	Andrew Robertson	1	59.815385	6.830769	13
1	Andrew Robertson	Georginio Wijnaldum	3	59.815385	6.830769	13
2	Andrew Robertson	James Philip Milner	3	59.815385	6.830769	13
3	Andrew Robertson	Jordan Brian Henderson	2	59.815385	6.830769	13
4	Andrew Robertson	Roberto Firmino Barbosa de Oliveira	2	59.815385	6.830769	13
5	Andrew Robertson	Virgil van Dijk	2	59.815385	6.830769	13
6	Dejan Lovren	James Philip Milner	1	41.690909	60.172727	11
7	Dejan Lovren	Jordan Brian Henderson	1	41.690909	60.172727	11
8	Dejan Lovren	Loris Karius	2	41.690909	60.172727	11
9	Dejan Lovren	Mohamed Salah	1	41.690909	60.172727	11

• Finally, we will again perform a merge on these updated datasets for adding the average locations of the pass receivers and the number of times the receiver received the ball. A last touch of data cleaning will fetch us the dataset sufficient to start visualizing the pass networks for both the teams

pass_Real = pass_Real.merge(av_loc_Real, left_on = 'pass_receiver', 
                            right_index = True, suffixes = ['', '_receipt'])
pass_Real.rename(columns = {'pass_maker_x_receipt':'pass_receiver_x', 
                            'pass_maker_y_receipt':'pass_receiver_y', 
                            'count_receipt':'number_of_passes_received'}, inplace = True)
pass_Real = pass_Real[pass_Real['pass_maker'] != pass_Real['pass_receiver']].reset_index()

pass_Real

	index	pass_maker	pass_receiver	number_of_passes	pass_maker_x	pass_maker_y	count	pass_receiver_x	pass_receiver_y	number_of_passes_received
0	0	Carlos Henrique Casimiro	Daniel Carvajal Ramos	1	60.845455	31.836364	11	64.341667	73.875	24
1	6	Cristiano Ronaldo dos Santos Aveiro	Daniel Carvajal Ramos	3	81.580000	29.160000	10	64.341667	73.875	24
2	21	Francisco Román Alarcón Suárez	Daniel Carvajal Ramos	2	62.323529	27.082353	17	64.341667	73.875	24
3	29	Karim Benzema	Daniel Carvajal Ramos	2	65.081818	27.936364	11	64.341667	73.875	24
4	39	Luka Modrić	Daniel Carvajal Ramos	10	60.604762	55.028571	21	64.341667	73.875	24
...	...	...	...	...	...	...	...	...	...	...
73	16	Daniel Carvajal Ramos	Keylor Navas Gamboa	1	64.341667	73.875000	24	10.870000	41.810	10
74	30	Karim Benzema	Keylor Navas Gamboa	1	65.081818	27.936364	11	10.870000	41.810	10
75	57	Raphaël Varane	Keylor Navas Gamboa	2	37.436364	58.354545	22	10.870000	41.810	10
76	64	Sergio Ramos García	Keylor Navas Gamboa	1	41.282353	24.514706	34	10.870000	41.810	10
77	74	Toni Kroos	Keylor Navas Gamboa	1	51.190000	24.275000	40	10.870000	41.810	10

78 rows × 10 columns

pass_Liv = pass_Liv.merge(av_loc_Liv, left_on = 'pass_receiver', 
                          right_index = True, suffixes = ['', '_receipt'])
pass_Liv.rename(columns = {'pass_maker_x_receipt':'pass_receiver_x', 
                           'pass_maker_y_receipt':'pass_receiver_y', 
                           'count_receipt':'number_of_passes_received'}, inplace = True)
pass_Liv = pass_Liv[pass_Liv['pass_maker'] != pass_Liv['pass_receiver']].reset_index()

pass_Liv

	index	pass_maker	pass_receiver	number_of_passes	pass_maker_x	pass_maker_y	count	pass_receiver_x	pass_receiver_y	number_of_passes_received
0	12	Georginio Wijnaldum	Andrew Robertson	4	76.390909	28.518182	11	59.815385	6.830769	13
1	18	James Philip Milner	Andrew Robertson	1	72.353333	36.153333	15	59.815385	6.830769	13
2	28	Jordan Brian Henderson	Andrew Robertson	1	61.035294	37.152941	17	59.815385	6.830769	13
3	36	Loris Karius	Andrew Robertson	1	12.914286	40.385714	7	59.815385	6.830769	13
4	54	Trent Alexander-Arnold	Andrew Robertson	1	64.666667	72.550000	12	59.815385	6.830769	13
...	...	...	...	...	...	...	...	...	...	...
59	55	Trent Alexander-Arnold	Dejan Lovren	1	64.666667	72.550000	12	41.690909	60.172727	11
60	61	Virgil van Dijk	Dejan Lovren	3	43.366667	25.433333	9	41.690909	60.172727	11
61	25	James Philip Milner	Sadio Mané	2	72.353333	36.153333	15	86.275000	22.075000	4
62	33	Jordan Brian Henderson	Sadio Mané	1	61.035294	37.152941	17	86.275000	22.075000	4
63	43	Mohamed Salah	Sadio Mané	1	77.550000	64.710000	10	86.275000	22.075000	4

64 rows × 10 columns

• We will replace the player names with their jersey numbers and create another pair of new datasets:

pass_Real_new = pass_Real.replace({"pass_maker": players_Real, "pass_receiver": players_Real})

pass_Real_new

	index	pass_maker	pass_receiver	number_of_passes	pass_maker_x	pass_maker_y	count	pass_receiver_x	pass_receiver_y	number_of_passes_received
0	0	14	2	1	60.845455	31.836364	11	64.341667	73.875	24
1	6	7	2	3	81.580000	29.160000	10	64.341667	73.875	24
2	21	22	2	2	62.323529	27.082353	17	64.341667	73.875	24
3	29	9	2	2	65.081818	27.936364	11	64.341667	73.875	24
4	39	10	2	10	60.604762	55.028571	21	64.341667	73.875	24
...	...	...	...	...	...	...	...	...	...	...
73	16	2	1	1	64.341667	73.875000	24	10.870000	41.810	10
74	30	9	1	1	65.081818	27.936364	11	10.870000	41.810	10
75	57	5	1	2	37.436364	58.354545	22	10.870000	41.810	10
76	64	4	1	1	41.282353	24.514706	34	10.870000	41.810	10
77	74	8	1	1	51.190000	24.275000	40	10.870000	41.810	10

78 rows × 10 columns

pass_Liv_new = pass_Liv.replace({"pass_maker": players_Liv, "pass_receiver": players_Liv})

pass_Liv_new

	index	pass_maker	pass_receiver	number_of_passes	pass_maker_x	pass_maker_y	count	pass_receiver_x	pass_receiver_y	number_of_passes_received
0	12	5	26	4	76.390909	28.518182	11	59.815385	6.830769	13
1	18	7	26	1	72.353333	36.153333	15	59.815385	6.830769	13
2	28	14	26	1	61.035294	37.152941	17	59.815385	6.830769	13
3	36	1	26	1	12.914286	40.385714	7	59.815385	6.830769	13
4	54	66	26	1	64.666667	72.550000	12	59.815385	6.830769	13
...	...	...	...	...	...	...	...	...	...	...
59	55	66	6	1	64.666667	72.550000	12	41.690909	60.172727	11
60	61	4	6	3	43.366667	25.433333	9	41.690909	60.172727	11
61	25	7	19	2	72.353333	36.153333	15	86.275000	22.075000	4
62	33	14	19	1	61.035294	37.152941	17	86.275000	22.075000	4
63	43	11	19	1	77.550000	64.710000	10	86.275000	22.075000	4

64 rows × 10 columns

• Now let us visualize the pass networks for both the teams.

pitch = Pitch(pitch_color='grass', goal_type = 'box', line_color='white', stripe = True, 
              constrained_layout=True, tight_layout=False)
fig, ax = pitch.draw()
arrows = pitch.arrows(pass_Real.pass_maker_x, pass_Real.pass_maker_y,
                         pass_Real.pass_receiver_x, pass_Real.pass_receiver_y, lw = 5,
                         color = 'black', zorder = 1, ax=ax)
nodes = pitch.scatter(av_loc_Real.pass_maker_x, av_loc_Real.pass_maker_y,
                           s=350, color = 'white', edgecolors='black', linewidth=1, alpha = 1, ax = ax)
                          
for index, row in av_loc_Real.iterrows():
    pitch.annotate(players_Real[row.name], xy=(row.pass_maker_x, row.pass_maker_y),
                   c ='black', va = 'center', ha = 'center', size = 10, ax = ax)
plt.title("Pass network for Real Madrid against Liverpool", size = 20)                   
plt.show()

pitch = Pitch(pitch_color='grass', goal_type = 'box', stripe = True, 
              line_color='white', constrained_layout=True, tight_layout=False)
fig, ax = pitch.draw()
arrows = pitch.arrows(120 - pass_Liv.pass_maker_x, pass_Liv.pass_maker_y,
                         120 - pass_Liv.pass_receiver_x, pass_Liv.pass_receiver_y, lw = 5,
                         color = 'black', zorder = 1, ax = ax)
nodes = pitch.scatter(120 - av_loc_Liv.pass_maker_x, av_loc_Liv.pass_maker_y,
                           s=350, color = 'red', edgecolors = 'black', linewidth=1, alpha = 1, ax = ax)
                           
for index, row in av_loc_Liv.iterrows():
    pitch.annotate(players_Liv[row.name], xy=(120 - row.pass_maker_x, row.pass_maker_y), 
                   c ='black', va = 'center', ha = 'center', size = 10, ax = ax)
plt.title("Pass network for Liverpool against Real Madrid", size = 20)
plt.show()

• In case of Liverpool's pass network visualization, we subtract the x coordinates from 120 just to reverse the x-axis.

• Now that we have been successful in correctly visualizing the pass networks of the teams involved in the game, we will now start analyzing our networks using metrics from the literature of complex network analysis.

• Note that both of our networks are directed weighted graphs, with number of passes as the weight for a directed edge.

• Let us first develop the isomorphic graph to the one we just visualized for Real Madrid, but this time using the networkx package. First we will use the relevant columns from the pass_Real_new dataset:

pass_Real_new = pass_Real_new[['pass_maker', 'pass_receiver', 'number_of_passes']]
pass_Real_new

	pass_maker	pass_receiver	number_of_passes
0	14	2	1
1	7	2	3
2	22	2	2
3	9	2	2
4	10	2	10
...	...	...	...
73	2	1	1
74	9	1	1
75	5	1	2
76	4	1	1
77	8	1	1

78 rows × 3 columns

• We will next convert pass_Real_new to a list of tuples, where each row is converted to a tuple. This is required for drawing a networkx graph.

L_Real = pass_Real_new.apply(tuple, axis=1).tolist()
print(L_Real)

[('14', '2', 1), ('7', '2', 3), ('22', '2', 2), ('9', '2', 2), ('10', '2', 10), ('12', '2', 2), ('5', '2', 3), ('4', '2', 3), ('8', '2', 1), ('14', '10', 1), ('7', '10', 1), ('2', '10', 7), ('22', '10', 1), ('12', '10', 1), ('5', '10', 5), ('4', '10', 2), ('8', '10', 5), ('14', '12', 1), ('7', '12', 4), ('22', '12', 2), ('1', '12', 2), ('10', '12', 1), ('4', '12', 9), ('8', '12', 4), ('14', '5', 1), ('2', '5', 5), ('1', '5', 2), ('10', '5', 3), ('12', '5', 2), ('4', '5', 5), ('8', '5', 4), ('14', '4', 1), ('7', '4', 1), ('22', '4', 5), ('9', '4', 1), ('1', '4', 4), ('10', '4', 1), ('12', '4', 2), ('5', '4', 6), ('8', '4', 10), ('14', '8', 6), ('2', '8', 1), ('22', '8', 4), ('9', '8', 4), ('1', '8', 1), ('10', '8', 4), ('12', '8', 5), ('5', '8', 4), ('4', '8', 9), ('7', '9', 1), ('2', '9', 1), ('22', '9', 1), ('1', '9', 1), ('10', '9', 1), ('12', '9', 3), ('5', '9', 1), ('8', '9', 2), ('2', '14', 2), ('9', '14', 2), ('10', '14', 1), ('12', '14', 2), ('5', '14', 1), ('8', '14', 2), ('2', '7', 2), ('22', '7', 2), ('9', '7', 1), ('12', '7', 2), ('4', '7', 1), ('8', '7', 2), ('2', '22', 3), ('12', '22', 4), ('4', '22', 4), ('8', '22', 8), ('2', '1', 1), ('9', '1', 1), ('5', '1', 2), ('4', '1', 1), ('8', '1', 1)]

• Now, we can draw the directed weighted graph:

G_Real = nx.DiGraph()

for i in range(len(L_Real)):
    G_Real.add_edge(L_Real[i][0], L_Real[i][1], weight = L_Real[i][2])

edges_Real = G_Real.edges()
weights_Real = [G_Real[u][v]['weight'] for u, v in edges_Real]

nx.draw(G_Real, node_size=800, with_labels=True, node_color='white', width = weights_Real)
plt.gca().collections[0].set_edgecolor('black') # sets the edge color of the nodes to black
plt.title("Pass network for Real Madrid vs Liverpool", size = 20)
plt.show()

• Now for Liverpool too, let us first clean the pass_Liv_new dataset and then draw the isomorphic weighted directed graph:

pass_Liv_new = pass_Liv_new[['pass_maker', 'pass_receiver', 'number_of_passes']]

pass_Liv_new

	pass_maker	pass_receiver	number_of_passes
0	5	26	4
1	7	26	1
2	14	26	1
3	1	26	1
4	66	26	1
...	...	...	...
59	66	6	1
60	4	6	3
61	7	19	2
62	14	19	1
63	11	19	1

64 rows × 3 columns

L_Liv = pass_Liv_new.apply(tuple, axis=1).tolist()
G_Liv = nx.DiGraph()

for i in range(len(L_Liv)):
    G_Liv.add_edge(L_Liv[i][0], L_Liv[i][1], weight = L_Liv[i][2])

edges_Liv = G_Liv.edges()
weights_Liv = [G_Liv[u][v]['weight'] for u, v in edges_Liv]

nx.draw(G_Liv, node_size = 800, with_labels = True, node_color = 'red', width = weights_Liv)
plt.gca().collections[0].set_edgecolor('black') # sets the edge color of the nodes to black
plt.show()

• Let us discuss some of the important functions from the networkx package that we have employed for drawing graphs:

  • DiGraph() function sets the base class for generating directed graphs,
  • add_edge() function adds an edge between two nodes given by the first two arguments and the weight parameter sets the weight for this edge
  • draw() function visualizes a networkx graph and its parameters are self-explanatory

• Let us now understand the degree, indegree and outdegree of a node from a directed weighted graph. Indegree of a node is the total number of edges that are directed towards the node, i.e, for our case, the total number of passes received by a player (node). Similarly, outdegree means the total number of edges that are directed outwards from the node, i.e, the total number of passes given by a player. Finally, the degree of a node is the total number of edges connected to a node (ignoring the directions of the edges), i.e, sum of the total number of passes given and the total number of passes received by a player. It is evident that the degree of a node is the sum of its indegree and outdegree.

We will use networkx to find out the node degrees from the pass network of Real Madrid.

# Prepare a dictionary with jersey numbers as the node ids, 
# i.e, the dictionary keys and degrees as the dictionary values
deg_Real = dict(nx.degree(G_Real)) 
# convert a dictionary to a pandas dataframe
degree_Real = pd.DataFrame.from_dict(list(deg_Real.items())) 
degree_Real.rename(columns = {0:'jersey_number', 1: 'node_degree'}, inplace = True)

degree_Real

	jersey_number	node_degree
0	14	12
1	2	17
2	7	11
3	22	11
4	9	14
5	10	15
6	12	16
7	5	14
8	4	17
9	8	19
10	1	10

• Out of the 11 starting players for Real Madrid in that game, we notice that the player with jersey number 8 (i.e, Toni Kroos) had the highest degree value of 19. On second are ranked the players with jersey number 2 and 4 with degree value 17, i.e, our favorite Spanish defenders 'Daniel Carvajal Ramos' and 'Sergio Ramos García' respectively. Tremendous! Let us use seaborn to visualize the deg_Real dictionary via histogram plot:

X = list(deg_Real.keys())
Y = list(deg_Real.values())
sns.barplot(x = Y, y = X, palette = "magma")
plt.xticks(range(0, max(Y)+5, 2))
plt.ylabel("Player Jersey number")
plt.xlabel("degree")
plt.title("Player pass degrees for Real Madrid vs Liverpool", size = 16)
plt.show()

• Let us build the dataframe for Liverpool too:

# Prepare a dictionary with jersey numbers as the node ids, 
# i.e, the dictionary keys and degrees as the dictionary values
deg_Liv = dict(nx.degree(G_Liv)) 
# convert a dictionary to a pandas dataframe
degree_Liv = pd.DataFrame.from_dict(list(deg_Liv.items()))
degree_Liv.rename(columns = {0:'jersey_number', 1: 'node_degree'}, inplace = True)
degree_Liv

	jersey_number	node_degree
0	5	12
1	26	11
2	7	17
3	14	17
4	1	7
5	66	13
6	4	12
7	11	11
8	6	12
9	9	10
10	19	6

• We see that for Liverpool the degree value is highest (17) for players having jersey number 14 and 7, i,e 'Jordan Brian Henderson' and 'James Philip Milner' respectively. We will visualize the deg_Liv dictionary via histogram plot:

X = list(deg_Liv.keys())
Y = list(deg_Liv.values())
sns.barplot(x = Y, y = X, palette = "magma")
plt.xticks(range(0, max(Y)+5, 2))
plt.ylabel("Player Jersey number")
plt.xlabel("degree")
plt.title("Player pass degrees for Liverpool vs Real Madrid", size = 16)
plt.show()

• We will visualize similar histogram plots for the indegrees and the outdegrees too:

indeg_Real = dict(G_Real.in_degree()) 
indegree_Real = pd.DataFrame.from_dict(list(indeg_Real.items())) 
indegree_Real.rename(columns = {0:'jersey_number', 1: 'node_indegree'}, inplace = True)
X = list(indeg_Real.keys())
Y = list(indeg_Real.values())
sns.barplot(x = Y, y = X, palette = "hls")
plt.xticks(range(0, max(Y)+5, 2))
plt.ylabel("Player Jersey number")
plt.xlabel("indegree")
plt.title("Player pass indegrees for Real Madrid vs Liverpool", size = 16)
plt.show()

indeg_Liv = dict(G_Liv.in_degree()) 
indegree_Liv = pd.DataFrame.from_dict(list(indeg_Liv.items())) 
indegree_Liv.rename(columns = {0:'jersey_number', 1: 'node_indegree'}, inplace = True)
X = list(indeg_Liv.keys())
Y = list(indeg_Liv.values())
sns.barplot(x = Y, y = X, palette = "hls")
plt.xticks(range(0, max(Y)+5, 2))
plt.ylabel("Player Jersey number")
plt.xlabel("indegree")
plt.title("Player pass indegrees for Liverpool vs Real Madrid", size = 16)
plt.show()

outdeg_Real = dict(G_Real.out_degree()) 
outdegree_Real = pd.DataFrame.from_dict(list(outdeg_Real.items())) 
outdegree_Real.rename(columns = {0:'jersey_number', 1: 'node_outdegree'}, inplace = True)
X = list(outdeg_Real.keys())
Y = list(outdeg_Real.values())
sns.barplot(x = Y, y = X, palette = "hls")
plt.xticks(range(0, max(Y)+5, 2))
plt.ylabel("Player Jersey number")
plt.xlabel("outdegree")
plt.title("Player pass outdegrees for Real Madrid vs Liverpool", size = 16)
plt.show()

outdeg_Liv = dict(G_Liv.out_degree()) 
outdegree_Liv = pd.DataFrame.from_dict(list(outdeg_Liv.items())) 
outdegree_Liv.rename(columns = {0:'jersey_number', 1: 'node_outdegree'}, inplace = True)
X = list(outdeg_Liv.keys())
Y = list(outdeg_Liv.values())
sns.barplot(x = Y, y = X, palette = "hls")
plt.xticks(range(0, max(Y)+5, 2))
plt.ylabel("Player Jersey number")
plt.xlabel("outdegree")
plt.title("Player pass outdegrees for Liverpool vs Real Madrid", size = 16)
plt.show()

• Now, let us generate the adjacency matrices fr both G_Real and G_Liv graphs:

A_Real = nx.adjacency_matrix(G_Real)
A_Liv = nx.adjacency_matrix(G_Liv)
A_Real = A_Real.todense()
A_Liv = A_Liv.todense()

sns.heatmap(A_Real, annot = True, cmap ='gnuplot')
plt.title("Adjacency matrix for Real Madrid's pass network")
plt.show()

sns.heatmap(A_Liv, annot = True, cmap ='gnuplot')
plt.title("Adjacency matrix for Liverpool's pass network")
plt.show()

• If we look into the diagonal of the adjacency matrices, we notice that all the values in the diagonals are 0. This depicts that their isn't any self loops in any nodes, indicating a player cannot pass to themselves.

• The next step is to calculate the degree correlation coefficient of a graph. More specifically, we will calculate Pearson's degree correlation coefficient value. A positive value of the metric shows an overall positive relationship between the degrees (number of successful passes) of two adjacent nodes (players). Whereas a negative value shows an overall negative relationship. If it is 0, there is no relationship. Also the metric lies in [-1, 1], indicating -1 as the prefect negative relationship and 1 as the perfect positive relationship.

r_Real = nx.degree_pearson_correlation_coefficient(G_Real, weight = 'weight')
r_Liv = nx.degree_pearson_correlation_coefficient(G_Liv, weight = 'weight')
print(r_Real, r_Liv)

-0.17983836432860179 -0.2412372196699064

• Now we work on a metric that focuses on the geodesic distance between two player nodes in a graph. One way to implement this is to divide 1 by the 'weight' column in the pass network. Let us create a new graph for Real Madrid:

pass_Real_mod = pass_Real_new[['pass_maker', 'pass_receiver']]
pass_Real_mod['1/nop'] = 1/pass_Real_new['number_of_passes']
pass_Real_mod.head(5)

	pass_maker	pass_receiver	1/nop
0	14	2	1.000000
1	7	2	0.333333
2	22	2	0.500000
3	9	2	0.500000
4	10	2	0.100000

L_Real_mod = pass_Real_mod.apply(tuple, axis=1).tolist()

G_Real_mod = nx.DiGraph()

for i in range(len(L_Real_mod)):
    G_Real_mod.add_edge(L_Real_mod[i][0], L_Real_mod[i][1], weight = L_Real_mod[i][2])

edges_Real_mod = G_Real_mod.edges()
weights_Real_mod = [G_Real_mod[u][v]['weight'] for u, v in edges_Real_mod]

nx.draw(G_Real_mod, node_size=800, with_labels=True, node_color='white', width = weights_Real_mod)
plt.gca().collections[0].set_edgecolor('black')
plt.title("Modified pass network for Real Madrid vs Liverpool", size = 20)

plt.show()

• We will perform the same operations to create a modified graph for Liverpool too:

pass_Liv_mod = pass_Liv_new[['pass_maker', 'pass_receiver']]
pass_Liv_mod['1/nop'] = 1/pass_Liv_new['number_of_passes']
pass_Liv_mod.head(5)

	pass_maker	pass_receiver	1/nop
0	5	26	0.25
1	7	26	1.00
2	14	26	1.00
3	1	26	1.00
4	66	26	1.00

L_Liv_mod = pass_Liv_mod.apply(tuple, axis=1).tolist()

G_Liv_mod = nx.DiGraph()

for i in range(len(L_Liv_mod)):
    G_Liv_mod.add_edge(L_Liv_mod[i][0], L_Liv_mod[i][1], weight = L_Liv_mod[i][2])

edges_Liv_mod = G_Liv_mod.edges()
weights_Liv_mod = [G_Liv_mod[u][v]['weight'] for u, v in edges_Liv_mod]

nx.draw(G_Liv_mod, node_size=800, with_labels=True, node_color='red', width = weights_Liv_mod)
plt.gca().collections[0].set_edgecolor('black')
plt.title("Modified pass network for Liverpool vs Real Madrid", size = 20)

plt.show()

• Now using these modified graphs we can calculate the all pair shortest paths between the nodes (players) for both the teams. Let us compute first for Real Madrid:

dis_Real = nx.shortest_path(G_Real_mod, weight = 'weight')
print(dis_Real)

{'14': {'14': ['14'], '2': ['14', '8', '10', '2'], '10': ['14', '8', '10'], '12': ['14', '8', '4', '12'], '5': ['14', '8', '5'], '4': ['14', '8', '4'], '8': ['14', '8'], '9': ['14', '8', '9'], '7': ['14', '8', '7'], '22': ['14', '8', '22'], '1': ['14', '8', '5', '1']}, '2': {'2': ['2'], '10': ['2', '10'], '5': ['2', '5'], '8': ['2', '10', '8'], '9': ['2', '5', '4', '12', '9'], '14': ['2', '14'], '7': ['2', '7'], '22': ['2', '22'], '1': ['2', '5', '1'], '12': ['2', '5', '4', '12'], '4': ['2', '5', '4']}, '7': {'7': ['7'], '2': ['7', '2'], '10': ['7', '2', '10'], '12': ['7', '12'], '4': ['7', '12', '8', '4'], '9': ['7', '12', '9'], '5': ['7', '2', '5'], '8': ['7', '12', '8'], '14': ['7', '12', '14'], '22': ['7', '12', '22'], '1': ['7', '2', '5', '1']}, '22': {'22': ['22'], '2': ['22', '2'], '10': ['22', '8', '10'], '12': ['22', '4', '12'], '4': ['22', '4'], '8': ['22', '8'], '9': ['22', '4', '12', '9'], '7': ['22', '7'], '5': ['22', '4', '5'], '1': ['22', '4', '5', '1'], '14': ['22', '8', '14']}, '9': {'9': ['9'], '2': ['9', '2'], '4': ['9', '8', '4'], '8': ['9', '8'], '14': ['9', '14'], '7': ['9', '8', '7'], '1': ['9', '1'], '10': ['9', '8', '10'], '12': ['9', '8', '4', '12'], '5': ['9', '8', '5'], '22': ['9', '8', '22']}, '10': {'10': ['10'], '2': ['10', '2'], '12': ['10', '8', '4', '12'], '5': ['10', '2', '5'], '4': ['10', '8', '4'], '8': ['10', '8'], '9': ['10', '8', '9'], '14': ['10', '2', '14'], '7': ['10', '2', '7'], '22': ['10', '8', '22'], '1': ['10', '2', '5', '1']}, '12': {'12': ['12'], '2': ['12', '2'], '10': ['12', '8', '10'], '5': ['12', '8', '5'], '4': ['12', '8', '4'], '8': ['12', '8'], '9': ['12', '9'], '14': ['12', '14'], '7': ['12', '7'], '22': ['12', '22'], '1': ['12', '8', '5', '1']}, '5': {'5': ['5'], '2': ['5', '10', '2'], '10': ['5', '10'], '4': ['5', '4'], '8': ['5', '8'], '9': ['5', '4', '12', '9'], '14': ['5', '8', '14'], '1': ['5', '1'], '12': ['5', '4', '12'], '7': ['5', '8', '7'], '22': ['5', '8', '22']}, '4': {'4': ['4'], '2': ['4', '2'], '10': ['4', '8', '10'], '12': ['4', '12'], '5': ['4', '5'], '8': ['4', '8'], '7': ['4', '12', '7'], '22': ['4', '8', '22'], '1': ['4', '5', '1'], '9': ['4', '12', '9'], '14': ['4', '12', '14']}, '8': {'8': ['8'], '2': ['8', '10', '2'], '10': ['8', '10'], '12': ['8', '4', '12'], '5': ['8', '5'], '4': ['8', '4'], '9': ['8', '9'], '14': ['8', '14'], '7': ['8', '7'], '22': ['8', '22'], '1': ['8', '5', '1']}, '1': {'1': ['1'], '12': ['1', '4', '12'], '5': ['1', '4', '5'], '4': ['1', '4'], '8': ['1', '4', '8'], '9': ['1', '4', '12', '9'], '2': ['1', '4', '2'], '10': ['1', '4', '8', '10'], '7': ['1', '4', '12', '7'], '22': ['1', '4', '8', '22'], '14': ['1', '4', '12', '14']}}

• Suppose we want to calculate the shortest path from 'Keylor Navas Gamboa' (jersey number 1) to 'Cristiano Ronaldo dos Santos Aveiro' (jersey number 7). We will type the following:

print(dis_Real['1']['7'])

['1', '4', '12', '7']

• So, we see that the fastest way possible to pass the ball from 'Keylor Navas Gamboa' (jersey: 1), to 'Cristiano Ronaldo dos Santos Aveiro' (jersey: 7) was to pass the ball first to 'Sergio Ramos García' (jersey: 4) who would pass to 'Marcelo Vieira da Silva Júnior' (jersey: 12) with him ultimately passing to 'Cristiano Ronaldo dos Santos Aveiro'. This seems like a good post-match analysis tool. I got this idea after discussing with Sarath Babu.

• Let us do the same analysis for Liverpool:

dis_Liv = nx.shortest_path(G_Liv_mod, weight = 'weight')
print(dis_Liv)

{'5': {'5': ['5'], '26': ['5', '26'], '7': ['5', '26', '7'], '14': ['5', '14'], '4': ['5', '4'], '11': ['5', '11'], '66': ['5', '26', '7', '66'], '9': ['5', '26', '9'], '1': ['5', '14', '1'], '6': ['5', '14', '6'], '19': ['5', '26', '7', '19']}, '26': {'26': ['26'], '5': ['26', '5'], '7': ['26', '7'], '14': ['26', '14'], '9': ['26', '9'], '4': ['26', '4'], '11': ['26', '9', '11'], '66': ['26', '7', '66'], '1': ['26', '14', '1'], '6': ['26', '14', '6'], '19': ['26', '7', '19']}, '7': {'7': ['7'], '26': ['7', '66', '5', '26'], '5': ['7', '66', '5'], '14': ['7', '14'], '9': ['7', '66', '9'], '4': ['7', '4'], '1': ['7', '1'], '11': ['7', '66', '11'], '66': ['7', '66'], '6': ['7', '14', '6'], '19': ['7', '19']}, '14': {'14': ['14'], '26': ['14', '5', '26'], '5': ['14', '5'], '7': ['14', '7'], '4': ['14', '4'], '1': ['14', '1'], '66': ['14', '7', '66'], '6': ['14', '6'], '19': ['14', '7', '19'], '11': ['14', '7', '66', '11'], '9': ['14', '5', '26', '9']}, '1': {'1': ['1'], '26': ['1', '26'], '14': ['1', '14'], '4': ['1', '6', '4'], '6': ['1', '6'], '7': ['1', '6', '7'], '11': ['1', '6', '66', '11'], '66': ['1', '6', '66'], '5': ['1', '6', '66', '5'], '9': ['1', '6', '66', '9'], '19': ['1', '6', '7', '19']}, '66': {'66': ['66'], '26': ['66', '5', '26'], '5': ['66', '5'], '14': ['66', '14'], '9': ['66', '9'], '11': ['66', '11'], '6': ['66', '14', '6'], '7': ['66', '14', '7'], '4': ['66', '5', '4'], '19': ['66', '11', '19'], '1': ['66', '14', '1']}, '4': {'4': ['4'], '26': ['4', '26'], '5': ['4', '26', '5'], '14': ['4', '26', '14'], '66': ['4', '6', '66'], '6': ['4', '6'], '7': ['4', '26', '7'], '9': ['4', '26', '9'], '1': ['4', '6', '1'], '11': ['4', '6', '66', '11'], '19': ['4', '26', '7', '19']}, '11': {'11': ['11'], '5': ['11', '66', '5'], '7': ['11', '9', '7'], '9': ['11', '9'], '4': ['11', '4'], '66': ['11', '66'], '19': ['11', '19'], '14': ['11', '9', '14'], '6': ['11', '9', '14', '6'], '26': ['11', '66', '5', '26'], '1': ['11', '9', '14', '1']}, '6': {'6': ['6'], '7': ['6', '7'], '14': ['6', '66', '14'], '4': ['6', '4'], '1': ['6', '1'], '11': ['6', '66', '11'], '66': ['6', '66'], '26': ['6', '4', '26'], '5': ['6', '66', '5'], '9': ['6', '66', '9'], '19': ['6', '7', '19']}, '9': {'9': ['9'], '7': ['9', '7'], '14': ['9', '14'], '11': ['9', '11'], '66': ['9', '11', '66'], '6': ['9', '14', '6'], '5': ['9', '14', '5'], '4': ['9', '14', '4'], '19': ['9', '7', '19'], '26': ['9', '14', '5', '26'], '1': ['9', '14', '1']}, '19': {'19': ['19'], '7': ['19', '7'], '14': ['19', '14'], '9': ['19', '9'], '11': ['19', '9', '11'], '66': ['19', '9', '11', '66'], '6': ['19', '14', '6'], '5': ['19', '14', '5'], '4': ['19', '14', '4'], '26': ['19', '14', '5', '26'], '1': ['19', '14', '1']}}

print(dis_Liv['1']['9'])

['1', '6', '66', '9']

• Now we will calculate another important metric called eccentricity, which is based on shortest distance. Eccentricity of a player node p tells us how far the furthest player node from p is positioned in the pass network. Let us calculate the eccentricities for all the 11 nodes for Real Madrid.

E_Real = nx.eccentricity(G_Real_mod)
print(E_Real)

{'14': 2, '2': 2, '7': 2, '22': 2, '9': 2, '10': 2, '12': 2, '5': 2, '4': 2, '8': 1, '1': 2}

• We can calculate the average eccentricity:

av_E_Real = sum(list(E_Real.values()))/len(E_Real)
print(av_E_Real)

1.9090909090909092

• For Liverpool:

E_Liv = nx.eccentricity(G_Liv_mod)
print(E_Liv)

{'5': 2, '26': 2, '7': 1, '14': 2, '1': 2, '66': 2, '4': 2, '11': 2, '6': 2, '9': 2, '19': 2}

• We can calculate the average eccentricity:

av_E_Liv = sum(list(E_Liv.values()))/len(E_Liv)
print(av_E_Liv)

1.9090909090909092

• We can also calculate the average clustering coefficient of a graph. Let us first compute this metric for G_Real (note that this graph should not be the modified version)

cc_Real = nx.average_clustering(G_Real, weight = 'weight')
print(cc_Real)

0.182334851979709

• for Liverpool:

cc_Liv = nx.average_clustering(G_Liv, weight = 'weight')
print(cc_Liv)

0.27664278424505534

• The average clustering coefficient lies in the range [0, 1] where, a value of 0 denotes the fact that none of the nodes are connected to each other and a value of 1 denotes that the network is a clique, that is each node is connected to all the other nodes of the network. We see that interestingly the average clustering coefficient is lesser for Real Madrid's pass network stating the fact that a lesser number of players passed the ball among each other, compared to that of Liverpool.

• Finally, we can compute the centrality (especially the betweenness centrality) for each node in either team's pass network and understand which player was the most important in their pass network. For Real Madrid:

bc_Real = nx.betweenness_centrality(G_Real, weight = 'weight')
print(bc_Real)

{'14': 0.15222222222222223, '2': 0.10685185185185186, '7': 0.05592592592592593, '22': 0.0, '9': 0.14462962962962964, '10': 0.12407407407407407, '12': 0.009259259259259259, '5': 0.007407407407407408, '4': 0.06851851851851852, '8': 0.031481481481481485, '1': 0.11703703703703704}

• we can find the node which has the maximum betweenness centrality measure.

max_bc_Real = max(bc_Real, key = bc_Real.get)
print(max_bc_Real)

14

• For Liverpool:

bc_Liv = nx.betweenness_centrality(G_Liv, weight = 'weight')
print(bc_Liv)
max_bc_Liv = max(bc_Liv, key = bc_Liv.get)
print(max_bc_Liv)

{'5': 0.06296296296296296, '26': 0.016666666666666666, '7': 0.2453703703703704, '14': 0.12407407407407407, '1': 0.002777777777777778, '66': 0.075, '4': 0.07222222222222222, '11': 0.05555555555555556, '6': 0.1259259259259259, '9': 0.021296296296296296, '19': 0.03888888888888889}
7

• So we see that the betweenness centrality measure is max for 'Carlos Henrique Casimiro' (jersey: 4) from Real Madrid and 'James Philip Milner' (jersey: 7) from Liverpool. We have been able to compute some interesting results using complex network analysis on our pass networks. This completes my presentation. 😌😌😌😌😌😌😌😌😌

References

• FCPython Blog,
• Book Soccermatics by Dr. David Sumpter,
• Friends of Tracking youtube channel managed by Dr. Sumpter,
• Youtube channel by McKay Johns, and
• Book Graph Theory and Complex Networks: An Introduction by Dr. Maarten van Steen

The End! Thank You! Wear Masks 😷😷, Get Vaccinated and Stay Stafe!