Citation: Skoki, A.; Rossi, A.; Cintia,
P.; Pappalardo, L.; Štajduhar, I.
Extended Energy-Expenditure Model
in Soccer: Evaluating Player
Performance in the Context of the
Game. Sensors 2022, 22, 9842.
https://doi.org/10.3390/s22249842
Academic Editor: Michael E. Hahn
Received: 18 October 2022
Accepted: 12 December 2022
Published: 14 December 2022
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sensors
Article
Extended Energy-Expenditure Model in Soccer: Evaluating
Player Performance in the Context of the Game
Arian Skoki 1
, Alessio Rossi 2,3,*
, Paolo Cintia 2
, Luca Pappalardo 2,3
and Ivan Štajduhar 1,4
1
Department of Computer Engineering, Faculty of Engineering, University of Rijeka, Vukovarska 58,
51000 Rijeka, Croatia
2
Department of Computer Science, University of Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy
3
Institute of Information Science and Technologies (ISTI), National Research Council of Italy (CNR),
Giuseppe Moruzzi 1, 56124 Pisa, Italy
4
Center for Artiﬁcial Intelligence and Cybersecurity, University of Rijeka, R. Matejcic 2, 51000 Rijeka, Croatia
*
Correspondence: alessio.rossi@di.unipi.it
Abstract: Every soccer game inﬂuences each player’s performance differently. Many studies have
tried to explain the inﬂuence of different parameters on the game; however, none went deeper into
the core and examined it minute-by-minute. The goal of this study is to use data derived from
GPS wearable devices to present a new framework for performance analysis. A player’s energy
expenditure is analyzed using data analytics and K-means clustering of low-, middle-, and high-
intensity periods distributed in 1 min segments. Our framework exhibits a higher explanatory power
compared to usual game metrics (e.g., high-speed running and sprinting), explaining 45.91% of the
coefﬁcient of variation vs. 21.32% for high-, 30.66% vs. 16.82% for middle-, and 24.41% vs. 19.12% for
low-intensity periods. The proposed methods enable deeper game analysis, which can help strength
and conditioning coaches and managers in gaining better insights into the players’ responses to
various game situations.
Keywords: game intensity; clustering; machine learning; fatigue; ﬁtness tracking
1. Introduction
The intensity of a soccer game is dependent on a wide range of factors: quality of the
opposition, period of the season, weather, team form, game status, etc. There is a lot of
work dealing with the inﬂuence of various parameters on said factors—such as location,
opponent quality, and game outcome—by using the most important metrics derived from
wearable sensors (e.g., total distance, accelerations, and decelerations). However, one
of the most dominant factors in soccer is the quality of the opposition. Higher-quality
opponents usually require higher physical demands during the game, which, in turn,
results in increased values of the total distance (TD), maximal speed, average speed,
frequency of high-intensity actions (HIAs) [1], and events related to changes in velocity
(accelerations and decelerations) [2]. This is not always true, because it heavily depends
on the context and the play styles of each team. According to Garcıa-Unanue et al. [3],
away games accumulate signiﬁcantly more TD (+230.65 m, 95% IC: 21.94 to 438.19, ES: 0.46,
p = 0.031), but there were no differences found that depended on the opponent quality.
However, an analysis between the ﬁrst and second half revealed a signiﬁcant reduction in
TD covered by the players against lower-level teams (−290.42 m, 95% CI: −557.82 to −23.01,
ES: 0.72, p = 0.033) and medium-level teams (−374.56 m, 95% CI: −549.21 to −199.70, ES:
0.71, p < 0.001). Congested periods can also have a great impact on player performance
and reduce the number of HIAs that a player can sustain [4]. Differences in intensities
are present across playing positions [5]. Therefore, central midﬁelders (CM) and wide
midﬁelders (WM) cover greater TD and have higher average speed, whereas WMs and
fullbacks (FB) cover higher distances at high-speed running (HSR) and sprinting [6]. Center
Sensors 2022, 22, 9842. https://doi.org/10.3390/s22249842
https://www.mdpi.com/journal/sensors
Sensors 2022, 22, 9842
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backs (CB) and forwards (FW) usually cover the smallest distances [7], but FWs cover more
HSR distance than CMs [6]. Concerning the game outcome, recent work reported higher
workloads in won games compared to losses and draws, higher TD and HSR distance
in the second half of defeats, and lower average speed in wins compared to draws and
losses [8]. When looking at score change inﬂuence on the game demands, there have been
reports that CMs, WMs, and FWs have increased TD while winning, but CBs and WBs
have higher TD and HSR while losing [9,10]. Interpretation of scoreline inﬂuence needs
to be done carefully, because there is a need for a clear scoreline deﬁnition for which to
consider scoreline effects [11].
Several studies [3,6,7,11,12] have described various context situations and their effects
on the wearable-derived metrics. Nevertheless, there were no attempts to increase the
level of data sampling and examine physical demand change in a game on a minute-by-
minute basis. Another problem is the usage of different GPS providers, which have various
thresholds for determining sprint distance, HSR distance, number of sprints, number of
detected acceleration and deceleration phases, etc.; hence, the concept cannot be easily
transferred. Nowadays, most providers allow users to set their own preferred thresholds.
However, this invokes other problems, such as many different thresholds used for the same
parameters (no consensus). In addition, accumulated values (which are the most-used
ones) provide an overall image, but often that is not particularly useful as it represents
an average of the game. A team can play an average-intensity game overall but actually
perform a very intensive ﬁrst half and a less-intensive second half of the game [8]. This
information is very important, along with individual analysis of a particular player’s effort
within the game. Intensity inspection within the context of scored and conceded goals can
provide information about which player could be a better substitute depending on the game
scoreline. Not every game is the same—each one provides unique demands [13]. Therefore,
the training load in the preceding week should be adjusted according to expenditure in the
previous game, and player ﬁtness needs to be tracked regularly to evaluate season meso-
and macro- cycles [14]. For this purpose, better methods for game analysis are needed than
the ones that are currently used.
Hence, the aim of this study is to minimize the effect of various GPS provider thresh-
olds by taking an energy expenditure approach. The study shows how to develop a
framework of data analytics for evaluating workload intensity as the game goes on. In
particular, this enables a detailed examination of the workload throughout the game and
provides a baseline for better understanding of the game demands depending on the
context. Moreover, methods proposed in this study can be used for objective tracking of
the players through meso- and macro-cycles of the season.
2. Materials and Methods
2.1. Study Design
The data were acquired during ofﬁcial and preseason games of a professional soccer
club. The process of data collection was executed by using GPS wearable sensors, GPexe
pro2 (Exelio Srl, Udine, Italy), with a sampling rate of 18 Hz. According to position, the
players were divided into ﬁve categories: center back (CB), wing back (WB), midﬁelder
(MF), wide forward (WF), and forward (FW). The sensor provider enabled the usage of
two types of data: (1) GM-5MIN (GPS metrics of expenditure through 5 min intervals) and
(2) metabolic power events (MPEs), (HIAs, which occur throughout the whole course of
a game).
2.2. Subjects
In total, there were 38 male soccer players (age 25 ± 3 years; height 1.81 ± 0.06 m;
weight 76 ± 5 kg) that played at least one game during the acquisition period. The goal-
keeper (GK) position was not recorded and therefore it was not used for analysis. All the
players that were wearing the sensor during the games were included in the dataset. This
applies to the substitute players, too. Playing positions counted 11 CBs, 7 WBs, 8 MFs, 3
Sensors 2022, 22, 9842
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WFs, and 9 FWs. The club allowed the research team to access players’ data, and informed
consent was provided.
2.3. Data Acquisition
The data collection process started in January 2021 and ended in March 2022, which
rounded a period of two half-seasons (including preseasons) and included 80 games. The
game data were acquired using GPexe pro2 devices that collected all of the standard
parameters for analysis [15] with the addition of metabolic expenditure features [16].
Furthermore, GPS metrics derived from the whole game (90 min data) were used as a
baseline for explaining and validating the descriptive power of the proposed clustering
methods. In the rest of the paper, we refer to this data type as GM-GAME.
2.4. Procedures and Variables
Before each game, players would put on the GPexe pro2 device, which was located
in a wearable vest. The sensor notiﬁed the wearer with a red blinking light when there
was a need for re-calibration. This was done very easily by spinning the device for a
couple of seconds. After the match, collected data were downloaded from the device and
uploaded to the manufacturer’s platform using the GPexe bridge application (version 8.3.6).
The online web application (version 7.4.46) computed all the metrics in a 5 min sampling
window. In order to minimize problems due to different thresholds and varying results,
only energy-based metrics and TD were used in the analysis. This included: total time
played (min), distance (m), average metabolic power (W/kg), energy (J/kg), anaerobic
energy (J/kg), MPE count, MPE average recovery time (s), MPE average recovery power
(W/kg), walk distance (m), running distance (m), walk energy (J/kg), and running energy
(J/kg).
Average metabolic power was calculated by multiplying speed and energy cost (the
description of parameter calculation was taken from the GPexe dictionary for athletic
performance monitoring, which is an internal document accessible only to their users),
which has been thoroughly described by di Prampero et al. [16]. The energy variable is an
estimation of both the energy required to cover a given distance at a constant speed and
the energy needed to perform speed variations. The same is true for calculating anaerobic
energy, with a difference of taking into account the player’s maximal VO2 as a measurement
threshold [17]. The MPEs are deﬁned as phases during the exercise (or a game) based
on a difference between the estimated metabolic power and oxygen consumption (the
description of parameter calculation was taken from the GPexe dictionary for athletic
performance monitoring, which is an internal document accessible only to their users).
Since the maximal VO2 of each athlete can be directly or indirectly assessed, this value
allows individual analysis and overcomes limitations of other models that are based on
speciﬁc speed or acceleration thresholds. The MPE recovery (power and time) is detected
by the power decrease that happens in order to repay previously contracted oxygen debt
(the description of parameter calculation was taken from the GPexe dictionary for athletic
performance monitoring, which is an internal document accessible only to their users). The
features regarding walking and running are not deﬁned by a ﬁxed speed threshold but
depend rather on different combinations of speed and acceleration [16].
All the presented features are shown in Table 1. Many of them were related to
metabolic power for the reason of avoiding difﬁculties involving speed, acceleration, and
deceleration threshold values [17]. The accounted features were aggregated and derived
from GM-5MIN and MPE data, which are described thoroughly in the following sections.
2.4.1. MPE Data
A special feature of GPexe wearables is the focus on metabolic expenditure using MPE.
The main difference and beneﬁt of the approach using MPE is that it does not take into
account only acceleration and deceleration for detecting HIA [16], but instead it is focused
on energy expenditure; thus, the problem of setting the threshold is avoided. An issue
Sensors 2022, 22, 9842
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regarding the acceleration approach lies in setting up a threshold for detecting these events,
which heavily inﬂuences the resulting values. Moreover, there exists a lack of agreement
and information regarding the choice of methods for acceleration ﬁltering [18]. Instead,
the alternative approach proposed by di Prampero et al. in 2005 is used [19], which sets
the standard for calculating MPE. This approach assumes that accelerated running on
ﬂat terrain is equivalent to constant running uphill at a constant speed at a certain angle.
Power events happen often in the game, and they are the most important factor in energy
expenditure. In the full game, there are more than 100 MPEs per player, which differ in
duration and power. An example of the data for one player and a single game can be seen
in Figure 1. The MPE dataset contained information about the start and end timestamp
of an event, duration in seconds, maximal speed, and average power spent. The energy
expenditure of an MPE was calculated by multiplying the average power and duration of
the event, which is shown in Equation (1).
EMPE = Pavg ∗ t
(1)
Figure 1. MPE in-game distribution for a single player.
This could be done because most of the events are short in duration, up to 20 s, with a
median value of 5.8, a mean value of 6.5, and a standard deviation of 3.35 s. The distribution
of event duration can be seen in Figure 2. The described data provide information about
the peak energy expenditure. However, this is not enough for a complete understanding of
expenditure within a game because there are no data about the period in which a player
was recovering (see Figure 3). Data regarding what is happening in the recovery period
are lacking; therefore, if one would use only MPE data, then only the information about
the HIA would be considered. The reality is that recovery can be passive or active: a
player can stand, walk, jog or run. This information is crucial for understanding in-game
player recovery.
Sensors 2022, 22, 9842
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Figure 2. MPE duration histogram. The distribution median value is 5.8, the mean is 6.5, and the
standard deviation is 3.35.
Figure 3. Recovery time within the power events (blue) in a 60 s time frame.
2.4.2. GM-5MIN Data
MPE data occurrence is discrete across the whole game. That means that these events
(short in duration) are always separated by periods of recovery. The energy that is spent
during MPEs is equivalent to 30% of the total energy consumption (the description of
parameter calculation was taken from the GPexe dictionary for athletic performance moni-
toring, which is an internal document accessible only to their users), which can be seen in
Figure 4. The remaining 70% of energy expenditure is ignored by this type of data. The
lack of information about a player’s expenditure during the recovery periods is addressed
with the introduction of GM-5MIN data, which contains an average of values in a given
5 min period. All the events within the 5 min interval were hence taken into consideration,
including walking, jogging, running, sprinting, TD, energy, etc. This enabled the acqui-
sition of the full 100% of energy expenditure within the observed period. An example
of the GM-5MIN and MPE energy expenditure for one player and a game can be seen in
Figure 4. Ideally, one would like to have these values in the 1 min interval and thus have a
Sensors 2022, 22, 9842
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detailed image of expenditure. Unfortunately, due to the intrinsic limits of the GPS tracking
device, the processing time for shorter intervals exponentially increases with regard to the
duration of the interval and could not be extracted in a reasonable time. This is the reason
for settling on a 5 min period: it is short enough to capture game details but also long
enough for calculating accumulation metrics such as average metabolic power, average
recovery power, etc.
Figure 4. GM-5MIN vs. MPE expenditure across 90 min. Blue bar charts represent GM-5MIN across
the 90 min of the game. Orange bars represent the energy expenditure of MPEs.
2.5. Data Preprocessing
To fully describe the intensity of a game, the MPE and GM-5MIN parameters needed
to be combined together. This was done by iterating through each game for all the players.
As the exact times and durations of both MPEs and GM-5MIN were known, they could
be combined. The process consisted of merging three main data sources, which included:
(1) GM-5MIN features in the preceding 5 min period (GM-5MIN-PRIOR), (2) MPE features
in the preceding 3 and 5 min periods (MPE-PRIOR), and (3) MPE features in the observed
minute (MPE-CURRENT). The entire processing workﬂow is shown in Figure 5.
The resulting dataset counted 25 parameters, which are described in Table 1. The
process to create GM-5MIN-PRIOR consisted of using the GM-5MIN data of a 5 min
period that preceded the current processing minute. The aim of this was to measure the
overall expenditure just before the observed minute. The second step was adding MPE-
PRIOR features, which gave information about the peak intensity in the period preceding
the observed minute. Finally, information about the observed minute was added by the
introduction of MPE-CURRENT features.
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Figure 5. Preprocessing and clustering ﬂowchart is divided into 3 parts. The ﬁrst step shows how
GM-5MIN-PRIOR, MPE-PRIOR, and MPE-CURRENT are combined. Next, dimensionality reduction
using PCA is performed to prepare the data for K-means clustering. The ﬁnal step consists of using
the clustering algorithm to obtain low-, middle-, and high-intensity events throughout the game and
to perform MFit analysis on the players.
Sensors 2022, 22, 9842
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Table 1. A list and description of features used for clustering. Features are divided into 3 categories
depending on the data source: GM-5MIN-PRIOR, MPE-PRIOR, and MPE-CURRENT.
Feature Name
Description
GM-5MIN-PRIOR
Distance (m)
Distance covered in the last 5 min.
MPE count
Number of MPEs in the last 5 min
Anaerobic energy (J/kg)
Anaerobic energy spent in the last 5 min
Average metabolic power (W/kg)
Average metabolic power spent in the last 5 min
Average MPE time (s)
Average MPE duration in the last 5 min
Average MPE recovery time (s)
Average recovery time in the last 5 min
Average MPE recovery power (W/kg)
Average recovery power in the last 5 min
Walk energy (J/kg)
Energy spent walking in the last 5 min
Running energy (J/kg)
Energy spent running in the last 5 min
General energy (J/kg)
Energy spent on all activities in the last 5 min
Total number of MPEs
Number of MPEs up to that moment in the game
Total energy spent (J/kg)
Energy spent up to that moment in the game
MPE-PRIOR
MPE energy (3 min)
Energy spent on MPEs in the last 3 min
MPE energy (5 min)
Energy spent on MPEs in the last 5 min
MPE count (3 min)
Number of MPEs in the last 3 min
MPE count (5 min)
Number of MPEs in the last 5 min
Recovery time (s) (3 min)
Recovery time (s) in the last 3 min
Recovery time (s) (5 min)
Recovery time (s) in the last 5 min
Average recovery time (s) (3 min)
Average recovery time (s) in the last 3 min
Average recovery time (s) (5 min)
Average recovery time (s) in the last 5 min
Total recovery time (s)
Recovery time up to that moment in the game
MPE-CURRENT
MPE energy spent (J/kg)
Energy spent on MPEs in the observed minute
Event count
Number of MPEs in the observed minute
Average recovery time (s)
Average recovery time in the observed minute
Recovery time (s)
Recovery time in the observed minute
On top of described variables in Section 2.4, additional ones were derived from these
data and incorporated into the feature set. In order to keep information about the duration
of the game and the inﬂuence of fatigue, cumulative (total) features were created. This
group of features comprised: the total number of MPEs, total energy spent (J/kg), and total
recovery time (s). Information about MPE average recovery time was only available for a
5 min period preceding the observed minute. To get information about the average recovery
time in the 3 min preceding and the observed minute, a new metric was derived from MPE
data. The metric represents absolute recovery time in seconds (within the observed period)
divided by the number of events in that period. An example is shown in Figure 3, where
there are 4 MPEs and 5 recovery periods, which gives 18 s of work and 42 s of recovery. An
average recovery time is thus equal to Equation (2), which gives an average of 8.4 s for the
observed example.
tavg_recovery =
trecovery
NMPE + 1
(2)
The MPE features were used to explain the work done in the current processing
minute and also the last 3 and 5 min periods. Combined with GM-5MIN, the dataset had
information about (1) overall energy consumption and recovery time in the preceding
5 min, (2) MPE energy consumption and recovery time in the preceding period of 3 and
5 min, and (3) MPE energy consumption and recovery time in the current minute. After all
the players and games were processed, extreme values for every feature were limited to ﬁt
the ceiling value in order to denoise the data. This value was determined by calculating
the threshold at which 99.5% of the data would ﬁt in that range. All the values that were
higher than the ceiling threshold were limited to that threshold.
Sensors 2022, 22, 9842
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2.6. Clustering Analysis
To account for the scarcity of data instances (limited number of games and players)
and to suppress overﬁtting, the number of features was reduced to successfully apply the
clustering algorithm. We used principal component analysis (PCA) for dimensionality
reduction. Before that, each feature was normalized by applying a min–max normalization.
The next step was to divide the resulting data points (after min–max normalization) into
different categories. As this was a new approach and the labels were unknown beforehand,
an unsupervised clustering algorithm had to be used. For this purpose, K-means was
selected to evaluate how many intensity zones were present in the dataset. Before ﬁtting
centroids on the data, halftime and the start of the game needed to be excluded from
training. By analyzing the data, a threshold of 200 m was set as the minimum distance;
thus, all the instances that were lower than that value were ignored. Inspection showed
that these outlier distance values were part of the halftime recovery and the ﬁrst 5 min of
the game (lacking information about the energy expenditure in the 5 min that preceded).
The chosen threshold of 200 m enabled the exclusion of all the outlier values. Failure to do
so would have heavily affected the results for the low-intensity zone, which is described
later in Section 3.2. The K-means algorithm was tested for k ∈ [2, 3, 4, . . . , 15] clusters
using the within-cluster sum of squares (WCSS). The best number of clusters was deﬁned
through the elbow method on WCSS values. Clustering analysis is a prerequisite for
better understanding the physical demands of the game and for future research about the
inﬂuence of various game context variables on players’ physical behavior.
2.7. Clustering Application
After the dataset had been created (see Figure 5), we clustered intensity proﬁles
(groups) that enabled assessment of the effort performed by the players as the game
goes on. Moreover, a Markov chain analysis was conducted in order to estimate players’
capabilities of intensity shifts during a game. This part of the paper may be more interesting
for speciﬁc readers; therefore, a detailed description of the methods used and the newly
created MFit index can be found in the Supplementary Materials. Section S1 explains the
process of creating an MFit index, while Section S2 shows the results of such analysis by
tracking the players’ ﬁtness through meso- and macro- cycles of the season.
3. Results
In this section, we explain how the proposed clustering method can be used for
detailed minute-by-minute game analysis that can be performed both individually or on a
team basis. It also provides an example of game load comparison in Section 3.3, with the
premise that each game has unique physical demands.
3.1. Clustering Analysis Results
PCA analysis showed that the optimal number of components for dimensionality
reduction is seven, preserving 92.8% of data variance (see Figure 6). Table 2 presents the
most important features of every component, with the minimal importance of a single
feature being 0.3 (explaining 30% of the data). Based on these seven principal components,
the elbow of the score was obtained by analyzing a different number of classes by the K-
means algorithm. We determined that the optimal number of clusters was three (Figure 6),
corresponding to low, middle, and high intensities in the game. The most important
features and their distributions across clusters are shown in Table 3.
Sensors 2022, 22, 9842
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Figure 6. Analysis of K-means clustering with WCSS method and PCA component inspection. The
optimal number of clusters is chosen using an elbow method. The resulting cluster number is 3, with
the number of PCA components being 7, which corresponds to 92.8% of the original data variance.
Table 2. The most important features (above 0.3) for every PCA component.
Feature
PC1
PC2
PC3
PC4
PC5
PC6
PC7
Distance (m)
✓
MPE count
✓
Anaerobic energy (J/kg)
✓
Average metabolic power (W/kg)
✓
✓
Average MPE time (s)
✓
Average MPE recovery time (s)
✓
Walk energy (J/kg)
✓
✓
Running energy (J/kg)
✓
General energy (J/kg)
✓
Total event count
✓
Total energy spent (J/kg)
✓
✓
MPE energy (3 min)
✓
✓
✓
MPE energy (5 min)
✓
Average recovery time (s) (3 min)
✓
Average recovery time (s) (5 min)
✓
✓
Total recovery time (s)
✓
MPE energy spent (J/kg)
✓
Event count
✓
✓
Average recovery time (s)
✓
✓
The K-means algorithm assigns each particular minute in the game to one of the three
possible groups. It is expected that higher intensity causes more energy consumption and
an increased number of MPEs but less time spent in recovery. To distinguish between low,
middle, and high intensity, the groups needed to be examined in more detail. For this
purpose, each feature distribution across classes was inspected by calculating the mean
Sensors 2022, 22, 9842
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and standard deviation. As described in Section 2.5, clustering features were divided
into three groups: (1) MPE-CURRENT, (2) MPE-PRIOR, and (3) GM-5MIN-PRIOR. The
ﬁrst one gives information about the current intensity, while the latter two explain what
actually caused the current state. It can be seen that the low-intensity group does not
contain any MPEs, but at the same time, it has the highest energy consumption in the last 5
min (GM-5MIN features—Energy (J)). The low-intensity group is a result of higher energy
consumption in the preceding period and can be characterized as an active recovery period
for the player.
Table 3. Clustering group results. Darker background color represents higher intensity. The low-
intensity group shows no MPE activity in the observed minute, but this is likely a result of very
high expenditure in the 5 min period that preceded it. The middle-intensity group exhibits higher
expenditure according to MPE features but shows lower values of GM-5MIN in 5 min prior. The
high-intensity group produces the highest expenditure in all types of features.
Parameter Name
Low Group
Middle Group
High Group
MPE features (1 min)
µ
σ
µ
σ
µ
σ
Energy (J)
0
0
180
150
230
280
Event count
0
0
1.8
0.9
2
1
Average recovery time (s)
60
0
20
7
18
8
MPE features (3 min before)
µ
σ
µ
σ
µ
σ
Energy (J/kg) 3 min
400
350
400
330
700
350
MPE count (3 min)
3.8
2.2
4.0
2.2
6
2
Recovery time (s) (3 min)
155
16
154
15
140
16
GM-5MIN features (5 min before)
µ
σ
µ
σ
µ
σ
Energy (J/kg)
2900
1000
1300
1000
2800
500
MPE count
6
3.5
4
3.5
9
2.5
Anaerobic energy (J/kg)
750
400
500
400
1000
150
Avg. MPE recovery time (s)
60
80
50
60
23
8
Running energy (J/kg)
1400
800
1000
800
2250
450
3.2. In-Depth Game Visualization
Every game is unique to each player. Therefore, a visual representation of intensity
zones throughout the game for a single player in a particular game is shown in Figure 7.
It can be clearly seen that a player needs to make a stop after a certain number of high-
intensity actions. The period following (middle and low intensity) could be a recovery
period; however, the reader should note that it is dependent on the game context (e.g.,
penalty, set-piece, video-assisted referee decision). Scoring minutes are shown in order to
better visualize the potential effect of scored and conceded goals on the game tempo. The
distribution of the intensity zones across the span of the game is shown in Figure 8. It can
be clearly seen that the high-intensity periods decrease as the game goes toward the end. At
the same time, middle intensity periods start high and then slowly increase from the 10th
min. Low intensity periods stay stable and slightly increase towards the end. This is mostly
due to the effect of fatigue. The same inspection can be made for the whole team, but this
requires additional analysis. Average minute-by-minute intensity can be aggregated by
grouping playing positions and showing their average minute-by-minute intensity values
for each position or by taking an average intensity for each minute using all the players in
the team. It should be noted that this kind of analysis is inferior to individual inspection,
and a lot of information can be lost in the aggregation.
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Figure 7. Intensity clusters across a 90-min period with the score-change timestamps for a single
player in a particular game. High intensity is represented with brown–red, middle with yellow–
orange, and low intensity with blue. Vertical discontinued red lines are goals conceded, and green
ones are goals scored.
Figure 8. High-, middle-, and low-intensity cluster distribution across a period of a game in 5 min
intervals.
3.3. Evaluation through Game Load
To show the effect and beneﬁts of the proposed clustering approach, the results are
compared with the GM-GAME data (each GPS feature separately) that is regularly used for
athlete load monitoring. The premise that each game is unique was tested by looking at the
distribution of high-, middle-, and low-intensity minutes for the whole team. The clustering
algorithm provides information about the three groups (i.e., high, middle, and low), and
the same thing needs to be done for GM-GAME data to enable comparison. Currently,
by using GM-GAME data, there exists no consensus on how one could measure intensity
using particular parameters. In order to compare the approach presented in this study with
GM-GAME data, we need to draw parallels between the intensity clusters and a single
GM-GAME feature. Therefore, the assumption was that GM-GAME data equivalents for
Sensors 2022, 22, 9842
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the high-intensity group would be the distance covered above 20 km/h; for low intensity,
it would be equal to walking distance (m); and for middle intensity, it would be equal to
running distance (<20 km/h, walking excluded).
Table 4 provides the percentage of intensity groups in both the clustering algorithm
and GM-GAME features. To compare the variability of each group, the coefﬁcient of
variation (CV) was calculated for each column. The results (row CV) show the variance in
% for the particular column. The aim of this was to assess between-game variability and the
potential for describing each game’s unique demands. Clearly, the clustering approach has
superior CV results with the additional capability of detailed in-game inspection. Further,
the distribution of values is more natural–mostly middle- and high-intensity clusters and a
smaller numer of low-intensity clusters, which is a reasonably competitive game-demand
distribution. On the other hand, GM-GAME puts focus on middle- and low-, with very
little inﬂuence due to high-intensity. According to this, soccer players are not giving their
maximal effort very often in competitive games, which is hard to believe. This conﬁrms that
tracking the intensity of the game is not a trivial problem, and that it is very hard to explain
game intensity by using a single GPS parameter. Hence, based on these results and using
only GM-GAME, we can speculate that there is no distinction between scoreline change,
quality of the opponent, or some other context of the game. This shows the limitation of
GM-GAME data and a need for better methods for intensity evaluation. A comparison
of the MFit index approach (mentioned in Section 2.7) and GM-GAME parameters can be
seen in Figure S5 of the Supplementary Materials.
Table 4. Comparison of clustering algorithm and GM-GAME data for describing game load (63 games)
based on CV. Bolded values mark higher explanatory power for a particular cluster.
Game Id
Clustering with K-Means
GM-GAME Data
High
Middle
Low
High
Middle
Low
1
0.3572
0.4042
0.2538
0.0743
0.5845
0.4497
2
0.2456
0.5178
0.2507
0.0881
0.5116
0.4089
3
0.3300
0.5092
0.1737
0.0511
0.5717
0.4257
...
...
...
...
...
...
...
79
0.4338
0.3946
0.1863
0.0679
0.6124
0.4352
80
0.2611
0.3997
0.3487
0.0695
0.5011
0.3963
µ ± σ
0.31 ± 0.14
0.51 ± 0.16
0.20 ± 0.05
0.07 ± 0.01
0.57 ± 0.1
0.42 ± 0.08
CV
45.91%
30.66%
24.41%
21.32%
16.82%
19.12%
4. Discussion
This study provides a deep dive into game intensity in soccer by using data ac-
quired from wearable sensors. Every game is unique and, therefore, should be treated
independently. In the literature, a lot of work has analyzed the intensity concerning the
scoreline [9,11,12,20]. This was done by comparing relevant metrics (e.g., HSR, distance,
and sprint distance) depending on the score and also the quality of the opponent. However,
all of the research was only focused on comparing the GM-GAME data from wearable
sensors, which give overall information about the game. There have been no attempts to
understand how players perform on a minute-to-minute basis and how fatigue inﬂuences
the ﬁnal minutes of the game.
To go deep into the game intensity, the proposed analytical approach takes into
consideration two data sources (GM-5MIN and MPE data) as the game goes by. Surely,
the possibility of including 1 min periods instead of 5 min periods would yield a better
representation of the game. On the other hand, by using smaller periods of the game,
accumulation error would go up, and this amount would vary between the providers [21].
Moreover, processing smaller intervals would be very long or even impossible with state-
of-the-art tracking devices. To account for this, the framework of data analytics provided
in this study enabled a detailed inspection of the game. In particular, the intensity of the
Sensors 2022, 22, 9842
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game could be grouped into three main zones, i.e., low-, middle-, and high-intensity. As
shown in Table 3, in low-intensity actions, players do not engage in any activity (recovery
period), but this was a result of the preceding 5 min intense period. Differently, the middle-
and high-intensity groups show medium and strong MPE activity, respectively, and shorter
periods of recovery. However, the middle-intensity group shows low-intensity actions 5
min prior, while the high-intensity group is preceded by strong GM-5MIN expenditure.
These groups enable us to analyze player status as the game goes on. As a matter of fact,
Figures 7 and 8 show intensity groups of a single player for the entire game. The ﬁgures
suggest that there are several high-intensity periods in the starting part of the game, which
recedes as the game goes by, indicating the fatigue status of the player or a change in the
game intensity. Moreover, based on Figure 7, the game score seems to have no correlation
with the intensity period. However, more research is needed to assess the effect of different
intensity patterns on game scoring status, the tactical approach of a team, the roles of the
players, and other game events.
The proposed framework provides a basis for additional analysis of the game con-
text. This includes the changes in intensity cluster distribution depending on: the team’s
possession style, the quality of the opponent, or the change of scoreline. By using more
seasons and acquiring more data about the substitute players, a better analysis of their
energy expenditure can be made. Currently, there are not enough substitute players with
similar playing time and the same playing position. Further, with the addition of multiple
teams with different playing styles, the model can be adapted according to e.g., possession
or counter-attacking football. This, however, needs further investigation and is out of the
scope of this study.
The applicability of the model was shown using in-game visualization of the player’s
low-, middle-, and high- intensity clusters. The ability to provide better information about
the game intensity compared to GM-GAME parameters was shown by calculating the CV
of each cluster. The results proved that tracking the game intensity is not a trivial task,
i.e., it cannot be observed from the aggregation level. However, the approach proposed in
this study gives promising results because it takes into account minute-by-minute changes
in energy expenditure. However, the reader should note that all of these analyses can
be affected by the game characteristics, which can inﬂuence intensity and, consequently,
physical demands.
The main limitation of this study is that only one team was used in the analysis.
Therefore, we should inspect this on more teams to provide information about the accuracy
and validity of this approach. However, in this study, we present a new approach for
analyzing real-time intensity during a game that could be applied to each team. Hence,
every team could create its own personalized model in accordance with individual players’
characteristics by applying our analytical approach.
5. Conclusions
This study is focused on diving deeper into players’ energy expenditure throughout
the full length of a soccer game. It provides procedures for processing and clustering
the data for the purpose of inspecting the physical game performance of the players on
a minute-by-minute basis. This approach can help practitioners to better understand the
speciﬁc context of the game (i.e., when the team decreases physical performance) but also
provide ground for further inspection of fatigue, match context, and how the energy of the
players is spent through the course of a game.
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Supplementary Materials: The following supporting information can be downloaded at: https:
//www.mdpi.com/article/10.3390/s22249842/s1, Section S1. MFit Methodology; Section S2. MFit
Analysis: Tracking Players’ Fitness Status. Figure S1: Maximum high-intensity repetitions per game
for a particular player; Figure S2: Transition probability matrix used in MFit analysis for the example
shown in Figure 7 of the main paper. The player has a very high possibility (83.33%) of remaining
in the high-intensity zone given that he is already performing in the high-intensity zone; Figure S3:
MFit-5 through the season, made with a 5-min high-intensity repetition probability. An example is
provided for each role, based on a single player. The red dotted line refers to the probability repetition
average of all the players in the dataset; Figure S4: MFit-10 through the season, made with a 10-min
high-intensity repetition probability. An example is provided for each role, based on a single player.
The red dotted line refers to the probability repetition average of all the players in the dataset; Figure
S5: Analytical comparison between widely used GM-GAME and a MFit-10 for a player in CB position.
GM-GAME features show very low variability and, therefore, an inability to express player physical
effort differences on a game-to-game basis. Reference [22] is cited in the Supplementary Materials.
Author Contributions: A.S. carried out data collection, analysis, and interpretation. A.R. and P.C.
made substantial contributions to the concept and design. A.S. and A.R. wrote the ﬁrst manuscript
draft, and all the authors were involved in revising it critically. L.P. and I.Š. did supervision of the
work done as well as in-depth revision and editing of the manuscript. All authors have read and
agreed to the published version of the manuscript.
Funding: This work was supported by the Horizon 2020 project EuroCC 951732 National Competence
Centres in the Framework of EuroHPC and by the University of Rijeka, Croatia, grant number
uniri-tehnic-18-15. Moreover, this work was also supported by the European Community’s H2020
Program under the funding scheme INFRAIA-2019-1: Research Infrastructures grant agreement
871042, www.sobigdata.eu, SoBigData. The funders had no role in the study design, data collection
and analysis, decision to publish, or preparation of the manuscript.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.
Data Availability Statement: Not applicable.
Acknowledgments: We would like to thank the Transnational Access program of SoBigData++ for
their support, which permitted meeting between the researchers authoring this study.
Conﬂicts of Interest: The authors declare that they have no conﬂicts of interest relevant to the content
of this article.
Abbreviations
The following abbreviations are used in this manuscript:
GPS
Global Positioning System
TD
Total Distance
HSR
High-Speed Running
MPE
Metabolic Power Event
HIA
High Intensity Action
CB
Center Back
FB
Full Back
WB
Wing Back
MF
Midﬁelder
WM
Wide Midﬁelder
WF
Wide Forward
FW
Forward
PCA
Principal Component Analysis
WCSS
Within-Cluster Sum of Squares
CV
Coefﬁcient of Variation
MFit
Markov Fitness
GM
GPS Metrics
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Extended Energy-Expenditure Model in Soccer: Evaluating Player Performance in the Context of the Game.
Skoki, Arian,Rossi, Alessio,Cintia, Paolo,Pappalardo, Luca,Štajduhar, Ivan