# What Happened Next? Using Deep Learning to Value Defensive Actions in
Football Event-Data

Charbel Merhej  University of SouthamptonSouthamptonUnited Kingdom
<EMAIL_ADDRESS>,  Ryan J Beal  University of SouthamptonSouthamptonUnited
Kingdom<EMAIL_ADDRESS>,  Tim Matthews  Sentient
SportsSouthamptonUnited Kingdom<EMAIL_ADDRESS>and  Sarvapali
Ramchurn  University of SouthamptonSouthamptonUnited Kingdom<EMAIL_ADDRESS>
(2021)

###### Abstract.

Objectively quantifying the value of player actions in football (soccer) is a
challenging problem. To date, studies in football analytics have mainly
focused on the attacking side of the game, while there has been less work on
event-driven metrics for valuing defensive actions (e.g., tackles and
interceptions). Therefore in this paper, we use deep learning techniques to
define a novel metric that values such defensive actions by studying the
threat of passages of play that preceded them. By doing so, we are able to
value defensive actions based on what they prevented from happening in the
game. Our Defensive Action Expected Threat (DAxT) model has been validated
using real-world event-data from the 2017/2018 and 2018/2019 English Premier
League seasons, and we combine our model outputs with additional features to
derive an overall rating of defensive ability for players. Overall, we find
that our model is able to predict the impact of defensive actions allowing us
to better value defenders using event-data.

Sports Analytics; Football; Deep Learning; Neural Networks; Applied Machine
Learning; Defensive Actions

††journalyear: 2021††copyright: acmcopyright††conference: Proceedings of the
27th ACM SIGKDD Conference on Knowledge Discovery and Data Mining; August
14–18, 2021; Virtual Event, Singapore††booktitle: Proceedings of the 27th ACM
SIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’21), August
14–18, 2021, Virtual Event, Singapore††price: 15.00††doi:
10.1145/3447548.3467090††isbn: 978-1-4503-8332-5/21/08††ccs: Applied
computing††ccs: Computing methodologies Model development and analysis††ccs:
Computing methodologies Neural networks

##  1\. Introduction

Valuing the actions of humans and agents in the real-world is a problem in
many industries. By assigning values to actions committed, we can help
evaluate the performance of agents and aid the learning and improvement of
future actions. To date, examples of work that explore methods for valuing
actions are shown in industrial optimisation (Phan et al., 2018), agent
negotiation (Liang et al., 2012) and sports analytics (Decroos et al., 2019;
Schulte et al., 2017). Although all these papers aim to assign value to what a
human or agent has helped happen, there are many domains in the real-world
where some humans/agents are tasked with preventing actions from happening
(e.g., in security games agents aim to protect bases or ports and prevent
attacks (Shieh et al., 2012)).

One domain where this is also key is in the sports world. In games such as
football, American football and basketball, there are players in each team who
are tasked with stopping actions (e.g., an American footballer defensive
player aims to prevent touchdowns). Therefore in this paper, we focus our
attentions on valuing the actions of defenders in Association Football
(soccer).111Referred to as just “football” throughout this paper (as it is
known outside the U.S.).

Due to the rapid advancements in technology in football, the past decade has
seen a growing line of data science research and football analysis. Multiple
companies222Examples of these companies include but are not limited to:
STATSPerform, WyScout and StatsBomb. have implemented advanced methods for
collecting detailed match actions in the form of event stream data, and more
recently in the form of tracking data. The growing availability of these
datasets have led to wider applications of artificial intelligence (AI)
techniques in football analytics such as machine and deep learning (Beal et
al., 2019).

An area where this has been particularly true is in the creation of new models
for descriptive player performance metrics. This is due to the immense
benefits it can provide for football clubs. As explained in (Beal et al.,
2019), measuring player performance is an important factor in the decision
making processes in team sport. However, due to the low scoring and dynamic
nature of football, this presents a unique challenge to AI to value actions
that often do not impact the scoreline directly but have important longer-term
effects (Decroos et al., 2019). In recent years, multiple successful metrics
have been adopted and used universally. One such example is the “Expected
Goals (xG)” metric (Rathke, 2017), which provides the probability of a shot
resulting in a goal in comparison to other similar shots.

A key limitation of such event-based action models is the lack of application
for defensive actions. This is an inherent problem with event-based data due
to the fact that defensive actions mainly prevent events from completion and
are therefore a challenge to value. This leads to a lot of players not getting
truly acknowledged for their defensive duties. To combat this problem, we
propose a novel data-driven model that focuses on defensive and out of
possession actions by quantifying these actions in a unique and accurate way.
What differentiates this model from other traditional football metrics (Beal
et al., 2020; Decroos et al., 2019; Rathke, 2017; Altman, 2015) is that,
instead of studying actions that lead to events happening, our model values
defensive actions that stop events from occurring. Thus, this paper advances
the state of the art in the following ways:

  1. (1)

Introduces a novel model to value defensive actions in football named DAxT
(Defensive Action Expected Threat). The model is targeted at the football
analytics community and brings together new research in football with deep
learning techniques to accurately value defensive actions based on what they
have stopped from happening.

  2. (2)

Using real-world data from 760 real-world football games from the past two
seasons of the English Premier League (EPL), we train and test our model and
find that we can accurately predict the impact of future events to an MAE of
0.015.

  3. (3)

We use this model to identify the top football defenders in the EPL and
validate this against leading providers of football performance statistics.

The rest of this paper is structured as follows. In Section 2 we review the
literature around player performance metrics in football and introduce basic
concepts about defending. Section 3 formally defines the goal of our model. In
Sections 4 and 5 we discuss how we created and solved the model and illustrate
the multiple experiments conducted to validate it. Section 6 shows the results
of applying our model on real-world datasets. Finally, in Section 7 we discuss
the outcomes obtained and we conclude in Section 8.

##  2\. Background

In this section, we present an overview of related work regarding player
performance metrics. Moreover, we introduce a background on basic concepts in
football and the importance of defensive actions.

###  2.1. Related Work

One of the key areas in football analytics is the study of new player
performance metrics. Because of the fast-paced and continuous nature of the
game, player performance analysis has been a difficult task in football. As
mentioned in (Kumar, 2013), “Baseball, for example, is a less fluid sports
than soccer. It is easier to break down a baseball game into discrete events
to be analyzed. The same cannot be said about soccer”. However, with the
increased interest in football analytics and advances in technology, more
researchers have focused their studies on this specific area.

As previously mentioned, xG is a metric used to describe the quality of a
certain shot. To accomplish this, the authors in (Lucey et al., 2014) analysed
the spatio-temporal patterns of the ten-second window of play before a shot
for 10,000 shots. In addition to the historical data, they used strategic
features such as defender proximity, speed of play, shot location, and game
phase to determine the likelihood of a goal being scored. A similar study was
done in (Rathke, 2017), where the authors used distance of the shot taken from
goal, the angle in relation to goal and the type of assist as features to
calculate xG. The model proved accurate for mid-table teams, whereas the top
table teams and lower table teams over and under achieved respectively. Both
papers mentioned above used logistic regression in their models. The different
features that could be used for xG models are highlighted in Figure 1 (Cronin,
[n.d.]).

Figure 1. Distance to goal, angle, and type of assist as features used to
calculate xG

Since xG only measures scoring actions, players on the pitch who are not
tasked to score goals cannot be evaluated using this metric. This is why the
authors in (Fernández et al., 2019) defined a metric called “Expected
Possession Value” (EPV), that quantifies the expected outcome at every moment
in a possession. Their model studies passes and turnover probabilities, action
likelihood, and pass/ball-drive value expectations that were estimated
independently using logistic regression, convolutional neural network and deep
neural networks respectively.

Contrarily, instead of measuring periods of possession, the value of each
action in a game was studied in (Decroos et al., 2019). Their VAEP (Valuing
Actions by Estimating Probabilities) model calculates this value $V(a_{i})$ by
estimating the change in probability of scoring and conceding a goal after
every action. This is shown in Equation 1.

(1) $V(a_{i})=\Delta P_{scores(a_{i},x)}+(-\Delta P_{concedes(a_{i},x)})$

where $\Delta P_{scores(a_{i},x)}$ is the offensive value of team x, denoting
the change in probability of scoring after an action $a_{i}$ is committed, and
$(-\Delta P_{concedes(a_{i},x)})$ is the defensive value of team x, denoting
the change in probability of conceding after $a_{i}$ is committed.

The VAEP metric performed better than traditional player performance metrics
and successfully identified promising young players and minor league talents.
To estimate the probabilities mentioned above, the authors used features such
as the action type, the location of action start and end, time elapsed, etc.
Moreover, since the probability of one team scoring is equal to the
probability of the other conceding, only two probability estimates were needed
for Equation 1. The task was then divided into two separate binary
classification problems, where the authors trained both models using CatBoost
algorithm.

Another important player performance metric is the Expected Threat (xT)
(Singh, [n.d.]), which is explained in further details in Section 4.1, as it
directly correlates to our model.

###  2.2. Defending in Football

Similar to some other team sports, football is an invasion game where the
whole team attacks when in possession of the ball, and defends when out of
possession. Even though scoring a goal directly contributes to the scoreline,
not conceding one is equally as important. Although the main goal of defending
is for teams not to concede goals, the way it happens varies according to
teams’ different tactics and styles of play. Some teams sit deep in their half
of the pitch (field) and stack up defenders, while others press high on the
field to gain possession back and attack.

There are two main defensive actions that happen in a football game:
Interceptions and Tackles. An interception is when the defending player
intentionally intercepts a pass by moving into the line of the intended ball
direction333https://www.mlssoccer.com/glossary. According to (pro tips,
[n.d.]), intercepting a pass takes the ability to anticipate, read the play
and keep the receiving player guessing. Getting the ball after a misplaced
pass is also counted as an interception.

A tackle can be of 2 different types (Weiyang, [n.d.]). A blocking/standing
tackle is one where the defender remains on his feet. It is generally used
when the player with the ball is coming directly towards the defender. The
other type is the sliding tackle, where the defender is off his feet and
slides to get the ball (SPIFFYD, [n.d.]).

Due to a strong focus in football analysis on attacking metrics that lead to
direct contributions, there is a lack of research on the defensive actions
mentioned above. In this paper, we aim to quantify different interceptions and
tackles happening on the pitch by using our DAxT model - how we model these
actions is explained in the following section.

##  3\. Modelling Defensive Actions

In this paper, our goal is to model defensive actions in football to be able
to better value the impact they have on the overall game. When modelling
attacking actions in games (such as in (Decroos et al., 2019; Rathke, 2017)),
the effect of a specific action can be seen according to what happened next
and the impact it had on the game. However, the same cannot be said about
defensive actions as they usually prevent further actions from happening.
Therefore, a logical way to value defensive actions is by assessing what they
have prevented from happening and predicting what would have happened if not
for that defensive action. By doing so, we present a model for valuing actions
that prevent other actions from happening. Although in this paper we focus on
football as an application domain, this model could be applied elsewhere where
it is important to understand the value of players or agents who prevent
actions from happening in games e.g., security games (Kiekintveld et al.,
2009; Grossklags et al., 2008) and emergency response (Ramchurn et al., 2015;
Ramchurn et al., 2016).

In football, events (such as passes, shots and tackles) happen in a sequence
or passage of play. We define a sequence of events as
$S=\\{e_{1},e_{2},…,e_{N}\\}$ where $S$ is the sequence, $e$ is an event and
$N$ is the number of events in the sequence. Each sequence of events can end
in a number of ways, for example the ball may go out of play, there may be a
foul leading to a free kick, or a defensive action $DA$ occurs for the
opposition to win the ball back from the attacking team. Two key types of
defensive actions that we focus on this paper are tackles and interceptions,
defined in Section 2.2. These actions can be valued in different ways
depending on the game context.

To value these actions, we aim to predict what was the ‘threat’ of the passage
of play that the defensive action has stopped. To calculate this, we use a
metric called ‘Expected Threat (xT)’ from (Singh, [n.d.]). This model assigns
a value to each attacking event based on the probability they have added to
the attacking team’s likelihood to score a goal from that passage of play
(defined in more details in Section 4.1).

We define the function to calculate xT as $f(e)$. We use this model to
calculate the xT value of each event $e$ in a sequence $S$, which then allows
us to train a machine learning model that is able to predict the xT of $e$
that should have happened after a sequence $S$. This can be defined as
$f(e_{n})=\Theta(S_{a})$ where $\Theta$ is the trained machine learning model
to predict xT, $e_{n}$ is the event we aim to predict, $S_{a}$ is the passage
of play made of $a$ events before a $DA$, and $f(e_{n})$ is the xT of the
event.

Using the model to predict the ‘threat’ of an event that did not happen means
that we can then value defensive actions by predicting the xT of the event
that the defensive action stopped from happening. In the following sections,
we give more details regarding the techniques and experiments conducted to
create the model described in this paper.

##  4\. The DAxT Model

In this section we present how we assign values to the defensive actions
discussed in the previous section. We discuss how we applied deep learning to
predict the xT of an event that a $DA$ has stopped, which led to the valuation
of all interceptions and tackles in games. The first challenge for us to be
able to predict what was stopped from happening is assigning the threat of the
actions that have happened. This is achieved through the Expected Threat (xT)
model discussed in the next subsection.

###  4.1. Expected Threat (xT)

The model defined in (Singh, [n.d.]) aims to measure the threat of any single
game state at any moment in a game. In order to do so, the model calculates
the probability that the player with the ball will shoot and score, with the
probability he will move the ball to another location. This is shown by the
following equation:

(2) $\textbf{xT}_{x,y}=(s_{x,y}\times
g_{x,y})+(m_{x,y}\times\sum_{z=1}^{16}\sum_{w=1}^{12}T_{(x,y)\rightarrow(z,w)}\textbf{xT}_{z,w})$

The left side of the equation ($s_{x,y}\times g_{x,y}$) represents the
probability of shooting from position x,y (how often players opt to shoot from
this position), and the probability that this shot is scored (xG (Rathke,
2017) of the shot). For the right side (after the + sign) , the author is
calculating the probability the player will move the ball to another zone, and
the value of this movement. It is worth noting that since players can only
shoot or move, then $s_{x,y}+m_{x,y}=100\%$.

As seen in Equation 2, in order to calculate the xT at zone (x,y), we need to
know beforehand the xT at all other zones. To solve this problem, the author
suggests starting with $xT_{x,y}=0$ at first for all zones, and then
evaluating this formula iteratively until convergence. For each evaluation, we
use the xT value of the previous iteration. When implementing this model, we
ran xT for 43 iterations until full convergence.

To illustrate an example, Figure 2 shows a passage of play by Manchester
United in a game with the xT of each action shown. The first pass (1 to 2) and
dribble (2 to 3) have negative xT value since they are moving away from goal,
decreasing the probability of the attacking team to score. However, the
successful pass of Alexis Sanchez into the penalty box resulted in a large
positive xT value, indicating the increased threat of scoring a goal.

Figure 2. Passage of play showing xT of each action

In the next subsection we look at how we can use xT to train a model that can
predict what would happen after a sequence of events.

###  4.2. Predicting What Was Stopped

Due to its generalization mechanism (Lawrence et al., 1998), and application
to large sets of data (such as game events), we built a simple neural network
model to predict the future xT of the events. Specifically, we have built a
Multi Layer Perceptron (Tang et al., 2015) model using the
Keras444https://keras.io library. As explained in Section 3, $\Theta$ is fed
as input a fixed number of actions $S_{a}$ in a passage of play (Section 5.1
shows the experiment done to determine the number of actions $a$), and as
output the xT of the action after this passage of play. Table 1 shows an
example of one input instance $S_{a}$ with $a=3$. Each event $e$ in $S_{a}$ is
represented by its xT ($f(e)$) and x,y coordinates. The output in this case
would be “xT4”, signaling the xT of the action after this passage of play.

Table 1. Input example for our Neural Network model xT1 | x1 | y1 | xT2 | x2 | y2 | xT3 | x3 | y3
---|---|---|---|---|---|---|---|---

Due to the distribution of the target values being mainly Laplacian with few
outliers (explained further in Section 5.3), the network was trained using a
Mean Absolute Error (MAE) loss function, shown in Equation 3.

(3) $MAE=\displaystyle\frac{1}{n}\sum_{t=1}^{n}|\hat{y_{t}}-y_{t}|$

where n is the number of data points used, $\hat{y_{t}}$ is the predicted xT
for a specific instance, and $y_{t}$ is the actual xT for this instance.

We generate and use three main datasets. The first was formed by collecting
all sequences $S_{a}$ (of $a$ consecutive actions) where each sequence
precedes a successful event $e$ such that $e\neq DA$. These instances (example
in Table 1) are used as input for $\Theta$, with the xT of the following event
as output. All training and testing (random 80-20 split) of $\Theta$ will be
done on this dataset. The other two were made up of valid passages of play
$S_{a}$ that came before failed events that were interrupted by a $DA$ (one
dataset for interceptions and one for tackles). After validating $\Theta$, it
will be fed as input these datasets to predict $f(e_{n})$ (equation in Section
3) i.e to predict the xT of event $e_{n}$ that would have happened without the
$DA$. This xT output would thus be the valuation of each interception and
tackle.

In the next subsection we discuss how we assign value to each event as well as
to the ability of an individual player in a given game for interceptions,
tackles, and overall score.

###  4.3. Assigning Value to Events

As previously mentioned, we apply our DAxT model on the 2 defensive action
datasets to predict the xT of the event that was interrupted by a $DA$. After
having each interception and tackle assigned its corresponding Interception
value $I_{V}$ and Tackle value $T_{V}$, we grouped these defensive actions
according to the player committing them. We then calculated the total $I_{V}$
and $T_{V}$ for each player by summing all values together and also computed
the average for each per interception and tackle respectively. The results are
shown in Section 6.

Moreover, we used these metrics to deduce an overall defender score. In total,
four features were used to obtain the score: $I_{V}$, $T_{V}$, Clearance xT,
and Pass xT. We combined the two metrics we got from the DAxT model with the
latter two to derive a final score. Clearance xT is the expected threat of a
clearance555When a player kicks the ball away from their own goal (Almazov,
[n.d.]). committed by a defender. The advantage of clearances is that they are
moving actions (unlike interceptions and tackles), thus have an xT value which
correlates to the DAxT calculated. The final feature is Pass xT, which
considers the expected threat of each pass committed by a defender. This
feature was used to value the importance of defenders from an attack
perspective in build up play, as this is becoming increasingly important at
the top levels.

We used the cumulative values of each feature for each player, and normalized
them to a score between 0-100. When simply calculating the average score of
the four features, the rankings were topped by defensive-minded players. This
is why we introduced weights to the equation. We applied the weights in such a
way where the impact of defensive values will be equal to the impact of
offensive values. This can be seen in the following equation:

(4) $Sc=((I_{V}+T_{V}+CxT)\div 3+PxT)\div 4$

where $Sc$ is the final defender score, $CxT$ is the Clearance xT, and $PxT$
is the Pass xT. The division by 3 was done in order to get the mean of the
defensive values and the whole equation was divided by 4 to get the average of
all values. Section 7.1 illustrates and analyzes the real-world results.

##  5\. Empirical Evaluation

To evaluate and optimise our models, we used a dataset collected from two
seasons (2017/18 and 2018/19) from the English Premier League (EPL).666All
data provided by StatsBomb - www.statsbomb.com. The dataset breaks down each
of the games from the tournament into an event-by-event analysis where each
event gives different metrics including: event type (e.g., pass, shot, tackle
etc.), the pitch coordinates of the event and the event outcome. This is a
rich real-world dataset that allows us to rigorously assess the value of our
model. The experiments777Experiments have been run using Keras and TensorFlow.
performed are as follows:

###  5.1. Experiment 1: Setting the Model Parameters

First, to test the model generalisation, we separated our data into training
and validation sets (random split of 80-20). The experiments were then ran on
both sets and the MAE (Equation 3) was the metric used.

We ran an experiment to determine the number of actions $a$ that should be
taken into consideration in $S_{a}$. There could be an argument about using
$a=1$, since having the xT and location of an event could be enough “threat”
evidence. Another argument would be that using more actions would be
beneficial to our model since it is learning more details about the passages
of play. Table 2 shows the training and validation losses, amount of training
data, and number of each $DA$ with different number of previous actions.

Table 2. MAE and instances for different number of actions | $a=1$ | $a=2$ | $a=3$
---|---|---|---
Training Loss | 0.0174 | 0.0154 | 0.0123
Validation Loss | 0.0169 | 0.0153 | 0.012
Training Data | 950,139 | 802,046 | 686,529
Interceptions | 98,235 | 75,691 | 59,593
Tackles | 22,124 | 17,423 | 13,676

The number of training data and defensive actions available decreases as $a$
increases. This is logical, since finding 3 consecutive, successful, and
moving actions in the dataset is harder than finding 2 or even 1. Thus, this
leads to having less available defensive actions to value as the passages of
play become longer.

As highlighted in the table, we chose $a=2$ as the optimal number of actions
for passages of play. This result was selected to balance between minimizing
the loss of the model and maximizing the number of defensive actions being
valued. Although their number was decreasing, not valuing these $DA$ was worth
the increase in accuracy. This is due to the fact that by choosing 2 actions
instead of 1, we minimized the randomness of having only $a=1$ in $S_{a}$
(which could be considered as outliers that confuse the model), thus allowing
better and more accurate sequences to be considered. This decrease in $DA$
eliminated the repeated actions that occur in some games, with actions
happening quickly after one another that would not interpret a defender’s true
ability.

###  5.2. Experiment 2: Selecting the Features

Another experiment was conducted in order to test different feature sets for
our model. According to (Altman, 2015), most existing models that analyze
football event data only use location and action type. Since our action type
is constant, we tested different combinations of features that include body
part, time of game and team ID, other than the already mentioned xT and
location.

After testing different combinations, the results showed that xT and x,y
coordinates were truly the most important features. The omission of either one
of them (or both) resulted in an increase in MAE ¿ 0.002, whereas trying both
features with others resulted in differences of $\approx$ 0.001. The best
model according to the lowest MAE value and best learning curve was the model
that uses both of these features alone. Adding other variables was either
overfitting the model (team ID), which was expected since it disturbs the
initial tactical interpretation, or was too general to make a difference (body
part, where the large majority of actions was with foot).

###  5.3. Experiment 3: Model Prediction

The first step towards validating our model is by checking whether its
predictive performance deteriorates when applied to unseen data. When
exercised on the test set, the model returned an MAE loss of 0.016, which is
an accepted result according to the training and validation loss functions in
Section 5.1.888For comparative purposes a baseline model predicting 0’s would
have a MAE of 0.0267.

The first statistical test we performed was comparing the residuals of the
training and testing datasets. The residuals (errors) are the differences
between the actual and predicted values of the model. To make sure our model
does not over fit to our training data, we used the Levene test (Schultz,
1985) and Kolmogorov-Smirnov (KS) (Massey Jr, 1951) test on both residuals.
These tests are conducted to compare the variance (Levene) and probability
distribution (KS) of our training and testing residuals, which are expected to
be similar for our model to be considered a good fit. The Levene test returned
a statistic value $v=1.209$ and a p-value $p=0.272$. Since the p-value is
greater than our 5% threshold, we can then conclude that there is evidence
that both residuals have the same variance. Similarly, the KS test’s return of
$v=0.0174$ and $p=0.8333>0.05$ suggests that the two probability distributions
are the same.

When sketching the fitted line of the probability plot (also known as Q-Q plot
(Kumar, 2005)) in Figure 3, we could see that the residual’s distribution is
somewhat normal with long tails on both sides. By visualizing the predictions
yielded by our model and comparing them to the actual values, we observed that
96.1% of the data was between 0.05 and -0.05, explaining the tails in the
plot. This reasoning was logical since actions with very high xT (or very low)
rarely happen in games compared to regular, less significant actions.

Figure 3. Q-Q plot of normalized residuals

Finally, to show that there is a correlation between the model’s predictions
and the actual values, we ran a Pearson correlation test which resulted in an
r-value $r=0.0985$ and a p-value less than 0.05. These results are
statistically significant and show that, using the data available, we have
been able to train a model that can predict the xT of the next event in games
of football.

###  5.4. Experiment 4: Valuing Defenders

After applying our model on all defensive actions, we used Equation 4 to
calculate the overall defender score for all players. In order to validate the
results, we compared the score of the top 25 center backs, full backs, and
defensive midfielders respectively, with their market value999according to
transfermarkt.com at the beginning of 2019. Figure 4 shows the scatter plot
that illustrates the correlation between the overall defender score and their
market value (in millions of €).

Figure 4. Correlation between Defender Score and Market Value (in millions of
€)

After plotting the regression line, we calculated the Pearson correlation
coefficient $r$ and the p-value. This resulted in $r=0.533$ and
$p=$3.37\text{\times}{10}^{-6}$$. These values show that there is a positive
correlation between our defender score and their market value, thus validating
the results generated by our model. The reason for not having a stronger
correlation coefficient is due to the many factors that add noise to this data
away from the actual ability and performance of the player (intangibles that
affect market value). For example, other factors include but are not limited
to age, nationality, political factors, current club and even popularity
(Müller et al., 2017). One example in the plot would be Fernandinho who,
although considered a world class player and has a high defensive score, was
34 years old in 2019 and arguably past his prime meaning he would have a lower
market value.

##  6\. Model Application to English Premier League

In this section, we show the results of our model when applied on the English
Premier League data for the 2017/18 and 2018/19 seasons. As mentioned in
Section 4.3, we separated interceptions from tackles and used our DAxT metric
to calculate the Interception Value $I_{V}$ and Tackle Value $T_{V}$. Tables 3
and 4 show the results after combining all interceptions and tackles
respectively for individual players over the 2 Premier League seasons.

The results shown in both tables are logical since almost all players that
appear are defenders that play with teams that finished in the bottom half of
the table, meaning they tend to commit more defensive actions as their teams
on average have a smaller share of possession in each game. This could be
normalized based on the possession of the team to assess how much defending a
player does. This is also proved in the number of goals conceded column (GC).
Although not directly related, committing more defensive actions increases the
overall DAxT of defenders as the sum shown in Tables 3 and 4 are cumulative
sums for 2 Premier League seasons.

Table 3. Top 10 players with most cumulative $I_{V}$ Player Name | $I_{V}$ | Count | GC | Team
---|---|---|---|---
James Tarkowski | 1.605 | 641 | 93 | Burnley
Ben Mee | 1.576 | 660 | 95 | Burnley
Nathan Aké | 1.537 | 616 | 129 | AFC Bournemouth
Lewis Dunk | 1.508 | 566 | 109 | Brighton & Hove Albion
Shane Duffy | 1.473 | 604 | 106 | Brighton & Hove Albion
Harry Maguire | 1.457 | 593 | 100 | Leicester City
Virgil van Dijk | 1.447 | 657 | 50 | Southampton/Liverpool
Christopher Schindler | 1.411 | 620 | 124 | Huddersfield Town
Jamal Lascelles | 1.386 | 565 | 67 | Newcastle United
Steve Cook | 1.357 | 612 | 109 | AFC Bournemouth
Table 4. Top 10 players with most cumulative $T_{V}$ Player Name | $T_{V}$ | Count | GC | Team
---|---|---|---|---
Wilfred Ndidi | 0.435 | 169 | 95 | Leicester City
Christopher Schindler | 0.4 | 118 | 124 | Huddersfield Town
Idrissa Gana Gueye | 0.384 | 142 | 86 | Everton
James Tarkowski | 0.38 | 85 | 93 | Burnley
César Azpilicueta | 0.353 | 120 | 77 | Chelsea
Nathan Aké | 0.335 | 90 | 129 | AFC Bournemouth
Luka Milivojević | 0.318 | 110 | 91 | Crystal Palace
Aaron Wan-Bissaka | 0.315 | 108 | 56 | Crystal Palace
Ben Mee | 0.292 | 68 | 129 | Burnley
Harry Maguire | 0.286 | 67 | 100 | Leicester City

To get a clearer idea about which players carried out the most important $DA$,
we normalized the values by $DA$ committed i.e. showing the average $I_{V}$
and $T_{V}$ for all interceptions and tackles committed respectively by each
player. We set thresholds to only include players that committed more than 100
interceptions and more than 50 tackles (this is so we remove the players who
had not played a high number of minutes and skew the results). Tables 5 and 6
show the top 10 players with highest average values for each category.

Table 5. Top 10 players with highest average $I_{V}$ per interception Player Name |  $I_{V}$ Average | Count | GC | Team
---|---|---|---|---
Fabián Balbuena | 0.0031 | 232 | 32 | West Ham United
James Ward-Prowse | 0.00306 | 125 | 92 | Southampton
Paul Pogba | 0.00305 | 138 | 70 | Manchester United
Cheikhou Kouyaté | 0.00294 | 176 | 97 | West Ham United/Crystal Palace
Geoff Cameron | 0.00294 | 122 | 30 | Stoke City
Isaac Hayden | 0.00291 | 162 | 65 | Newcastle United
Jefferson Lerma | 0.0029 | 140 | 61 | Bournemouth
Solomon March | 0.00288 | 125 | 106 | Brighton & Hove Albion
Patrick van Aanholt | 0.00288 | 289 | 84 | Crystal Palace
Joe Bennett | 0.00287 | 168 | 50 | Cardiff City
Table 6. Top 10 players with highest average $T_{V}$ per tackle Player Name |  $T_{V}$ Average | Count | GC | Team
---|---|---|---|---
James Tarkowski | 0.00448 | 85 | 93 | Burnley
Shane Duffy | 0.00444 | 54 | 106 | Brighton & Hove Albion
Jamal Lascelles | 0.00443 | 53 | 67 | Newcastle United
Ben Mee | 0.00429 | 68 | 95 | Burnley
Harry Maguire | 0.00427 | 67 | 100 | Leicester City
James Tomkins | 0.00426 | 62 | 69 | Crystal Palace
Issa Diop | 0.00416 | 51 | 43 | West Ham United
Wesley Hoedt | 0.00414 | 69 | 66 | Southampton
Adrian Mariappa | 0.00413 | 53 | 74 | Watford
David Luiz | 0.00404 | 51 | 49 | Chelsea/Arsenal

The inputs were first standardized when training the model, but an inverse
transform function was then applied to get back the original corresponding
output values. This way, the outputs can be more interpretable and
understandable i.e. Fabian Balbuena’s $I_{V}$ average directly correlates to
the fact that on average, his interceptions prevented actions of xT = 0.0031
of happening.

##  7\. Discussion

One advantage this model offers is a framework to compare defensive players
against each other. To take 2 examples, we used N’Golo Kanté and Aaron Wan-
Bissaka as benchmarks (Worville, [n.d.]). Although both players are world
class in many ways, their most well-known important trait (affects their
market value) is their ability to intercept (Kanté) and tackle (Wan-Bissaka).
We searched for players having similar number of defensive actions as both and
compared their defensive and market values.101010according to
transfermarkt.com

Table 7. Comparing players by $I_{V}$ and market value Player Name |  $I_{V}$ Average | Interceptions | Market Value
---|---|---|---
N’Golo Kanté | 0.00255 | 247 | €100M
Pierre-Emile Højbjerg | 0.00216 | 241 | €12M
Fernando | 0.00205 | 264 | €5M
Table 8. Comparing players by $T_{V}$ and market value Player Name |  $T_{V}$ Average | Tackles | Market Value
---|---|---|---
Aaron Wan-Bissaka | 0.00291 | 108 | €30M
DeAndre Yedlin | 0.00139 | 89 | €8M
Pablo Zabaleta | 0.00128 | 97 | €4M

In Tables 7 and 8, our benchmark players are compared with other players
having similar number of defensive actions and playing in the same position.
Their $I_{V}$ and $T_{V}$ average per interception and tackle respectively are
observed, as well as their market value at the beginning of 2019. As we can
see in both tables, the $I_{V}$ and $T_{V}$ are directly proportional to the
market value, with our benchmark players having much higher market value than
the others. Without the results yielded by our model, we would only be able to
compare the raw numbers of interceptions and tackles, without truly
understanding why our benchmarks players are top of the class in their
defensive ability.

To make sure our model is outputting logical results, we plotted the defensive
actions of players in each category and colored each action according to its
DAxT. The blue color signals a very high DAxT (top 10 % of all DAxT in the
dataset), with green (top 30%), yellow (top 50%) and red (the rest) coming
after.

Figure 5. Interceptions committed by Fabian Balbuena Figure 6. Tackles
committed by Andrew Robertson

Figure 5 illustrates the interceptions committed by Fabian Balbuena. The ones
closest to goal (defensively) are shown to be the most important defensive
actions (top 10%). These interceptions illustrate that the preceding passages
of play were of high threat, thus increasing the $I_{V}$ of each interception.
The values gradually decrease as actions occur further up the pitch, which is
logical since passages of play in the middle of the pitch do not usually lead
to conceding goals. The same concept applies to Figure 6, that illustrates the
tackles committed by Robertson. The ones which directly led to stopping
actions of high threat are in blue, and most of the tackles are on the left
side of the pitch due to Robertson’s position as a left back.

###  7.1. Overall Defender Score

We applied the overall defender score (introduced in Section 4.3) for ranking
and filtered out according to position (center back or full back). We then
used CIES Football Observatory and InStat Performance Index (Football and
InStat, [n.d.]) for the 2019 season as a means of comparison for our rankings
(CIES). Moreover, we calculated the number of goals conceded (GC), appearances
(A), goals conceded per appearance (GC/A), and assists (AST) for full backs.
Table 9 shows our rankings for center backs while Table 10 shows the rankings
for full backs.

Table 9. Ranking Center Backs according to defender score Player Name | Score | GC | A | GC/A | Rank | CIES
---|---|---|---|---|---|---
Virgil Van Dijk | 37.901 | 50 | 64 | 0.781 | 1 | 1
Harry Maguire | 36.3 | 100 | 69 | 1.449 | 2 | 4
Ben Mee | 35.942 | 95 | 67 | 1.418 | 3 | 37
James Tarkowski | 34.733 | 93 | 66 | 1.409 | 4 | 13
Shkodran Mustafi | 34.636 | 70 | 58 | 1.207 | 5 | 20
Jan Vertonghen | 34.426 | 54 | 58 | 0.931 | 6 | 20
Toby Alderweireld | 33.459 | 44 | 48 | 0.916 | 7 | 11
Aymeric Laporte | 33.284 | 26 | 44 | 0.591 | 8 | 6
Nathan Aké | 33.25 | 129 | 76 | 1.697 | 9 | 31
Michael Keane | 31.913 | 85 | 63 | 1.349 | 10 | 37
Lewis Dunk | 30.572 | 109 | 74 | 1.472 | 11 | 26
David Luiz | 30.536 | 49 | 46 | 1.065 | 12 | 20
Antonio Rüdiger | 29.975 | 57 | 60 | 0.95 | 13 | 17
Shane Duffy | 28.295 | 106 | 72 | 1.472 | 14 | 20
Nicolas Otamendi | 27.826 | 32 | 52 | 0.615 | 15 | 17
Table 10. Ranking Full Backs according to defender score Player Name | Score | GC | A | GC/A | AST | Rank | CIES
---|---|---|---|---|---|---|---
César Azpilicueta | 47.823 | 77 | 75 | 1.026 | 11 | 1 | 6
Andrew Robertson | 40.047 | 38 | 58 | 0.655 | 16 | 2 | 2
Patrick van Aanholt | 38.568 | 84 | 64 | 1.3125 | 3 | 3 | 24
Kyle Walker | 31.464 | 39 | 65 | 0.6 | 7 | 4 | 12
Trent Alexander-Arnold | 31.31 | 32 | 48 | 0.66 | 13 | 5 | 5
Kieran Trippier | 31.082 | 44 | 51 | 0.86 | 8 | 6 | N/A
Ryan Bertrand | 27.206 | 91 | 59 | 1.54 | 4 | 7 | 27
Pablo Zabaleta | 26.69 | 97 | 63 | 1.54 | 2 | 8 | N/A
Ben Davies | 26.44 | 46 | 56 | 0.82 | 6 | 9 | 24
Marcos Alonso | 24.691 | 58 | 64 | 0.906 | 6 | 10 | 1
Ben Chilwell | 24.442 | 73 | 60 | 1.216 | 6 | 11 | 8
Aaron Wan-Bissaka | 23.331 | 56 | 42 | 1.33 | 3 | 12 | 9
Ricardo Pereira | 23.046 | 45 | 35 | 1.285 | 6 | 13 | 4
Luke Shaw | 22.994 | 41 | 40 | 1.025 | 4 | 14 | 13
Cédric Soares | 22.73 | 75 | 50 | 1.5 | 5 | 15 | 19

Although there is a season difference between the rankings, we can see many
similarities in player standings. Most of the players mentioned are found in
both studies, assuring that our results are logical. Moreover, our findings
match the top defenders identified by experts in the press for that
season111111https://www.mirror.co.uk/sport/football/news/top-10-central-
defenders-premier-13772574. This indicates the importance of applying
statistical models such as our metrics and xT, rather than using raw data.

Furthermore, the tables illustrate consistency between our defender score and
the other variables. For example, we can see that 5 of our top 6 full backs
have a low average of goals conceded/appearance with a high number of assists
relative to the rest. Also, although Harry Maguire and Nathan Aké, for
instance, have a high number of goals conceded/appearance due to the teams
they were playing for, their transfer fees (transfermarkt.com) of €87M to
Manchester United and €45M to Manchester City respectively show why they are
top of our ranking.

As different teams have different playing styles, valuing defenders as such
has many advantages. Other than using it directly to compare between players,
scouts and teams could use the same metrics but change the weights according
to their needs. Instead of equally weighing the defensive and attacking side
of players, some teams (such as relegation-threatened ones) could want to
focus more on specific defensive metrics, weighing each one accordingly.
Moreover, the same defender score could also be used for defensive
midfielders. Table 11 shows the top 10 defensive midfielders according to
score.

Table 11. Ranking Defensive Midfielders according to defender score Rank | Player Name | Score
---|---|---
1 | Granit Xhaka | 37.648
2 | Fernandinho | 37.437
3 | Nemanja Matić | 30.737
4 | Jorginho | 27.652
5 | Luka Milivojević | 27.299
6 | Abdoulaye Doucouré | 25.734
7 | Idrissa Gueye | 24.633
8 | Oriol Romeu | 24.629
9 | Mark Noble | 23.197
10 | Wilfred Ndidi | 23.107

###  7.2. Remaining Challenges

One limitation of our DAxT model is that some defensive actions will be valued
less than they should be due to unique passages of plays. For instance, the
opposition could counterattack and be in a 3vs1 situation (3 players attacking
while only 1 is defending) in the middle of the pitch. If the defender
intercepts the ball, our model would not highly reward this action because
similar passages of play are not usually of high threat (without taking into
consideration the number of defenders behind the ball). This is why future
work for valuing defenders’ contributions should be centered around the
growing collection of tracking data. This will allow analysts to assess the
off-ball contributions and movement of defenders with models such as pitch
control (Spearman, 2018), evaluations of opposition marking and stopping
events before they have happened. However, due to the low availability of
tracking data at this time, especially across different leagues, it is key to
have methods that allow defensive actions to be valued from event-data in
smarter ways.

A further challenge our model faces is the dependency on another player
metric. This becomes a problem in terms of interpretation, where people need
to understand Expected Threat first in order to comprehend our DAxT model.
Moreover, metrics such as Possession Adjusted Interceptions and True Tackle
Win % are slightly more intuitive than our ratings, which complicates the task
for analytically less inclined scouts to fully grasp our model.

##  8\. Conclusion

Even though the results have illustrated that our model works well, comparing
it to other baseline models remains difficult due to the lack of similar work.
One analogous paper is (Stöckl et al., [n.d.]), where the authors make use of
tracking data to understand the defensive impact of players.

In conclusion, we have presented a novel model for valuing defensive actions
by using deep learning to predict a future event that a defensive action has
stopped. We have introduced a new metric DAxT by focusing on the values of
tackles and interceptions made by defenders. This can help clubs to better
understand the contribution of defenders and identify new talent for
recruitment in the over 100 leagues that event-data is collected for.

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##  Appendix A Appendix on Reproducibility

In this appendix we give further details on our models and techniques used for
reproducibility purposes.

###  A.1. Data Conversion

For this project, we used StatsBomb’s event-based data for the 2017/2018 and
2018/2019 English Premier League seasons (total of 760 games). Due to the
inconsistency of events in terms of number of features, we used a data
abstraction package called SPADL (Soccer Player Action Description Language).
As mentioned in (Decroos et al., 2019), SPADL transforms the event stream data
of JSON format into “a common vocabulary that enables subsequent data
analysis.” This library was created to convert different data providers’ event
data into a consistent format. Therefore, our model is reproducible with any
data. Table 12 shows some features of the first 5 instances in the event-
stream data.

Table 12. StatBomb’s Premier League data converted to SPADL Game ID | Time in seconds | Team ID | Player ID | Start x | Start y | … | Result ID | Type name | Player name | Country name
---|---|---|---|---|---|---|---|---|---|---
14562 | 1 | 58 | 9923 | 52.0588 | 34.4304 | … | 1 | pass | Bobby Reid | England
14562 | 2 | 58 | 9917 | 41.4706 | 34.4304 | … | 1 | dribble | Joe Ralls | England
14562 | 2 | 58 | 9917 | 41.4706 | 34.4304 | … | 1 | pass | Joe Ralls | England
14562 | 4 | 58 | 9924 | 25.5882 | 19.7975 | … | 1 | dribble | Sean Morrison | England
14562 | 6 | 58 | 9924 | 26.4706 | 18.9367 | … | 0 | pass | Sean Morrison | England

We then calculated the xT of every moving successful action in the dataset.
Figure 7 illustrates the frequency of each action type.

Figure 7. Frequency of each action type in StatBomb’s data

After preparing the data, we extracted all 3 consecutive, moving, and
successful actions for our first database. Each extraction was 1 instance
where 2 actions were considered as input (xT and coordinates) and the third
one as output (xT only). This amounted to 802,046 instances. The next step was
extracting similar sequences (2 actions) that happened before a failed event
due to a defensive action by the opposition. We separated interceptions from
tackles which resulted in 75,691 interceptions to value and 17,423 tackles.

Before training, we applied Scikit-Learn’s MinMaxScaler 121212https://scikit-
learn.org/ on our dataset for normalization.

###  A.2. Model Setup

For our model, we used the implementation of a Multi Layer Perceptron from
Keras’ library. The network was trained using a Mean Absolute Error loss
function and an Exponential Linear Unit activation function. The deep network
was composed of 3 dense hidden layers with 10 neurons each, and ran using
Adadelta optimizer for 50 epochs.

For the experiments in the paper, we used the
scipy.stats131313https://docs.scipy.org/doc/scipy/reference/stats.html library
for the statistical outcomes and the matplotlib141414https://matplotlib.org/
library for all graphs.